EE 7730: Image Analysis I Introduction. Bahadir K. Gunturk2 EE 7730 Dr. Bahadir K. Gunturk Office:...

EE 7730: Image Analysis I

Introduction

Bahadir K. Gunturk 2

EE 7730

Dr. Bahadir K. Gunturk Office: EE 225 Email: [email protected] Tel: 8-5621 Office Hours: MW 2:40 – 4:30 Class Hours: MWF 1:40 – 2:30 (CEBA-3129)


EE 7730

We will learn the fundamentals of digital image processing, computer vision, and digital video processing

Lecture slides, problems sets, solutions, study materials, etc. will be posted on the class website. [www.ece.lsu.edu/gunturk/EE7730]

Textbook is not required. References:

Gonzalez/Woods, Digital Image Processing, Prentice-Hall, 2/e. Forsyth/Ponce, Computer Vision: A Modern Approach, Prentice-Hall. Duda, Hart, and Stork, Pattern Classification, John Wiley&Sons, 2001. Tekalp, Digital Video Processing, 1995 Jain, Fundamentals of Digital Image Processing, Prentice-Hall.


Grading Policy

Your grade will be based on Problem Sets + Semester Project: 35% Midterm: 30% Final: 35%

Problem Sets Theoretical problems and MATLAB assignments 4-5 Problem Sets Individually or in two-person teams

Semester Project Each student will give a 15 minute presentation


EE 7740 Image Analysis II

Semester Project Possible project topics will be provided in a month Projects will be done individually Projects will involve MATLAB or C/C++ implementation Each student will give a 15 minute presentation at the end of

the semester


EE 7740 Image Analysis II

Image Analysis I - Outline Digital image fundamentals 2D Fourier transform, sampling, Discrete Cosine Transfrom Image enhancement Human visual system and color image processing Image restoration Image compression Image segmentation Morphology Introduction to digital video processing


Digital Image AcquisitionSensor array

When photons strike, electron-hole pairs are generated on sensor sites.

Electrons generated are collected over a certain period of time.

The number of electrons are converted to pixel values. (Pixel is short for picture element.)


Digital Image Acquisition

Two types of quantization:1. There are finite number of

pixels. (Spatial resolution)2. The amplitude of pixel is

represented by a finite number of bits. (Gray-scale resolution)


Digital Image Acquisition


Digital Image Acquisition• 256x256 - Found on very cheap

cameras, this resolution is so low that the picture quality is almost always unacceptable. This is 65,000 total pixels.

• 640x480 - This is the low end on most "real" cameras. This resolution is ideal for e-mailing pictures or posting pictures on a Web site.

• 1216x912 - This is a "megapixel" image size -- 1,109,000 total pixels -- good for printing pictures.

• 1600x1200 - With almost 2 million total pixels, this is "high resolution." You can print a 4x5 inch print taken at this resolution with the same quality that you would get from a photo lab.

• 2240x1680 - Found on 4 megapixel cameras -- the current standard -- this allows even larger printed photos, with good quality for prints up to 16x20 inches.

• 4064x2704 - A top-of-the-line digital camera with 11.1 megapixels takes pictures at this resolution. At this setting, you can create 13.5x9 inch prints with no loss of picture quality.


Matrix Representation of Images A digital image can be written as a matrix

1 2

[0,0] [0,1] [0, 1]

[1,0] [1,1] [1, 1][ , ]

[ 1,0] [ 1, 1]MxN

x x x N

x x x Nx n n

x M x M N

35 45 20

43 64 52

10 29 39


Image Resolution


Bit Depth – Grayscale Resolution

8 bits 7 bits

6 bits 5 bits


Bit Depth – Grayscale Resolution

4 bits 3 bits2 bits 1 bit


Digital Color Images

1 2[ , ]Rx n n

1 2[ , ]Gx n n

1 2[ , ]Bx n n


Video

= vertical position

= horizontal position

= frame number

1 2 3[ , , ]x n n n

1n

2n

3n

~24 frames per second.


Why do we process images?

To facilitate their storage and transmission To prepare them for display or printing To enhance or restore them To extract information from them To hide information in them


Image Processing Example

Image Restoration

Original image Blurred Restored by Wiener filter



Noise Removal

Noisy image Denoised by Median filter



Image Enhancement

Histogram equalization


Image Processing Example Artifact Reduction in Digital Cameras

Original scene Captured by a digital camera

Processed to reduce artifacts



Image Compression

Original image 64 KB

JPEG compressed 15 KB

JPEG compressed 9

KB



Object Segmentation

“Rice” image Edges detected using Canny filter



Resolution Enhancement



Watermarking

Original image

Hidden message

Generate watermark

Watermarked image

Secret key



Face Recognition

Surveillance video

Search in the database



Fingerprint Matching



Segmentation



Texture Analysis and Synthesis

Pattern repeated Computer generated

Photo



Face detection and tracking

http://www-2.cs.cmu.edu/~har/faces.html



Face Tracking



Object Tracking



Virtual Controls



Visually Guided Surgery


Cameras

First camera was invented in 16th century. It used a pinhole to focus light rays onto a wall or

translucent plate.

Take a box, prick a small hole in one of its sides with a pin, and then replace the opposite side with a translucent plate.

Place a candle on the pinhole side, you will see an inverted image of the candle on the translucent plate.


Perspective Projection

Perspective projection equations

' ' 'x y z

x y z


Pinhole Camera Model If the pinhole were really reduced to a point, exactly one light ray would

pass through each point in the image plane. In reality, each point in the image place collects light from a cone of rays.


Pinhole Cameras

Pinhole too big - many directions are averaged, blurring the image Pinhole too small - diffraction effects blur the image


Cameras With Lenses

Most cameras are equipped with lenses. There are two main reasons for this:

To gather light. For an ideal pinhole, a single light ray would reach each point the image plane. Real pinholes have a finite size, so each point in the image plane is illuminated by a cone of light rays. The larger the hole, the wider the cone and the brighter the image => blurry pictures. Shrinking the pinhole produces sharper images, but reduces the amount of light and may introduce diffraction effects.

To keep the picture in sharp focus while gathering light from a large area.


Compound Lens Systems


Real Lenses

Rays may not focus at a single point.

Spherical aberration

Spherical aberration can be eliminated completely by designing aspherical lenses.


Real Lenses

Chromatic aberration

The index of refraction is a function of wavelength. Light at different wavelengths follow different paths.


Real Lenses

Chromatic Aberration


Real Lenses Special lens systems using two or more pieces of glass with different

refractive indeces can reduce or eliminate this problem. However, not even these lens systems are completely perfect and still can lead to visible chromatic aberrations.


Real Lenses Barrel Distortion & Pincushion Distortion

Stop (Aperture)

Causes of distortion

(normal)

Chief ray


Real Lenses Barrel Distortion & Pincushion Distortion

Distorted Corrected

http://www.vanwalree.com/optics/distortion.htmlhttp://www.dpreview.com/learn/?/Image_Techniques/Barrel_Distortion_Correction_01.htm


Real Lenses

Vignetting effect in a two-lens system. The shaded part of the beam never reaches the second lens. The brightness drop in the image perimeter.


Real Lenses

Optical vignetting example. Left: f/1.4. Right: f/5.6.

f-number

focal length to diameter ratio


Real Lenses

Long exposure time

Short exposure time


Real Lenses

Flare

Hood may prevent flares


Real Lenses

Flare


Compound Lens Systems

http://www.dpreview.com/learn/?/glossary/http://www.cartage.org.lb/en/themes/Sciences/Physics/Optics/Optical/Lens/Lens.htmhttp://www.vanwalree.com/optics.html


Digital Camera Pipeline

Auto-exposure algorithms measure brightness over discrete scene regions to compensate for overexposed or underexposed areas by manipulating shutter speed and/or aperture size. The net goals here are to maintain relative contrast between different regions in the image and to achieve a good overall quality.

(from Katz and Gentile)



Auto-focus algorithms divide into two categories. Active methods use infrared or ultrasonic emitters/receivers to estimate the distance between the camera and the object being photographed. Passive methods, on the other hand, make focusing decisions based on the received image in the camera.



Lens distortion correctionThis set of algorithms accounts for the physical properties of lenses that warp the output image compared to the actual scene the user is viewing. Different lenses can cause different distortions; for instance, wide-angle lenses create a "barrel distortion", while telephoto lenses create a "pincushion distortion“.



Vignetting (shading distortion) reduces image brightness in the area around the lens. Chromatic aberration causes color fringes around an image. The media processor needs to mathematically transform the image in order to correct for these distortions.



Sensor's output needs to be gamma-corrected to account for eventual display, as well as to compensate for nonlinearities in the sensor's capture response.



Image stability compensation, or hand-shaking correction is another area of preprocessing. Here, the processor adjusts for the translational motion of the received image, often with the help of external transducers that relate the real-time motion profile of the sensor.



White balance is another important stage of preprocessing. When we look at a scene, regardless of lighting conditions, our eyes tend to normalize everything to the same set of natural colors. For instance, an apple looks deep red to us whether we're indoors under fluorescent lighting, or outside in sunny weather. However, an image sensor's "perception" of color depends largely on lighting conditions, so it needs to map its acquired image to appear natural in its final output. This mapping can be done either manually or automatically.



Demosaicking (Bayer interpolation) estimates missing color samples in single-chip cameras.



In this stage, the interpolated RGB image is transformed to the targeted output color space (if not already in the right space). For compression or display to a television, this will usually involve an RGBYCbCr matrix transformation, often with another gamma correction stage to accommodate the target display. The YCbCr outputs may also be chroma subsampled at this stage to the standard 4:2:2 format for color bandwidth reduction with little visual impact.



PostprocessingIn this phase, the image is perfected via a variety of filtering operations before being sent to the display and/or storage media. For instance, edge enhancement, pixel thresholding for noise reduction, and color-artifact removal are all common at this stage.



Display / Compress / StoreOnce the image itself is ready for viewing, the image pipe branches off in two different directions. In the first, the postprocessed image is output to the target display, usually an integrated LCD screen (but sometimes an NTSC/PAL television monitor, in certain camera modes). In the second, the image is sent to the media processor's compression algorithm, where industry-standard compression techniques (JPEG, for instance) are applied before the picture is stored locally in some storage medium (e.g., Flash memory card).


Review: Linear Systems

We define a system as a unit that converts an input function into an output function.

System operatorIndependent variable


Linear Systems

Then the system H is called a linear system.

where fi(x) is an arbitrary input in the class of all inputs {f(x)}, and gi(x) is the corresponding output.

Let

If

A linear system has the properties of additivity and homogeneity.


Linear Systems

for all fi(x) {f(x)} and for all x0.

The system H is called shift invariant if

This means that offsetting the independent variable of the input by x0 causes the same offset in the independent

variable of the output. Hence, the input-output relationship remains the same.


Linear Systems

The operator H is said to be causal, and hence the system described by H is a causal system, if there is no output before there is an input. In other words,

A linear system H is said to be stable if its response to any bounded input is bounded. That is, if

where K and c are constants.


Linear Systems

(a)

ax

(x-a)

A unit impulse function, denoted (a), is defined by the expression


Linear Systems

A unit impulse function, denoted (a), is defined by the expression

Then


Linear Systems

is called the impulse response of H.

The term

From the previous slide

It states that, if the response of H to a unit impulse [i.e., h(x, )], is known, then response to any input f can be computed using the preceding integral. In other words, the response of a linear system is characterized completely by its impulse response.


Linear Systems

and the integral becomes

If H is a shift-invariant system, then

This expression is called the convolution integral. It states that the response of a linear, fixed-parameter system is completely characterized by the convolution of the input with the system impulse response.


Linear Systems

[ ]* [ ] [ ] [ ]m

f n h n f m h n m

Convolution of two functions is defined as

In the discrete case

( )* ( ) ( ) ( )f x h x f h x d


Linear Systems

1 2

1 2 1 2 1 2 1 1 2 2[ , ]** [ , ] [ , ] [ , ]m m

f n n h n n f m m h n m n m

1 2[ , ]h n n is a linear filter.

In the 2D discrete case


Example

1 1 11

1 1 19

1 1 1

* =


Example

* =1 1 1

1 8 1

1 1 1


Try MATLAB

f=imread(‘saturn.tif’);

figure; imshow(f);

[height,width]=size(f);

f2=f(1:height/2,1:width/2);

figure; imshow(f2);

[height2,width2=size(f2);

f3=double(f2)+30*rand(height2,width2);

figure;imshow(uint8(f3));

h=[1 1 1 1; 1 1 1 1; 1 1 1 1; 1 1 1 1]/16;

g=conv2(f3,h);

figure;imshow(uint8(g));

EE 7730: Image Analysis I Introduction. Bahadir K. Gunturk2 EE 7730 Dr. Bahadir K. Gunturk Office:...

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