IMAGE ENHANCEMENT TECHNIQUES FOR

FORENSIC CRIME SCENE INVESTIGATIONS

A Project report

Submitted in partial fulfillment of the

Requirement for the award of the degree of

BACHELOR OF TECHNOLOGY(B.Tech)

In

ELECTRONICS AND COMMUNICATION

ENGINEERING

By

A.SRIKANTH O. YUGANDHAR

(Y5EC281) (Y5EC301)

N.RAM PAVAN T.KARTEEK

(Y5EC307) (L6EC333)

Under the Esteemed Guidance of

Mr..M.S.G.PRASAD

Asst .Professor

Department of

ELECTRONICS AND COMMUNICATION ENGINEERING

KONERU LAKSHMAIAH COLLEGE OF ENGINEERING

(AUTONOMOUS)

GREEN FIELDS, VADDESWARAM

AFFILIATED TO ACHARYA NAGARJUNA UNIVERSITY,

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APPROVED BY AICTE.

Department of

ELECTRONICS AND COMMUNICATION ENGINEERING

KONERU LAKSHMAIAH COLLEGE OF ENGINEERING

CERTIFICATE

This is to certify that the project report entitled IMAGE

ENHANCEMENT TECHNIQUES FOR FORENSIC CRIME

SCENE INVESTIGATIONS is a bonafide record of work done by

SRIKANTH, O.YUGANDHAR, N.RAM PAVAN, T.KARTHIK

in partial fulfillment of the requirements of the award of Bachelor

of Technology in “Electronics and Communications Engineering ”

during the period 2005-09.

Guide Head Of The Department

Mr.M.S.G.PRASAD Dr. P. Siddaiah

Asst professor, Professor and Head,

ECE, KLCE ECE, KLCE

Acknowledgement

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The austerity and satisfaction that one gets on completing a

project cannot be fulfilled without mentioning the people who made it

possible with gratitude. I’m very much grateful to the Almighty who

helped us all the way through out the project and who has molded us

into what we are today.

It is great pleasure to acknowledge my profound sense of

gratitude to my project guide Asst. Prof. Mr.M.S.G.PRASAD for his

valuable and inspiring guidance, comments, suggestions and

encouragement throughout this project.

I would also like to thank all the staff members of the

department of electronics and communication of KLCE for their sound

support. And we are greatly thankful to Dr.P.SIDDAIAH,

Dr. K.S.RAMESH, Dr.S.LAKSHMI NARAYANA, Dr.HABIBULAH

KHAN, for their valuable suggestions for the development of this

report.

A.SRIKANTH O.YUGANDHAR

(Y5EC281) (Y5EC301)

N.RAM PAVAN T. KARTEEK

(Y5EC307) (L6EC333)

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ABSTRACT

The problem with collecting forensic evidence at a crime scene is that the

evidence is often masked behind backgrounds. This makes it difficult for extracting key

components from the evidence. Types of evidence that this can occur on is with finger

prints and shoe prints at the crime scene. To correct this problem, image enhancement

techniques can be used to obtain the relevant information that is needed for the

investigators.

FINGER PRINT SHOE PRINT

In this project we enhance these forensic images such as finger prints and foot

prints to have a clear image view by removing the unwanted background patterns using

different enhancement techniques such as Fast Fourier Transform (FFT), Image

Subtraction, Gamma Correction, Contrast Stretching and Histogram equalization. In

addition we develop Matlab codes for these enhancement techniques.

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IMAGE ENHANCEMENT TECHNIQUES FOR FORENSIC

CRIME SCENE INVESTIGATIONS

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CONTENTS:

CHAPTER 1

INTRODUCTION TO DIGITAL IMAGE PROCESSING

1.1 Basics of Digital Image Processing

1.2 Fundamentals steps in digital image processing

1.3 Components of an image processing system

CHAPTER 2

INTRODUCTION TO MATLAB

CHAPTER 3

FAST FOURIER TRANSFORM(FFT)

CHAPTER 4

IMAGE SUBTRACTION

CHAPTER 5

GAMMA CORRECTION

CHAPTER 6

CONTRAST STRETCHING

CHAPTER 7

HISTOGRAM EQUALIZATION

MATLAB CODES

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CHAPTER l

INTRODUCTION TO DIGITAL IMAGE PROCESSING

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Introduction

1.1 Basics of Digital Image Processing:

An image may be defined as a 2-dimensional function, f(x, y),

where x & y are spatial (plane) coordinates and the amplitude of ‘f’ at any pair of

coordinates of (x, y) is called the intensity or gray level of the image at that point. When

x, y are the amplitude values of ‘f’ are an finite, discrete quantities, we call the image a

digital image. The field of digital image processing refers to processing digital images

by means of a digital computer. Note that a digital image is composed of a finite number

of elements, each of which has a particular location and these elements are referred to as

picture elements, image elements, pels, and pixels. Pixel is the term most widely used to

denote the elements of a digital image.

Vision is the most advanced of our senses, so it is not surprising

that images play the single most important role in human perceptions. However, unlike

humans, who are limited to the visual band of the electromagnetic spectrum, imaging

machines cover almost the entire EM spectrum, ranging from gamma to. radio. waves.

They can operate on images generated by sources that humans are not accustomed to

associating with images. These include ultrasound, electron microscopy, and computer-

generated images. Thus, digital image processing encompasses a void and varied field of

applications..

There is no general agreement among authors regarding where

image processing stops and other related areas, such as image analysis and computer

vision, start. Some times distinction is made by defining image processing as a

discipline in which both the input and output of a process are images. We believe this to

be a limiting and somewhat artificial boundary. For example, under this definition, even

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the trivial task of computing the average intensity of an image would not be considered

an image processing operation. On the other hand, there are fields such as computer

vision whose ultimate goal is to use computers to emulate human vision, including

learning and being able to make inferences and take action based on visual inputs. This

area itself is a branch of a artificial intelligence whose objective is to emulate human

intelligence. The field of AI is in its earliest stages of infancy in terms of development,

with progress having been much slower than originally anticipated. The area of image

analysis in between image processing and computer vision.

There are no clear cut boundaries in the continuum from image

processing at one end to computer vision at the other. However, one useful paradigm is

to consider the three types of computerized processes in this continuum: low-mid, high-

level processes. Low level processes involve primitive I/O operations such as image pre-

processing to reduce noise, contrast enhancement and image sharpening. A low level

process is characterized by the fact that both its inputs and outputs are images. Mid-level

processing on images involves tasks such as segmentation, description of those objects

to reduce them to a form suitable for computer processing, and classifications of

individual objects. Amid-level process is characterized by the fact that its inputs

generally are images, but its outputs are attributes extracted from those images (e.g.

edges, contours). Higher level processing involves "making sense" of an ensemble of

recognized objects, as in image analysis and at the far end of the continuum, performing

the cognitive functions normally associated with vision.

1.2 Fundamentals steps in digital image processing:

Image acquisition is the first process shown in Figure 1.1 image

acquisition could be as simple as being given an image that is already in digital

form .Generally image acquisition involves pre-processing such as scaling.

Image enhancement is among the simplest and most appealing

areas of Digital image processing. Basically, the idea behind the enhancement

techniques is to bring out detail that is obscured, or simply to highlight certain features

of interest in an image. A familiar example of enhancement is when we increase the

contrast of an image because "it looks better". It is important to keep in mind that

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enhancement is a very subjective area of image processing. Image restoration is an area

that also deals with improving the appearance of an image. However, unlike

enhancement, which is subjective, image restoration is objective, in the sense that

restoration techniques tend to be based on the other hand, is based on human subjective

preferences regarding what constitutes a "good" enhancement result.

Figure 1.1: Fundamental Steps in Digital Image Processing

Color image processing is an area that has been gaining in

importance because of the significant increase in the use of digital images over the

Internet.

Wavelets are the foundations for representing images in various

degrees of resolution., In particular, this material is used for image data compression and

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for pyramidal representation, in which images are subdivided into smaller regions.

Compression, as the name implies, that deals with techniques for reducing

the storage required to save an image, or the bandwidth required to transmit it. Although

storage technology has improved significantly over the past decade, the same cannot be

said for transmission capacity. This is true particularly in uses of the Internet, which are

characterized by significant pictorial content. Image compression is familiar to most

users of computers in the form of image file extension, such as the jpg file extension

used in the JPEG (Joint Photographic Experts Group) image compression standard.

Morphological processing deals with tools for extracting image

components that are useful in the representation and description of shape. Segmentation

procedures partition an image into its constituent parts or objects. In general,

autonomous segmentation is one of the most difficult tasks in digital image processing.

A rugged segmentation procedure brings the process a long way towards successful

solution of imaging problems' that require objects algorithms almost always guarantee

eventual failure. In general, the more accurate the segmentation, the more likely

recognition is to succeed.

Representation and description almost always follow the output of

segmentation stage, which usually is raw pixel data, constituting either the boundary of a

region or all the points in the region itself. In either case, converting data to a form

suitable for computer processing. The decision that must be made is whether the data

should be represented as a boundary or as a complete region. Boundary representation is

appropriate when the focus is on external shape characteristics, such as corners and

inflections. Regional representation is appropriate when we focus on internal properties

such as texture or skeletal shape. In some applications these representations complement

each other. Choosing a representation is only part of the solution for transforming raw

data into a form suitable for subsequent computer processing. A method must also be

specified for describing the data so that features of interest or highlighted. Description,

also called feature selection, deals with extracting attributes that result in some

quantitative information of interest or are basic for differentiating one class of objects

from one another.

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Recognition is that process that assigns a label (e.g., "vehicle") to an

object based on its descriptors. We conclude our coverage of digital image processing

with the development methods for recognition of individual objects.

So far we have said nothing about the need for prior knowledge or about

the interaction between the knowledge base and the processing modules in Figure 1.1.

Knowledge about a problem domain is coded into an image processing system in the

form of a knowledge database. This knowledge may be as simple as detailing regions of

an image where the information of interest is known to be located, thus limiting the

search that has to be conducted in seeking that information. The knowledge base also

can be quite complex, such as an interrelated list of all major possible defects in a

material inspection problem or an image database containing high-resolution satellite

images of a region in 'connection with change-detection applications. In addition to

guiding the operation of each processing modules, the knowledge base also controls the

interaction between modules. This distinction is made in Figure 1.1 by the use of double-

headed arrows between the processing modules and the knowledge base, as opposed to

single headed arrows linking the processing modules.

Although we do not discuss image display explicitly at this point, it is

important to keep in mind that viewing the result of image processing can take place at

the output of any stage in Figure 1.1. We also note that not all image-processing

applications require the complexity of interaction implied by Figure 1.1. Intact, not even

all those modules are needed in some cases. For example image enhancement for human

visual interpretation seldom requires use of any of the other stages in Figure 1.1. In

general, however, as the complexity of an image processing task increases so does the

number of process required to solve the problem.

1.3 Components of an image processing system:

As recently as the mid 1980s, numerous models of image processing

systems being sold throughout the world were rather substantial peripheral device that

attached to equally substantial host computer. Late in the 1980s and early in the 1990s,

the market shifted to image processing hardware in the form of single boards designed to

be compatible with industry standard buses and to fit into engineering workstation

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cabinets and personal computers. In addition to lowering costs, this market shift also

served as a catalyst for a significant number of companies whose. Specialty is the

development of software written specially for image processing.

Although large-scale image processing still are being sold for massive

imaging applications, such as processing of satellite images, the trend continues towards

miniaturizing and blending of general-purpose small computers. With specialized image

processing hardware. Figure 1.2 shows the basic components comprising a typical

general-purpose system used for digital image processing. The function of each

component is followed

According to sensing, two elements are required to acquire digital

images. The first is a physical device i.e., sensitive to the energy radiated by the object

of the given image. The second called a digitizer is a device for converting the output of

the physical sensing device into digital form. For instance, in a digital video camera, the

sensors produce an electrical output proportional to light intensity. The digitizer converts

these outputs to digital data.

Specialized image processing hardware usually consists of the digitizer

and hardware that performs other primitive operations such as arithmetic logic unit

(ALU), which performs arithmetic and logical operations in parallel an entire images.

This type of hardware sometimes is called a front-end subsystem, and its most

distinguishing characteristic is speed. In other words this unit performs functions that

require fast data throughputs (e.g. Digitizing and averaging video images at 30

frames/sec) that the typical main computer cannot handle.

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Figure 1.2 : Components of an Image Processing System

The computer in an image processing system is a general-purpose

computer and can range from a PC to a super computer. In dedicated applications, some

times specially designed computers are used to achieve to a required level of

performance, but our interest here is on general-purpose image processing systems. In

this system, almost any well-equipped PC-type machine is Suitable for offline image

processing tasks.

Software for image processing consists of specialized modules that

perform specific tasks. A well-designed package also includes the capability for the user

to write code that, as a minimum, utilizes the specialized modules. More sophisticated

software packages allow the integration of those modules and general-purpose software

commands from at least one computer language.

Mass storage capability is a must in image processing applications. An

image of size 1024xl024 pixels, in which the intensity of each pixel is an 8-bit quantity,

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requires one mega byte of storage space if the image is not compressed. When dealing

with thousands, or even millions, of images, providing adequate storage in an image

processing system can be a challenge. Digital storage for image processing applications

falls into principle categories: (I) short term storage for use during processing, (2) online

storage for relatively fast recall, (3) archival storage, characterized by infrequent access.

Storage is measured in bytes, Kilobytes, Megabytes, Gigabytes, Terabytes.

One method of providing short-term storage is computer memory

another is by specialized boards called frame buffers that store one or more images and

can be accessed rapidly, usually at video rates. The later method allows virtually

instantaneous image zoom, as well as scroll and pan. Frame buffers usually are housed

in the specialized image processing hardware unit shown in Figure 1.2. On line storage

generally takes the form of magnetic discs or optical media storage. The key factor

characterizing on line storage is frequent access to the stored data. Finally, archival

storage is characterized by massive storage requirements but infrequent need for access.

Magnetic tapes & optical disc housed in 'jukeboxes' are the usual media for archival

applications.

Image displays in use today's are mainly color TV monitors. Monitors

are driven by the outputs of image & graphics display cards that are an integral part of

the computer system. Seldom are there requirements for image display applications that

can't be met by display cards available commercially as part of the computer system. In

some cases, it is necessary to have stereo displays, & these are implemented in the form

of headgear containing two small displays embedded in goggles won by the user.

Hard copy devices for recording images include laser printers, film

cameras, heat sensitive devices, ink jet units, digital units such as optical and cd-rom

discs. Film provides the highest possible resolution, but paper is the obvious medium

choice for written material. For presentations, images are displayed on film

transparencies or in a digital medium if image projection equipment is used. The later

approach is gaining acceptance as the standard for image presentations.

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Networking is almost a default function any computer system in use

today; Because of the large amount of data inherent in image processing applications,

the key consideration in image transmission is bandwidth. in dedicated networks, this

typically is not a problem ,but communications with remote sites via the internet are not

always as efficient. Fortunately, this situation is improving quickly as a result of optical

fibre and other broadband technologies.

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CHAPTER-2

INTRODUCTION TO MATLAB

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2.1 Basic Matlab Operations

MATLAB was originally developed as a MATrix LABoratory in the late

seventies.Today, it is much more powerful and remains convenient and fast in numeric matrices.

Hence, it is also powerful for graphics. MATLAB has many such as optimization, signal

processing and wavelet transforms.

MATLAB is case sensitive, e.g., pi is 3.14159 ... , but Pi isn't. To get help information such as

diff, you can use either the help menu, or type help diff or help(‘diff’).

% starts a comment in a line

; (the end of a statement) suppresses the display of the result

..... (at the end of a line) continues the statement to the next line

\ Left division, e.g., 3\15 equals 15/3 and A\b gives A^(-1) b

if A is invertible. A\b is also meaningful when A is singular.

ans default variable name of the result available to the next statement

i (or) j sqrt(-1)

eps machine precison

realmin the smallest positive floating point number

realmax the largest positive floating point number

inf infinity, e.g., 1/0

NaN Not-a-Number, e.g., 0/0

2.1.1 Numbers

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A number can be displayed in various formats in MATLAB. For example, the

answer to x = 100/7 is usually 14.2857 which is in the default display format short. However if

it is stored with 16 digits (default precision). If you type format longx you will see x =

14.28571428571429. But all later outputs will also be displayed in format long. If you want to

resume the original format, just type format short % or simply format , format rat % returns the

rational expression 100/7. help format % more information about format. The functions

round(x), floor(x), cei1(x), fix(x) return integer approximations to a floating point number x.

2.1.2 Arrays and Matrices

To create a one-dimensional array of five elements -2, 3, 0, 4.5, -1.5 (also known

as a row vector or a 1-by-5 matrix) named v, you can use

V = [-2 3 0 4.5 -1.5] % or

v = [-2, 3, 0,4.5, -1.5]

v(1) % the first element, -2

v(2:4) % the sub-array consisting of v(2), v(3) and v(4)

v(4 : -1 : 2) % the subarray consisting of v(4), v(3) and v(2)

4 : -1 : 2 % array 4, 3, 2 with increment -1

8 : 1 : 12 % array 8, 9, 10, 11, 12

8 : 12 % same as 8 : 1 : 12

x = linspace( -pi, pi, 21) % 21 is the number of elements in the row vector

A = [1 2 3; 4 5 6] % a 2-by-3 matrix

A = [12 3 % the same as above

A(1,2) % the element in row 1 and column 2

A(:,2) % the second column

A(2, :) % the second row

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A(2,1:2) % a row vector with two elements A(2, 1) and A(2, 2).

A(:) % all elements in A as a single column

% If A(:) is on the left side of an assignment, it fills A

% and the size of A remains the same as before.

A+B % matrix addition

A - B % matrix subtraction

2 * B % scalar multiplication

A * B % matrix multiplication

A . * B % element-by-element multiplication

A ./ B % element-by-element division

A .\ B % element-by-element left division

A.^B % element-by-element power

A' % complex conjugate transpose

A.' % transpose; when A is real, A.' = At

det(A) % determinant

A^(-1) % inverse

inv(A) % inverse

A =[1 2 3; 2 5 3; 1 0 8] % a square matrix

b = [2; 1; 0] % a column vector

x = inv(A) * b % solve A x = b if A is non-singular

x = A \ b % a better way to solve A x = b

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x = A \ b is better because it uses the LU factorization (a modification of Gaussian elimination)

which is much more efficient when the matrix is large, and because it can give least squares

solutions when A is singular or when A is not a square matrix.

[V, D] = eig(A) % returns the eigenvectors of A in the matrix V

% and the eigenvalues as the diagonal elements of

% diagonal matrix D

[V, D] = eig(A) % same as

[V D] = eig(A)

size(A)

length(A)

rank(A)

norm(A) % 2-norm, same as norm(A, 2)

norm(A, 1) % 1-norm

norm(A, int) % infinity norm

poly(A) % characteristic polynomial of matrix A

diag(v) % change a vector v to a diagonal matrix

diag(A) % get the diagonal elements of the matrix A

eye(n) % identity matrix of order n

zeros(m, n) % form an m-by-n zero matrix

ones(m, n) % form an m-by-n matrix with all entries equal 1

2.1.3 Control Flow Examples

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sum = 0; factorial = 1; % an example of loop

for n = 1 : 10

sum = sum +n;

factorial = factorial * n;

end

sum = 0; factorial = 1; n = 1; % an example of while-loop

while n <= 10

sum = sum + n; factorial = factorial * n; n = n + 1;

end

if x > 0 % an example of if-else-if-structure

disp('x is positive')

elseif x< 0

disp('x is negative')

else

disp('x is neither positive nor negative')

end

d = eig(A);

if A==A' & all(d > 0)

disp('A is positive definite')

end

2.1.4 Loading and saving variables in Matlab

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This section explains how to load and save variables in Matlab. Once you have

read a file, you probably convert it into an intensity image (a matrix) and work with this matrix.

Once you are done you may want to save the matrix representing the image in order to continue

to work with this matrix at another time. This is easily done using the commands save and load.

Loading and saving variables

Operation: Matlab command

Save the variable x Save x

Load the variable x Save x

2.1.5 M-file Scripts

To solve complicated problems, you don't have to use MATLAB

interactively. Instead, you can type all commands in an ASCII file named with .m extension.

It is called a script file or an M-file. For instance, you can type the while-loop example in a

file called example.m using any text editor or using the Open M-file item in the File menu.

In MATLAB, use cd path to change to the directory including example.m, then just type

example, and the commands in this file will be executed. You can also use pwd in

MATLAB to see your present working directory. When you choose a filename for an Mfile,

avoid the variable names you may use and the names of MATLAB built-in functions. You

can use the command who to see all variables you have used in a session, and use help to see

if a name is a built-in function.

2.1.6 M-file Functions

Function y = function name (x 1, x2, x3)% with one output; or function [y1, y2]

= function name (x 1, you can write your own functions in an M-file starting with a line such as

x2, x3) % with two outputs yl and y2. The function name must be the same as the M-file name.

The comment lines immediately following the first line can be seen with help function name

Variables inside a to certain function are local if they do not appear in the first line. All output

variables should be assigned values. The number of arguments passed to a function is stored in

the variable nargin. The following is an example M-file function and it should be stored in a file

called circle.m.

function [c, area] = circle(r) % [c, area] = circle(r) returns the circumference and

interior area % of a circle with radius r.

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if nargin ~= 1 % Error checking

error(‘There should be one input argument.'),

end

if r<0

error(‘Radius should be non-negative'),

end

c = 2 * pi * r;

area = pi * r^ 2;

2.1.7 Input/Output

The following is an example to read ten double precision numbers from an ASCII file named

in.dat to a column vector v.

»fid = fopen(‘in.dat', 'rt') % open a text file for reading

»v = fscanf(fid, '%lg', 10) % read 10 numbers from the file

»fclose(fid) % close the file

You may use fprintf( ) for output. When fid is 1 or is omitted in fprintf( ), it outputs to the

standard output, i.e., the screen

2.2 Image Processing Toolbox In Matlab

This is an introduction on how to handle images in Matlab. When working with

images in Matlab, there are many things to keep in mind such as loading an image, using the

right format, saving the data as different data types, how to display an image, conversion

between different image formats, etc. This worksheet presents some of the commands designed

for these operations. Most of these commands require you to have the Image processing tool box

installed with Matlab. To find out if it is installed, type ver at the Matlab prom))t.This gives you

a list of what tool boxes that- are installed on your system. For further reference on image

handling in Matlab use Matlab's help browser. There is an extensive (and quite good) on-line

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manual for the Image processing tool box that can be accessed via Matlab's help browser.

A digital Image is composed of pixels which can be thought of as small dots on

the screen. A digital image is an instruction of how to color each pixel. A typical size of an

image is 512-by-512 pixels. It is convenient to let the dimensions of the image to be a power of

2. For example, 20=512. In the general case we say that an image is of size m-by-n if it is

composed of m pixels in the vertical direction and n pixels in the horizontal direction.

Let us say that we have an image on the format 512-by-1024 pixels. This means

that the data for the image must contain information about 524288 pixels, which requires a lot

memory! Hence, compressing images is essential for efficient image processing.

When you store image, you should store it as a unit8 image since this requires far

less memory than double. When you are processing an image ( that is performing mathematical

operations on an image) you should convert it into double. Converting back and forth between

classes is easy.

2.2.1 Image formats supported by Matlab

The following image formats are supported by Matlab

BMP, HDF, JPEG, PCX, TIFF, XWB

Most images you find on the Internet are JPEG-images which is the name for

one of the most widely used compression standards for images. If you have stored an image you

can usually see from the suffix what format it is stored in. For example, an image named

myimage.jpg is stored in the JPEG format and we will see later on that we can load an image of

this format into MatIab. If an image is stored as a JPEG-image on your disc we first read it into

MatIab. However, in order to start working with an image, for example perform a wavelet

transform on the image, we must convert it into a different format. This section explains four

common formats.

a) Intensity image (gray scale image)

This is the equivalent to a "gray scale image" and this is the image we will mostly

work with in this project. It represents an image as a matrix where every element has a value

corresponding to how bright/dark the pixel at the corresponding position should be colored.

There are two ways to represent the number that represents the brightness of the pixel: The

double class (or data type). This assigns a floating number ("a number with decimals") between

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0 and 1 to each pixel. The value 0 corresponds to black and the value 1 corresponds to white.

The other class is called uint8 which assigns an integer between o and 255 to represent the

brightness of a pixel. The value 0 corresponds to black and 255 to white. The class uint8 only

requires roughly 1/8 of the storage compared to the class double. On the other hand, many

mathematical functions can only be applied to the double 'class.

b) Binary Image

This image format also stores an image as a matrix but can only color a pixel

black or 'white (and nothing in between). It assigns a 0 for black and a 1 for white.

c) Indexed Image

This is a practical way of representing color images. An indexed image stores an

image as two matrices. The first matrix has the same size as the image and one number for each

pixel. The second matrix is called the color map and its size may be different from the image.

The numbers in the first matrix is an instruction of what number to use in the color map matrix.

d) RGB Image

This is another format for color images. It represents an image with three

matrices of sizes matching the image format. Each matrix corresponds to one of the colors red,

green or blue and gives an instruction of how much of each of these colors a certain pixel should

use.

The following table shows how to convert between the different formats given in section

2.3

Image Format Conversion

Operation Matlab Command

Convert between intensity/indexed/RGB format to binary format. dither( )

Convert between intensity format to indexed format. gray2ind( )

Convert between indexed format to intensity format. ind2gray( )

Convert between indexed format to RGB format. ind2rgb( )

Convert a regular matrix to intensity format by scaling. mat2gray( )

Convert between RGB format to intensity format. rgb2gray( )

Convert between RGB format to indexed format. rgb2ind( )

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The command mat2gray is useful if you have a matrix representing an image but the values

representing the gray scale range between, let's say, 0 and 1000. The command mat2gray

automatically re scales all entries so that they fall within 0 and 255 (if you use the uint8 class) or

0 and 1 (if you use the double class).

2.4 Reading Image Files

When you encounter an image you want to work with, it is usually in form of a file (for

example, if you download an image from the web, it is usually stored as a JPEGfile). Once we

are done processing an image, we may want to write it back to a JPEG-file so that we

can, for example, post the processed image on the web. This is done using the imread

and imwrite commands. These commands require the Image processing tool box!

Reading and writing image files

Operation Matlab Command

Read an image. (Within the parenthesis you type the name of the image file you wish to read. Put the file name within single quotes ‘ ‘.)

imread( )

Write an image into a file.

(As the first argument within the parenthesis you type the name of the image you have worked with.

As a second argument within the parenthesis you type the file name of the file and format that you want to write the image to.

Put the file name within single quotes ‘ ‘.)

imwrite( )

Make sure to use semi-colon; after these commands, otherwise you will get LOTS OF number scrolling on you screen.

2.5 Displaying Images in MATLAB

Here are a couple of basic Matlab commands (do not require any tool box) for displaying an image.

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Displaying an image given on matrix form

Operation Matlab command

Display an image represented as a matrix X.imagesc(X)

Zoom in (using the left and right mouse button). brighten(s)

Turn off the zoom function. colormap(gray)

Sometimes your image may not be displayed in gray scale even though you might have converted it into a gray scale image. You can then use the command colormap(gray) to "force'" Matlab to use a gray scale when displaying an image.

If you are using Matlab with an Image processing tool box installed, we mostly use the command imshow to display an image.

Displaying an image given on matrix form (with Image Processing Toolbox)

Operation Matlab command

Display an image represented as a matrix X.imshow(X)

Zoom in (using the left and right mouse button). zoom on

Turn off the zoom function. zoom off

2.6 Commands in image processing tool box.

colorbar - Display colorbar (MATLAB Toolbox).

getimage - Get image data from axes.

image - Create and display image object (MATLAB Toolbox).

imagesc - Scale data and display as image (MATLAB Toolbox).

immovie - Make movie from multiframe image.

imshow - Display image.

montage - Display multiple image frames as rectangular montage.

movie - Play recorded movie frames (MATLAB Toolbox).

subimage - Display multiple images in single figure.

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truesize - Adjust display size of image.

warp - Display image as texture-mapped surface.

a) Image file I/O.

dicominfo - Read metadata from a DICOM message.

dicomread - Read a DICOM image.

dicomwrite - Write a DICOM image.

dicom-dict.txt - Text file containing DICOM data dictionary.

imfinfo - Return information about image file (MATLAB Toolbox).

imread - Read image file (MATLAB Toolbox).

irnwrite - Write image file (MATLAB Toolbox).

b) Image arithmetic.

imabsdiff - Compute absolute difference of two images ..

imadd - Add two images, or add constant to image.

imcomplement - Complement image.

imdivide - Divide two images, or divide image by constant.

imIincomb - Compute linear combination of images.

immultiply - Multiply two images, or multiply image by constant.

imsubtract - Subtract two images, or subtract constant from image.

c) Geometric transformations

checkerboard - Create checkerboard image.

findbounds - Find output bounds for geometric transformation.

fliptforrn - Flip the input and output roles of a TFORM struct.

imerop - Crop image.

imresize - Resize image.

imrotate - Rotate image.

imtransform - Apply geometric transformation to image.

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makeresampler - Create res ampler structure.

maketform - Create geometric transformation structure (TFORM).

tformarray - Apply geometric transformation to N-D array.

tformfwd - Apply forward geometric transformation.

tforminv - Apply inverse geometric transformation.

d) Image registration.

cpstruct2pairs - Convert CPSTRUCT to valid pairs of control points.

cp2tform - Infer geometric transformation from control point pairs.

cpcorr - Tune control point locations using cross-correlation.

cpselect - Control point selection tool.

normxcorr2 - Nonnalized two-dimensional cross-correlation.

e) Pixel values and statistics.

corr2 - Compute 2-D correlation coefficient.

imcontour - Create contour plot of image data.

imhist - Display histogram of image data.

impixel - Determine pixel color values.

improfile - Compute pixel-value cross-sections along line segments.

mean2 - Compute mean of matrix elements.

pixval - Display information about image pixels.

regionprops - Measure properties of image regions.

std2 - Compute standard deviation of matrix elements.

f) Image analysis.

edge - Find edges in intensity image.

qtdecomp - Perform quadtree decomposition.

qtgetblk - Get block values in quad tree decomposition.

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qtsetblk - Set block values in quadtree decomposition.

g) Image enhancement.

histeq - Enhance contrast using histogram equalization.

imadjust - Adjust image intensity values or colormap.

imnoise - Add noise to an image.

medfilt2 - Perform 2-D median filtering.

ordfilt2 - Perform 2-D order-statistic filtering.

stretchlim - Find limits to contrast stretch an image.

wiener2 - Perform 2-D adaptive noise-removal filtering.

h) Linear filtering.

convmtx2 - Compute 2-D convolution matrix.

fspecial - Create predefined filters.

imfilter - Filter 2-D and N-D images.

i)Linear 2-D filter design.

freqspace - Detem1ine 2-D frequency response spacing (MATLAB Toolbox).

freqz2 - Compute 2-D frequency response.

fsamp2 - Design 2-D FIR filter using frequency sampling.

ftrans2 - Design 2-D FIR filter using frequency transformation.

fwind1 - Design 2-D FIR filter using I-D window method.

fwind2 - Design 2-D FIR filter using 2-D window method.

j)Image deblurring.

deconvblind - Deblur image using blind deconvolution.

deconvlucy - Deblur image using Lucy-Richardson method.

deconvreg - Deblur image using regularized filter

deconvwnr - Deblur image using Wiener filter.

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edgetaper - Taper edges using point-spread function.

otf2psf - Optical transfer function to point-spread function.

psf2otf - Point-spread function to optical transfer function.

k) Image transforms.

dct2 - 2-D discrete cosine transform.

dctmtx - Discrete cosine transform matrix.

fft2 - 2-D fast Fourier transform (MATLAB Toolbox).

Fftn - N-D fast Fourier transform (MATLAB Toolbox).

fftshift - Reverse quadrants of output of FFT (MATLAB Toolbox).

idct2 -2-D inverse discrete cosine transform.

ifft2 - 2-D inverse fast Fourier transform (MATLAB Toolbox).

ifftn - N-D inverse fast Fourier transform (MAT LAB Toolbox).

iradon - Compute inverse Radon transform.

phantom - Generate a head phantom image.

radon - Compute Radon transform.

l)Neighbourhood and block processing.

bestblk - Choose block size for block processing.

blkproc - Implement distinct block processing for image.

col2im - Rearrange matrix columns into blocks.

colfilt - Column wise neighbourhood operations.

im2col - Rearrange image blocks into columns.

nlfilter - Perform general sliding-neighbourhood operations.

m) Morphological operations (intensity and binary images).

conndef - Default connectivity.

imbothat - Perform bottom-hat filtering.

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imclearborder - Suppress light structures connected to image border.

imclose - Close image.

imdilate - Dilate image.

imerode - Erode image.

imextendedmax - Extended-maxima transform.

imextendedmin - Extended-minima transform.

imfill - Fill image regions and holes.

imhmax - H-maxima transform.

imhmin - H-minima transform.

imimposemin - Impose minima.

imopen - Open image.

imreconstruct - Morphological reconstruction.

imregionalmax - Regional maxima .

imregionalmin - Regional minima.

imtophat - Perform top hat filtering.

watershed - Watershed transform.

n) Morphological operations (binary images)

applylut - Perform neighbourhood operations using lookup tables.

bwarea - Compute area of objects in binary image.

bwareaopen - Binary area open (remove small objects).

bwdist - Compute distance transform of binary image.

bweuler - Compute Euler number of binary image.

bwhitmiss - Binary hit-miss operation.

bwlabel - Label connected components in 2-D binary image.

bwlabeln - Label connected components in N-D binary image.

bwmorph - Perform morphological operations on binary image.

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bwpack - Pack binary image.

bwperim - Determine perimeter of objects in binary image.

bwselect - Select objects in binary image.

bwulterode - Ultimate erosion.

bwunpack - Unpack binary image.

makelut - Construct lookup table for use with applylut.

o) Structuring element (STREL) creation and manipulation.

getheight - Get strel height.

getneighbors - Get offset location and height of strel neighbours

getnhood - Get strel neighbuorhood.

getsequence - Get sequence of decomposed strels.

isflat - Return true for flat strels.

reflect - Reflect strel about its center.

strel - Create morphological structuring element.

translate - Translate strel.

p) Region-based processing.

roicolor - Select region of interest, based on color.

roifill - Smoothly interpolate within arbitrary region.

roifilt2 - Filter a region of interest.

roipoly - Select polygonal region of interest.

q) Colormap manipulation.

brighten - Brighten or darken colormap (MATLAB Toolbox).

cmpermute - Rearrange colors in colormap.

cmunique - Find unique colormap colors and corresponding image.

colormap - Set or get color lookup table (MAT LAB Toolbox).

imapprox - Approximate indexed image by one with fewer colors.

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rgbplot - Plot RGB colormap components (MATLAB Toolbox).

r) Color space conversions.

hsv2rgb - Convert HSV values to RGB color space (MATLAB Toolbox).

ntsc2rgb - Convert NTSC values to RGB color space.

rgb2hsv - Convert RGB values to HSV color space (MATLAB Toolbox).

rgb2ntsc - Convert RGB values to NTSC color space.

rgb2ycbcr - Convert RGB values to YCBCR color space.

ycbcr2rgb - Convert YCBCR values to RGB color space.

s) Array operations.

circshift - Shift array circularly. (MATLAB Toolbox).

padarray - Pad array.

t) Image types and type conversions.

dither - Convert image using dithering.

gray2ind - Convert intensity image to indexed image.

grayslice - Create indexed image from intensity image by thresholding.

graythresh - Compute global image threshold using Otsu's method.

im2bw - Convert image to, binary image by thresholding.

im2double - Convert image array to double precision.

im2java - Convert image to Java image (MATLAB Toolbox).

im2uint8 - Convert image array to 8-bit unsigned integers.

im2unit16 - Convert image array to 16-bit unsigned integers .

ind2gray - Convert indexed image to intensity image.

ind2rgb -Convert indexed image to RGB image (MATLAB Toolbox).

isbw - Return true for binary image.

isgray - Return true for intensity image.

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isind - Return true for indexed image.

isrgb - Return true for RGB image.

label2rgb - Convert label matrix to RGB image.

mat2gray - Convert matrix to intensity image.

rgb2gray - Convert RGB image or colormap to grayscale.

rgb2ind - Convert RGB image to indexed image.

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INTRODUCTION

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Introduction:

The problem with collecting forensic evidence at a crime scene is

that the evidence is often masked behind backgrounds. This makes it difficult for

extracting key components from the evidence. Often times, the background color of the

crime scene can overpower the faint detail of the evidence. Types of evidence that this

can occur on is with finger prints and shoe prints at the crime scene. To correct this

problem, image enhancement techniques can be used to obtain the relevant information

that is needed for the investigators.

Approach:

The general approach of this project is to acquire digital images

of a plain background without a finger print and with a finger print. These digital

images will be used to perform image subtraction.

Another task that will be performed is to replicate the

enhancement of a digital image of a shoeprint. Two approaches will be taken to

compare which one enhances the image better. Both will be done by taking the original

digital image after image subtraction, and inverting the values. This is done because of

the original image being on a dark carpet and the shoeprint being generated from a small

amount of dust. Both images will also be stretched for contrast and have gamma

corrections performed on it. The difference between the images is that one image will

use histogram equalization to compare it with the other image that hasn’t had this effect

performed on it.

The first step for image enhancement in this type of situation is to

remove the regular patterns, or the background, from the image. The Fast Fourier

Transform (FFT) is used to remove the regular patterns from the image.

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CHAPTER 3

FAST FOURIER TRANSFORM (FFT)

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3.Fourier Transform

Common Names: Fourier Transform, Spectral Analysis, Frequency Analysis

3.1 Brief Description

The Fourier Transform is an important image processing tool which is

used to decompose an image into its sine and cosine components. The output of the

transformation represents the image in the Fourier or frequency domain, while the input

image is the spatial domain equivalent. In the Fourier domain image, each point

represents a particular frequency contained in the spatial domain image.

The Fourier Transform is used in a wide range of applications, such as image

analysis, image filtering, image reconstruction and image compression.

3.2 How It Works

As we are only concerned with digital images, we will restrict this discussion to

the Discrete Fourier Transform (DFT).

The DFT is the sampled Fourier Transform and therefore does not contain all

frequencies forming an image, but only a set of samples which is large enough to fully

describe the spatial domain image. The number of frequencies corresponds to the

number of pixels in the spatial domain image, i.e. the image in the spatial and Fourier

domains are of the same size.

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For a square image of size N×N, the two-dimensional DFT is given by:

where f(a,b) is the image in the spatial domain and the exponential term is the basis

function corresponding to each point F(k,l) in the Fourier space. The equation can be

interpreted as: the value of each point F(k,l) is obtained by multiplying the spatial image

with the corresponding base function and summing the result.

The basis functions are sine and cosine waves with increasing frequencies, i.e.

F(0,0) represents the DC-component of the image which corresponds to the average

brightness and F(N-1,N-1) represents the highest frequency.

In a similar way, the Fourier image can be re-transformed to the spatial domain.

The inverse Fourier transform is given by:

To obtain the result for the above equations, a double sum has to be calculated for each

image point. However, because the Fourier Transform is separable, it can be written as

where

Using these two formulas, the spatial domain image is first transformed into an

intermediate image using N one-dimensional Fourier Transforms. This intermediate

image is then transformed into the final image, again using N one-dimensional Fourier

Transforms. Expressing the two-dimensional Fourier Transform in terms of a series of

2N one-dimensional transforms decreases the number of required computations.

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Even with these computational savings, the ordinary one-dimensional DFT has

complexity. This can be reduced to if we employ the Fast Fourier

Transform (FFT) to compute the one-dimensional DFTs. This is a significant

improvement, in particular for large images. There are various forms of the FFT and

most of them restrict the size of the input image that may be transformed, often to

where n is an integer. The mathematical details are well described in the

literature.

The Fourier Transform produces a complex number valued output image which

can be displayed with two images, either with the real and imaginary part or with

magnitude and phase. In image processing, often only the magnitude of the Fourier

Transform is displayed, as it contains most of the information of the geometric structure

of the spatial domain image. However, if we want to re-transform the Fourier image into

the correct spatial domain after some processing in the frequency domain, we must make

sure to preserve both magnitude and phase of the Fourier image.

The Fourier domain image has a much greater range than the image in the spatial

domain. Hence, to be sufficiently accurate, its values are usually calculated and stored in

float values.

3.3 Common Variants

Another sinusoidal transform (i.e. transform with sinusoidal base functions)

related to the DFT is the Discrete Cosine Transform (DCT). For an N×N image, the

DCT is given by

with

The main advantages of the DCT are that it yields a real valued output image and that it

is a fast transform. A major use of the DCT is in image compression --- i.e. trying to

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reduce the amount of data needed to store an image. After performing a DCT it is

possible to throw away the coefficients that encode high frequency components that the

human eye is not very sensitive to. Thus the amount of data can be reduced, without

seriously affecting the way an image looks to the human eye.

EXAMPLE:

An example of removing the background through FFT is shown in figure 1, which

shows a finger print on a form of currency. By removing the wavy parts of the currency

from the image, it’s easier to collect the finger print.

Figure 1: Image before and after FFT to remove the background.

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CHAPTER 4

BACKGROUND SUBTRACTION

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4.Background Subtraction Method:

When a FFT is not suitable to the particular situation, the background can also

be removed by finding regular patterns on the image and subtracting them from the

original. This is done by finding a number of identifying marks on each image, lining

the marks up, and subtracting the two images.

4.1 Pixel Subtraction

Common Names: Pixel difference, Pixel subtract

The pixel subtraction operator takes two images as input and produces as output a third

image whose pixel values are simply those of the first image minus the corresponding

pixel values from the second image. It is also often possible to just use a single image as

input and subtract a constant value from all the pixels. Some versions of the operator

will just output the absolute difference between pixel values, rather than the

straightforward signed output.

4.2 How It Works

The subtraction of two images is performed straightforwardly in a single pass. The

output pixel values are given by:

Or if the operator computes absolute differences between the two input images then:

Or if it is simply desired to subtract a constant value C from a single image then:

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If the pixel values in the input images are actually vectors rather than scalar values (e.g.

for color images) then the individual components (e.g. red, blue and green components)

are simply subtracted separately to produce the output value.

Implementations of the operator vary as to what they do if the output pixel values are

negative. Some work with image formats that support negatively-valued pixels, in which

case the negative values are fine (and the way in which they are displayed will be

determined by the display colormap). If the image format does not support negative

numbers then often such pixels are just set to zero (i.e. black typically). Alternatively,

the operator may `wrap' negative values, so that for instance -30 appears in the output as

226 (assuming 8-bit pixel values).

If the operator calculates absolute differences and the two input images use the same

pixel value type, then it is impossible for the output pixel values to be outside the range

that may be represented by the input pixel type and so this problem does not arise. This

is one good reason for using absolute differences.

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EXAMPLE:

An example of background subtraction is given in figure 2 and 3. This image is better

suited for image subtraction than for FFT because the background is very complex and

fairly random.

Figure 2: Image before image subtraction to remove the background

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Figure 3: Image after image subtraction to remove the background

Once the background has been removed, there are many options to enhance

the image to obtain the best possible picture of the forensic evidence. One such method

is to invert the image and adjust it for contrast. Other corrections such as brightness and

gamma adjustments can be applied if necessary.

Results:

The resulting figure for the first task is shown in figure 4. This image

shows two original images, one with a finger print and one without one, and subtracting

the background from the image with the finger print. This is done in hopes of isolating

the finger print from the background so that it will be easier to see.

This process didn’t turn out as well as hoped. The reason for this is the

difficulty of exactly lining up these images to do an exact pixel by pixel subtraction. In

order to get the pixels to line up correctly, the images must be taken at the exact distance

and the exact same shape. The original two images weren’t the same size, resulting in

the left one being cropped down to the pixel size of the left image. This resulted in parts

of the background still being present after image subtraction.

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Another approach that could have been used in doing background

subtraction would have been to make a finger print on an even background. However,

by doing this, the exercise would have been trivial and the desired results would have

been easy to get.

Figure 4: Results from image subtraction

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CHAPTER 5

GAMMA CORRECTION

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Gamma correction

Example of CRT gamma correction

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Gamma correction demonstration: Each panel shows the display gamma that the pixel

values have been adjusted for; for example, the pixels in the second panel are

proportional to intensity to the 1/2 power, so the image looks approximately correct on a

typical PC monitor.

Gamma correction, gamma nonlinearity, gamma encoding, or often simply gamma,

is the name of a nonlinear operation used to code and decode luminance or tristimulus

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values in video or still image systems.[1] Gamma correction is, in the simplest cases,

defined by the following power-law expression:

where the input and output values are non-negative real values, typically in a

predetermined range such as 0 to 1. A gamma value is sometimes called an

encoding gamma, and the process of encoding with this compressive power-law

nonlinearity is called gamma compression; conversely a gamma value is called

a decoding gamma and the application of the expansive power-law nonlinearity is

called gamma expansion.

Gamma compression, also known as gamma encoding, is used to encode

linear luminance or RGB values into video signals or digital video file values; gamma

expansion is the inverse, or decoding, process, and occurs largely in the nonlinearity of

the electron-gun current–voltage curve in cathode ray tube (CRT) monitor systems,

which acts as a kind of spontaneous decoder. Gamma encoding helps to map data (both

analog and digital) into a more perceptually uniform domain.

The following figure shows the behavior of a typical display when image signals are

sent linearly (γ = 1.0) and gamma-encoded (standard NTSC γ = 2.2). In the first case, the

resulting image over the CRT is notably darker than the original, while it is shown with

high fidelity in the second case. Digital cameras produce, and TV stations broadcast,

signals in gamma-encoded form, anticipating the standardized gamma of the

reproducing device, so that the overall system will be linear, as shown on the bottom; if

cameras were linear, as on the top, the overall system would be nonlinear. Similarly,

image files are almost always stored on computers and communicated across the Internet

with gamma encoding.

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Systems with linear and gamma-corrected cameras. The dashes in the middle represent

the storage and transmission of image signals or data files. The three curves represent

input–output functions of the camera, the display, and the overall system, respectively.

Generalized gamma

A gamma value is used to quantify contrast, for example of photographic film.

It is the slope of an input–output curve in log–log space, that is:

which is consistent with the power-law relation above, but applicable to more general

nonlinearities. In the case of film, such nonlinearities are called Hurter–Driffield curves.

Gamma values less than 1 are typical of negative film, and values greater than 1 are

typical of slide (reversal) film.

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Gamma Correction

The first step to gamma correction is to set the black level so that the blackest black is

just below the threshold of visibility. I'm trying to find a good way to do this in an

HTML page. Below are some things that might help you: a black box inside the blackest

box.

1 8 12

17

 

In each of the following sections, there are several test patterns which can be used to

determine the gamma of your system.

The left pattern is a circular zone plate, with increasing horizontal frequencies as you go

out from the center horizontally, and increasing vertical frequencies as you go away

from the center vertically. It is a very useful test pattern to determine the frequency

response of a digital filter at a glance. When the gamma is apprpriately adjusted, the

circles in the center of each quadrant should disappear. If the center of each quadrant

circle is too light, your actual gamma is lower than than that in the label; if the center of

each quadrant circle is too dark, your actual gamma is higher than than that in the label.

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The middle pattern is a ramp of four gray levels. There should be equal perceived

intensity differences between one step and the next. The background of this page is a

50% (actually 49.8%) gray. The two middle grays of the ramp should straddle the

background color (one darker than thebackground, one lighter).

The rightmost pattern is a dart board pattern drawn with antialiased lines. The lines

should look smooth, and they should not flare (moire) in the center.

Gamma = 1.0

If your monitor is properly gamma corrected, the zone plate below should have a minimum of

aliases. This means that there should be one full circle in the center, four half circles at the

edges, four quarter circles at the corners, and some phantom circles 1/4 and 3/4 of the way

from the top.

zone plate ramp dartboard

 

Gamma = 1.3

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Gamma = 1.6

 

Gamma = 1.9

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Gamma = 2.2

This is the default value for uncompensated monitors.

Real World Application

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In the real world, it isn't quite this simple, especially when an image needs to look good

on different systems, or platforms.

As we mentioned above, most monitors work in about the same way with respect to

gamma correction. Most computers, or more specifically, most computer systems, do

not work in exactly the same way, however.

By computer systems we mean everything from the software that is running (like

Netscape) to the graphics cards installed, to the standard hardware on the motherboard.

Different computers do different things and many "systems" have different

configurations of all of the above things.

Macintoshes, for example, have partial gamma correction built-in to their hardware.

Silicon Graphics computers also have built-in gamma correction, but it is different from

the Macintosh. Suns and PCs have no standard built-in gamma correction but some

graphics cards installed in these computers may provide this functionality.

System Gamma

The idea of system gamma, is the gamma correction that should be applied in the

software to reproduce an accurate image on the monitor for an uncorrected image on a

particular computer "system."

Macintosh

The Macintosh has built-in gamma correction of 1.4. This means that after the software

sends the signal to the framebuffer, there are internal hardware corrections which will

further process the signal, specifically by gamma correcting it another 1.4 - That is, the

signal is raised to the 1/1.4. Therefore, to get full correction, the software itself should

first adjust the signal by raising it to the 1/1.8 power. (2.5/1.4 = 1.8) Thus the system

gamma on a Macintosh is 1.8.

Note some graphics cards in Macintoshes may have their own software to change the

standard gamma and Adobe Photoshop 3.0 is now released with a gamma control panel

from Knoll software which allows the user to change the system gamma of their

Macintosh. The 1.8 standard is still accepted as the universal Mac System Gamma, but

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users should be aware that a Mac can be set differently. The Knoll software control

panel for the Mac rewrites the look up table, (LUT) with a value of g/2.5 where g is the

gamma the user selects. Thus selecting 1.8 will rewrite the LUT with 1.8/2.5 = 1/1.4 -

the default setting. (The values in the LUT are 1/1.4 and this is called a 1.4 correction)

SGI

The SGI is similar to the Macintosh but instead of a hardware correction of 1.4 the SGI

applies gamma correction of 1.7. Thus the system gamma for an SGI is 2.5/1.7 or

roughly 1.5. Sometimes you may see that an SGI has a system gamma of 1.4. This

calculation is made on the assumption that monitors have a response curve closer to a

2.4 power function.

SGI's also come with a utility to rewrite the internal hardware correction. These values

are stored in a look up table, (LUT) and can be altered. The default is 1/1.7 as mentioned

above. (The values in the table are 1/1.7, so we call this a 1.7 correction) Sometimes the

value in the LUT may be referred to as the SGI system gamma. This is not the definition

used on other platforms. Unlike the Mac gamma control panel, the SGI gamma utility

will rewrite the LUT with the actual value set by the user. Gamma Definitions

Suns and PCs

Suns and PCs have no standard hardware correction (although certain graphics cards for

these platforms may) and therefore their system gammas are roughly 2.5. (More about

Sun's SX hardware and gamma)

Common graphics software such as Adobe Photoshop allows the user to set the gamma

correction value they want. (In Photoshop it is found in Monitor Setup under Preferences

under the File Menu.)

More about software gamma correction

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CHAPTER 6

CONTRAST STRETCHING

6.Contrast Stretching

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Common Names: Contrast stretching, Normalization

6.1.Brief Description

Contrast stretching (often called normalization) is a simple image enhancement

technique that attempts to improve the contrast in an image by `stretching' the range of

intensity values it contains to span a desired range of values, e.g. the the full range of

pixel values that the image type concerned allows. It differs from the more sophisticated

histogram equalization in that it can only apply a linear scaling function to the image

pixel values. As a result the `enhancement' is less harsh. (Most implementations accept a

graylevel image as input and produce another graylevel image as output.)

6.2.How It Works

Before the stretching can be performed it is necessary to specify the upper and lower

pixel value limits over which the image is to be normalized. Often these limits will just

be the minimum and maximum pixel values that the image type concerned allows. For

example for 8-bit graylevel images the lower and upper limits might be 0 and 255. Call

the lower and the upper limits a and b respectively.

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The simplest sort of normalization then scans the image to find the lowest and highest

pixel values currently present in the image. Call these c and d. Then each pixel P is

scaled using the following function:

Values below 0 are set to 0 and values about 255 are set to 255.

The problem with this is that a single outlying pixel with either a very high or very low

value can severely affect the value of c or d and this could lead to very unrepresentative

scaling. Therefore a more robust approach is to first take a histogram of the image, and

then select c and d at, say, the 5th and 95th percentile in the histogram (that is, 5% of the

pixel in the histogram will have values lower than c, and 5% of the pixels will have

values higher than d). This prevents outliers affecting the scaling so much.

Another common technique for dealing with outliers is to use the intensity histogram to

find the most popular intensity level in an image (i.e. the histogram peak) and then

define a cutoff fraction which is the minimum fraction of this peak magnitude below

which data will be ignored. The intensity histogram is then scanned upward from 0 until

the first intensity value with contents above the cutoff fraction. This defines c. Similarly,

the intensity histogram is then scanned downward from 255 until the first intensity value

with contents above the cutoff fraction. This defines d.

Some implementations also work with color images. In this case all the channels will be

stretched using the same offset and scaling in order to preserve the correct color ratios.

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CHAPTER 7

HISTOGRAM EQUALIZATION

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7.Histogram Equalization

Common Names: Histogram Modeling, Histogram Equalization

7.1.Brief Description

Histogram modeling techniques (e.g. histogram equalization) provide a sophisticated

method for modifying the dynamic range and contrast of an image by altering that image

such that its intensity histogram has a desired shape. Unlike contrast stretching,

histogram modeling operators may employ non-linear and non-monotonic transfer

functions to map between pixel intensity values in the input and output images.

Histogram equalization employs a monotonic, non-linear mapping which re-assigns the

intensity values of pixels in the input image such that the output image contains a

uniform distribution of intensities (i.e. a flat histogram). This technique is used in image

comparison processes (because it is effective in detail enhancement) and in the

correction of non-linear effects introduced by, say, a digitizer or display system.

7.2.How It Works

Histogram modeling is usually introduced using continuous, rather than discrete, process

functions. Therefore, we suppose that the images of interest contain continuous intensity

levels (in the interval [0,1]) and that the transformation function f which maps an input

image onto an output image is continuous within this interval. Further, it

will be assumed that the transfer law (which may also be written in terms of intensity

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density levels, e.g. ) is single-valued and monotonically increasing (as is

the case in histogram equalization) so that it is possible to define the inverse law

. An example of such a transfer function is illustrated in Figure 1.

Figure 1 A histogram transformation function.

All pixels in the input image with densities in the region to will have

their pixel values re-assigned such that they assume an output pixel density value in the

range from to . The surface areas and will

therefore be equal, yielding:

where .

This result can be written in the language of probability theory if the histogram h is

regarded as a continuous probability density function p describing the distribution of the

(assumed random) intensity levels:

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In the case of histogram equalization, the output probability densities should all be an

equal fraction of the maximum number of intensity levels in the input image (where

the minimum level considered is 0). The transfer function (or point operator) necessary

to achieve this result is simply:

Therefore,

where is simply the cumulative probability distribution (i.e. cumulative

histogram) of the original image. Thus, an image which is transformed using its

cumulative histogram yields an output histogram which is flat!

A digital implementation of histogram equalization is usually performed by defining a

transfer function of the form:

where N is the number of image pixels and is the number of pixels at intensity level k

or less.

In the digital implementation, the output image will not necessarily be fully equalized

and there may be `holes' in the histogram (i.e. unused intensity levels). These effects are

likely to decrease as the number of pixels and intensity quantization levels in the input

image are increased.

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7.3.Common Variants

Histogram Specification

Histogram equalization is limited in that it is capable of producing only one result: an

image with a uniform intensity distribution. Sometimes it is desirable to be able to

control the shape of the output histogram in order to highlight certain intensity levels in

an image. This can be accomplished by the histogram specialization operator which

maps a given intensity distribution into a desired distribution using a

histogram equalized image as an intermediate stage.

The first step in histogram specialization, is to specify the desired output density

function and write a transformation g(c). If is single-valued (which is true when

there are no unfilled levels in the specified histogram or errors in the process of

rounding off to the nearest intensity level), then defines a mapping from

the equalized levels of the original image, . It is possible to combine

these two transformations such that the image need not be histogram equalized

explicitly:

Local Enhancements

The histogram processing methods discussed above are global in the

sense that they apply a transformation function whose form is based on the

intensity level distribution of an entire image. Although this method can enhance

the overall contrast and dynamic range of an image (thereby making certain

details more visible), there are cases in which enhancement of details over small

areas (i.e. areas whose total pixel contribution to the total number of image

pixels has a negligible influence on the global transform) is desired. The solution

in these cases is to derive a transformation based upon the intensity distribution

in the local neighborhood of every pixel in the image.

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The histogram processes described above can be adapted for local

enhancement. The procedure involves defining a neighborhood around each pixel and,

using the histogram characteristics of this neighborhood, to derive a transfer function

which maps that pixel into an output intensity level. This is performed for each pixel in

the image. (Since moving across rows or down columns only adds one new pixel to the

local histogram, updating the histogram from the previous calculation with new data

introduced at each motion is possible.) Local enhancement may also define transforms

based on pixel attributes other than histogram, e.g. intensity mean (to control variance)

and variance (to control contrast) are common.

Histogram Equalization

To transfer the gray levels so that the histogram of the resulting image is equalized to be a constant:

The purposes:

to equally use all available gray levels; for further histogram specification.

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This figure shows that for any given mapping function between the input and output images, the following holds:

i.e., the number of pixels mapped from to is unchanged.

To equalize the histogram of the output image, we let be a constant. In particular, if the gray levels are assumed to be in the ranges between 0 and 1 (

), then . Then we have:

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i.e., the mapping function for histogram equalization is:

where

is the cumulative probability distribution of the input image, which monotonically increases.

Intuitively, histogram equalization is realized by the following:

If is high, has a steep slope, will be wide, causing to be

low to keep ;

If is low, has a shallow slope, will be narrow, causing to be high.

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For discrete gray levels, the gray level of the input takes one of the discrete values:

and the continuous mapping function

becoems discrete:

where is the probability for the gray level of any given pixel to be (

):

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The resulting function is in the range and it needs to be converted to the

gray levels by one of the two following ways: 1.

2.

where is the floor, or the integer part of a real number , and adding is for

proper rounding. Note that while both conversions map to the highest gray

level , the second conversion also maps to 0 to stretch the gray levels of

the output image to occupy the entire dynamic range .

Example: Assume the images have pixels in 8 gray levels. The following table shows the equalization process corresponding to the two conversion methods above:

0/7 790 0.19 0.19 1/7 0.19 0.19 0/7 0.19 0.19

1/7 1023 0.25 0.44 3/7 0.25 0.44 2/7 0.25 0.44

2/7 850 0.21 0.65 5/7 0.21 0.65 4/7 0.21 0.65

3/7 656 0.16 0.81 6/7     5/7 0.16 0.81

4/7 329 0.08 0.89 6/7 0.24 0.89 6/7 0.08 0.89

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5/7 245 0.06 0.95 7/7     7/7    

6/7 122 0.03 0.98 7/7     7/7    

7/7 81 0.02 1.00 7/7 0.11 1.00 7/7 0.11 1.00

In the following example, the histogram of a given image is equalized. Although the resulting histogram may not look constant, but the cumulative histogram is a exact linear ramp indicating that the density histogram is indeed equalized. The density histogram is not guaranteed to be a constant because the pixels of the same gray level cannot be separated to satisfy a constant distribution.

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Programming Hints:

Find histogram of given image:

Build lookup table:

Image Mapping:

Histogram equalization is as a contrast enhancement technique with the objective

to obtain a new enhanced image with an uniform histogram. This can be

achieved by using the normalized cumulative histogram as the grey scale

mapping function.

The intermediate steps of the histogram equalization process are:

1. Take the cumulative histogram of the image to be equalized

2. Normalize the cumulative histogram to 255

3. Use the normalized cumulative histogram as the mapping function of the original

image

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These intermediate steps are illustrated below.

a) b)

a)original image; b)its histogram

a) b)

a)normalized cumulative histogram of the original image; b)histogram equalized image

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a) b)

a)histogram of the equalized image; b)cumulative histogram of the equalized image

Due to the discrete nature of the problem, the resultant histogram is not uniform as

desired, but you can see from the cumulative equalized histogram that it does

approximate to a straight line.

You can get a much uniformer histogram if you artificially increase the quantization of

the original image before applying the equalization. You can check this in the "Other

Examples" section.

APPLICATIONS: Histogram Equalization increases the contrast of images

Histogram equalized images

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The resulting figures for the second task are shown in figure 5 and 6. The

images in figure 5 show image subtraction, with gamma correction and contrast

stretching to further enhance the image. The images in figure 6 go further than the ones

shown in figure four. The images in figure 6 do image subtraction, contrast stretching,

gamma correction, and histogram equalization. The shoeprint that shows up best with

gamma correction occurs at using a correction value of 2.1.

Figure 5: Image Subtraction with gamma correction

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Figure 6: Image Subtraction, gamma correction and Histogram Equalization

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MATLAB CODES:

IMAGE SUBTRACTION

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Appendix A:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Image Subtraction

%

% This will read in two separate pictures, one with and without a finger

% print.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Read in both files

print = imread('treePrint.jpg');

noprint = imread('treeNoPrint.jpg');

white = imread('white_image_1992x1362.jpg');

size(white)

% Convert both pictures to grayscale

grayPrint = rgb2gray(print);

grayNoPrint = rgb2gray(noprint);

grayWhite = rgb2gray(white);

% Subtract the image without a finger print from the image with one.

result = imsubtract(grayPrint, grayNoPrint);

invertResult = imsubtract(grayWhite, result);

% Show the result

%figure1();

subplot(2,2,1), imshow(noprint), title('Original image without a finger print');

subplot(2,2,2), imshow(print), title('Original image with a finger print');

subplot(2,2,3), imshow(result), title('The result of background subtraction');

subplot(2,2,4), imshow(invertResult), title('The inverted result of background

subtraction');

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INPUTS:

treeNoPrint.jpg treePrint.jpg

White_image_1992*1362.jpg

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OUTPUTS:

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MATLAB CODE FOR GAMMA ENHANCEMENT AND

GAMMA ENHANCED HISTOGRAM EQUALIZATION

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Appendix B:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% General Enhancement

%

% This program does gamma enhancement and gamma enhancement with histogram

%equalization with a number of different parameters to get the best results.

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

clear all

%read in the image of footprint

i=imread('project1.jpg');

imshow(i);

%read in the image with all pixel values equal to 255

white1=imread('project2.jpg');

white=rgb2gray(white1);

imshow(white);

%create an image negative of the footprint

id=rgb2gray(i);

imshow(id);

ineg=imsubtract(white,id);

imshow(ineg);

imwrite(ineg, 'project1_neg.jpg', 'jpg');

%stretch the contrast of the negative image

jneg=imadjust(ineg,stretchlim(ineg),[]);

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imshow(ineg),title('negative image'), figure, imshow(jneg), title('contrast stretched

negative image');

pause

%perform gamma correction, try different perimeters to obtain best result

jgamma1=imadjust(jneg, [], [], 0.3);

jgamma2=imadjust(jneg, [], [], 1.5);

jgamma3=imadjust(jneg, [], [], 3);

jgamma4=imadjust(jneg, [], [], 2.1);

subplot(2,2,1), imshow(jgamma1), title('gamma=0.3'),

subplot(2, 2, 2),imshow(jgamma2), title('gamma=1.5'),

subplot(2, 2, 3), imshow(jgamma3), title('gamma=3'),

subplot(2, 2, 4), imshow(jgamma4), title('gamma=2.1');

pause

imwrite(jgamma4, 'project1_gamma.jpg', 'jpg');

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%

%Gamma Enhancement with Histogram Equalization

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%

h=histeq(jneg);

imshow(h);

%then perform gamma correction

hgamma1=imadjust(h, [], [], .85);

hgamma2=imadjust(h, [], [], .45);

hgamma3=imadjust(h, [], [], .25);

hgamma4=imadjust(h, [], [], .35);

subplot(2, 2, 1), imshow(hgamma1), title('gamma=0.85'),

subplot(2, 2, 2),imshow(hgamma2), title('gamma=0.45'),

subplot(2, 2, 3), imshow(hgamma3), title('gamma=0.2'),

subplot(2, 2, 4), imshow(hgamma4), title('gamma=0.35');

pause

imwrite(hgamma4, 'project1_gamma_histeq.jpg', 'jpg');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%

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INPUTS:

Project1.jpg

Project2.jpg

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OUTPUTS:

Project1_neg.jpg

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Image subtraction with gamma correction

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Im

age subtraction gamma correction and histogram equalization

project1_gamma_histeq.jpg

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Conclusion:

Image enhancement is a key tool for forensic investigators when searching

for evidence at a crime scene. It can be invaluable for evidence that is faint and tough to

make out. It is usually necessary for investigators to be able to get rid of the

background, which can be done by FFT or background subtraction. Finally,

investigators can use many different options for further enhancement, including gamma

corrections, contrast stretching, and histogram equalization. By doing these following

methods, forensic investigators can obtain the best possible evidence from a crime

scene.

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References:

1. Dalrymple, Brian, Shaw, Len, Woods, Keith. “Optimized Digital Recording of

Crime Scene Impressions.” Journal of Forensic Identification. 750 / 52 (6),

2002. <http://www.mediacy.com/apps/crimescenerecording.pdf>

2. Dalrymple, Brian. “Background subtraction through exhibit substitution.”

Journal of Forensic Identification. 54 (2), 2004 \ 157.

<http://www.mediacy.com/apps/backgrnd_sub_forensics.pdf>

3. “Image Analysis in Action: Image-Pro Plus Forensic Image Enhancement

Examples.” <http://www.mediacy.com/apps/enhance.htm>

4. D. Ballard and C. Brown Computer Vision, Prentice-Hall, 1982, pp 24 - 30.

5. R. Gonzales, R. Woods Digital Image Processing, Addison-Wesley Publishing

Company, 1992, pp 81 - 125.

6. B. Horn Robot Vision, MIT Press, 1986, Chaps 6, 7.

7. A. Jain Fundamentals of Digital Image Processing, Prentice-Hall, 1989, pp 15 -

20.

8. A. Marion An Introduction to Image Processing, Chapman and Hall, 1991,

Chap. 9.

9. R. Boyle and R. Thomas Computer Vision: A First Course, Blackwell Scientific

Publications, 1988, pp 35 - 41.

10. R. Gonzalez and R. Woods Digital Image Processing, Addison-Wesley

Publishing Company, 1992, Chap. 4.

11. A. Jain Fundamentals of Digital Image Processing, Prentice-Hall, 1986, pp 241

- 243.

12. A. Marion An Introduction to Image Processing, Chapman and Hall, 1991,

Chap. 6.

13. Charles A. Poynton (2003). Digital Video and HDTV: Algorithms and Interfaces.

Morgan Kaufmann. ISBN 1558607927. http://books.google.com/books?

id=ra1lcAwgvq4C&pg=RA1-PA630&dq=gamma-

encoding&lr=&as_brr=3&ei=WHfDR6q4J4OmswOGiZXPDw&sig=OYiWf7BJ

2ACTek1UAsbcXOIlvP0.

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