Lecture # 06 Image Enhancement in Spatial Domain · Lecture # 06 Image Enhancement in Spatial ......

Digital Image Processing

Lecture # 06

Image Enhancement in Spatial

Domain

Autumn 2012

Digital Image Processing Lecture # 6 2

Limitations of Point Operations

► They don’t know where they are in an image

► They don’t know anything about their neighbors

► Most image features (edges, textures, etc) involve a spatial neighborhood of pixels

► If we want to enhance or manipulate these features, we need to go beyond point operations


What Point Operations Can’t Do

►Blurring / Smoothing


What Point Operations Can’t Do

►Sharpening


Spatial Filtering

• Filter term in “Digital image processing” is referred to the subimage

• There are others term to call subimage such as mask, kernel, template, or window

• The value in a filter subimage are referred as coefficients, rather than pixels.

• The concept of filtering has its roots in the use of the Fourier transform for signal processing in the so-called frequency domain.

• Spatial filtering term is the filtering operations that are performed directly on the pixels of an image.


Spatial Filtering

A spatial filter consists of (a) a neighborhood, and (b) a predefined operation

Linear spatial filtering of an image of size MxN with a filter of size mxn is given by the expression

( , ) ( , ) ( , )a b

s a t b

g x y w s t f x s y t


Spatial Filtering


Spatial Correlation

The correlation of a filter ( , ) of size

with an image ( , ), denoted as ( , ) ( , )

w x y m n

f x y w x y f x y

( , ) ( , ) ( , ) ( , )a b

s a t b

w x y f x y w s t f x s y t


Spatial Convolution

The convolution of a filter ( , ) of size

with an image ( , ), denoted as ( , ) ( , )

w x y m n

f x y w x y f x y

( , ) ( , ) ( , ) ( , )a b

s a t b

w x y f x y w s t f x s y t


Spatial Smoothing Linear Filters

The general implementation for filtering an M N image

with a weighted averaging filter of size m n is given

( , ) ( , )

( , )

( , )

where 2 1

a b

s a t b

a b

s a t b

w s t f x s y t

g x y

w s t

m a

, 2 1.n b


Smoothing Spatial Filters

► used for blurring and for noise reduction

► blurring is used in preprocessing steps, such as

removal of small details from an image prior to object extraction

bridging of small gaps in lines or curves

► noise reduction can be accomplished by blurring with a linear filter and also by a nonlinear filter

► replacing the value of every pixel in an image by the average of the gray levels in the neighborhood will reduce the “sharp” transitions in gray levels. sharp transitions

► random noise in the image

► edges of objects in the image

► thus, smoothing can reduce noises (desirable) and blur edges (undesirable)


Two Smoothing Averaging Filter Masks


Example: Gross Representation of Objects


Example: Smoothing Filter

[3x3] [5x5] [7x7]

Original Image


Order-statistic (Nonlinear) Filters

— Nonlinear

— Based on ordering (ranking) the pixels contained in the filter mask

— Replacing the value of the center pixel with the value determined by the ranking result

E.g., median filter, max filter, min filter


Median Filters

► replaces the value of a pixel by the median of the gray levels in the neighborhood of that pixel (the original value of the pixel is included in the computation of the median)

► quite popular because for certain types of random noise (impulse noise salt and pepper noise) , they provide excellent noise-reduction capabilities, with considering less blurring than linear smoothing filters of similar size.


Example: Use of Median Filtering for Noise Reduction


Sharpening Spatial Filters

► Foundation

► Laplacian Operator

► Unsharp Masking and Highboost Filtering

► Using First-Order Derivatives for Nonlinear Image Sharpening — The Gradient


Sharpening Spatial Filters

► to highlight fine detail in an image

► or to enhance detail that has been blurred, either in error or as a natural effect of a particular method of image acquisition.

► Blurring Vs. Sharpening

as we know that blurring can be done in spatial domain by pixel averaging in a neighbors

since averaging is analogous to integration

thus, we can guess that the sharpening must be accomplished by spatial differentiation.


Derivative operator

► the strength of the response of a derivative operator is proportional to the degree of discontinuity of the image at the point at which the operator is applied.

► thus, image differentiation

enhances edges and other discontinuities (noise)

deemphasizes area with slowly varying gray-level values.


Sharpening Spatial Filters: Foundation

► The first-order derivative of a one-dimensional function f(x) is the difference

► The second-order derivative of f(x) as the difference

( 1) ( )f

f x f xx

2

2( 1) ( 1) 2 ( )

ff x f x f x

x


First and Second Derivative

► First Derivative

Must be zero in flat segments

Must be nonzero at the onset of a gray-level step or ramp; and

Must be nonzero along ramps.

► Second Derivative

Must be zero in flat areas;

Must be nonzero at the onset and end of a gray-level step or ramp;

Must be zero along ramps of constant slope


Sharpening Spatial Filters: Laplace Operator

The second-order isotropic derivative operator is the Laplacian for a function (image) f(x,y)

2 22

2 2

f ff

x y

2

2( 1, ) ( 1, ) 2 ( , )

ff x y f x y f x y

x

2

2( , 1) ( , 1) 2 ( , )

ff x y f x y f x y

y

2 ( 1, ) ( 1, ) ( , 1) ( , 1)

- 4 ( , )

f f x y f x y f x y f x y

f x y



Image sharpening in the way of using the Laplacian:

2

2

( , ) ( , ) ( , )

where,

( , ) is input image,

( , ) is sharpenend images,

-1 if ( , ) corresponding to Fig. 3.37(a) or (b)

and 1 if either of the other two filters is us

g x y f x y c f x y

f x y

g x y

c f x y

c

ed.


Unsharp Masking and Highboost Filtering

► Unsharp masking

Sharpen images consists of subtracting an unsharp (smoothed) version of an image from the original image

e.g., printing and publishing industry

► Steps

1. Blur the original image

2. Subtract the blurred image from the original

3. Add the mask to the original


Unsharp Masking and Highboost Filtering

Let ( , ) denote the blurred image, unsharp masking is

( , ) ( , ) ( , )

Then add a weighted portion of the mask back to the original

( , ) ( , ) * ( , )

mask

mask

f x y

g x y f x y f x y

g x y f x y k g x y

0k

when 1, the process is referred to as highboost filtering.k


Unsharp Masking: Demo


Unsharp Masking and Highboost Filtering: Example


Image Sharpening based on First-Order Derivatives

For function ( , ), the gradient of at coordinates ( , )

is defined as

grad( )x

y

f x y f x y

f

g xf f

fg

y

2 2

The of vector , denoted as ( , )

( , ) mag( ) x y

magnitude f M x y

M x y f g g

Gradient Image



2 2

The of vector , denoted as ( , )

( , ) mag( ) x y

magnitude f M x y

M x y f g g

( , ) | | | |x yM x y g g

z1 z2 z3

z4 z5 z6

z7 z8 z9

8 5 6 5( , ) | | | |M x y z z z z


Example


Example: Combining Spatial Enhancement Methods Goal: Enhance the image by sharpening it and by bringing out more of the skeletal detail

Lecture # 06 Image Enhancement in Spatial Domain · Lecture # 06 Image Enhancement in Spatial ......

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