IMAGE REPRESENTATION 1

2 IMAGE REPRESENTATION MEANS CONVERSION OF ANALOG IMAGE INTO DIGITAL IMAGE THIS CONVERSION OF ANALOG(3D) TO DIGITAL (2D) TAKES PLACE IN 3 STAGES 1) SAMPLING 2) QUANTIZING 3) CODING

3 SAMPLING means measuring the value of an image at a finite number of points. Sampling is done in two directions,ie x & y and we get a resolution of m*n pixels. The Three conditions that are to be considered while sampling an analog image are: 1) The sampling rate has to be very high. 2)while sampling the aspect ratio has to be has to be maintained. 3) The nyquist rate has to be maintained. At the end of the Sampling stage we obtain a discrete image which is given by I0(k,j) where k &j represents the x & y axis respectively.

The discrete image obtained is then quantized. Quantization is discretizing the analog image in brightness and is also called amplitude digitization. Quantized image is represented by a precision of ‘b’ binary digits. This results in 2^b intensity values or shades of gray/brightness. 4

In CODING STAGE the digital image I(k,j) consisting of a number of pixels is further coded or packed. Patterns of bits consists of 0’s and 1’s. Now the image of size(1KB,1MB) can be used for storing or transmisssion. This stage gives the Actual digital image. 5

Template Matching

Template Matching in Images General Idea of Template Matching –create a small “template” image of the feature we want to detect –center the template image over pixel(i,j) in a target image –calculate the pixel differences between the template image and the pixels centered at (i,j) if the distance is small, the template is similar to the window centered at (i,j) if the distance is large, the template is dissimilar –repeat for all pixels –the minimum distance is the best “match” –this is known as “template matching”

Source Image Representation Source Image : S(x, y)

Template Representation Template Image : T(x t, y t )

Procedure for Template Matching Template Target Image

Example Minimum Distance : Diff(x s, y s, x t, y t ) = | I s (x s, y s ) – I t (x t, y t ) |.

Polyhedral Objects

Edge Detection Reflected light intensity is constant over surface of objects (if surfaces are smooth, opaque, and lighting is uniform) At edges there is sudden change in light intensity, where the intensity changes from one grayscale level to another. The concept of jump discontinuity in light intensity at edges is used to locate edges of polyhedral object.

Gradient operators are used to determine edges in polyhedral objects. It is a vector having both magnitude and direction. At surfaces of objects, gradient of light intensity is uniform,constant. At edges of objects, gradient of light intensity is infinity.

Selection of edge threshold

Magnitude of gradient vector is used to determine edges of an object. Angle of gradient vector is used to determine which side of edge corresponds to which object in a image. The above two criteria are collectively called as the Robert cross operators.

Corner Point Detection Obtain analog image of 3D object Digitise it and give it to EDA Obtain a binary image L(k,j) as output Scan the image with 8 standard corner point templates using NCC If sigma(x,y) for some i is one, then the pixel is a corner pixel

Shape Analysis

Types of Descriptors Line Descriptors Area Descriptors

Line Descriptor Chain Coding Technique Chain coding  Relative Representation and Invariant to Translation 321 4P0 567

Algorithm Search for the Rightmost Foreground Pixel. Search for the Nearest Neighbor in Anti- clockwise direction. Write the Direction number as the Chain code.

Area Descriptor Descriptor based on analysis of points enclosed by the boundary. Moment - Sum of product of integer power’s of row and column number of foreground pixel. Moment is variant to Translation, Rotation and Scaling.

Formula Central Moment :- Moment :- Normalized Central Moment :-

Advantages of Area Descriptor over Line Descriptor Robust to Large Change in Boundary Large number of points are considered Less sensitive to Change in Boundary

Segmentation

It is the process by which items in an image are separated from background The set of all connected pixels with a particular gray level attribute is identified as a region and is assigned label

Segmentation Segmentation algorithms are generally based on one of the two basic properties –Discontinuities in intensity –Similarities in intensity Methods to achieve segmentation –Thresholding –Region labeling

THRESHOLDING

Simplest way of Segmentation Converts Gray level image into Binary Black-&-White image Thresholding works well if the object of interest has a uniform gray level and rest upon a background of different, but uniform, gray level

THRESHOLDING Process: Plot Image Histogram Select Threshold value All pixels at or above the threshold gray level are assigned to the object All pixels with gray level below the threshold fall outside the object

THRESHOLDING if r: row, c: column I: grayscale intensity, B: binary intensity T: intensity threshold

THRESHOLDING

REGION LABELLING

 Producing a labeled image from a segmented binary image is to use something called region growing.  Binary image is scanned for an unlabeled foreground pixel.  Each time one is found it serves as a seed for growing a new foreground region.

Algorithm for region labeling 1.Initialize k=1, j=1 2.If I(k,j)=1, set I(k,j)=255 3.Set k=k+1.If K≤m go to step 2 4.Set k=1, j=j+1. If j ≤n go to step 2 5.Initialize k=1, j=1, i=0 6.If I(k,j)=255 (a) set i=i+1 (b) Grow region I from seed (k,j) using region growing algo 7.Set k=k+1. If k ≤m go to step 6 8.Set k=1, j=j+1. If j ≤n go to step 6

Algorithm for region growing 1. Set I(k,j)=I, push(k,j) push(0,0) 2. If j<n & I(k,j+1)=255 (a) Set I(j+1)=I (b) Push (k,j+1) 3. If k>1 & I(k-1,j)=255, (a) Set I(k-1,j)=I (b) Push(k-1,j) 4. If j<1 & I(k,j-1)=255 (a) set I(k,j-1)=I (b) Push(k, j-1) 5. If k<m & I(k+1, j)=255 (a) Set I(k+1,j)=I (b) push(k+1, j) 6. pop(k,j). If (k,j)≠0 go to step 2 7. pot(k,j), return

SHRINK AND SWELL OPERATORS BY PREETI RUPANI PRIYADARSHANI SAFAYA

ITERATIVE PROCESSING Iterative processing of images is defined as the removal of stray noises in the images. It makes use of iterative operations such as the shrink and swell operators. i.e. smoothening of images.

SHRINK OPERATOR

Let I(k,j) be a (mxn) binary image. p(k,j) is a pixel function at spatial coordinates (k,j) & has 8 neighbors. This is given by: p(k,j)=[ Σ Σ I(k+u, j+v)]- I(k,j) where, l<k<m, l<j<n

SHRINK OPERATOR Shrink (i) I(k,j)=I(k,j) AND 1(i-1-[8-p(k,j)]); where, 0<=i<=8 [8-p(k,j)]→the no of background pixels i.e. zeroes surrounding p(k,j) p(k,j) is the pixel function. 1( ) is the unit step function.

KEY POINTS The ith shrink operator is monotonic in nature. Shrink operator converges in the finite steps. It smoothes out rough edges and removes of the noise. It eliminates the small region from the background.

SWELL OPERATOR

Swell (i)I(k,j) = I(k,j) OR 1[ p(k,j) - i ] ; 0 ≤ i ≤ 8 Here, p(k,j) is the pixel function. i th swell operator turns pixel p(k,j) into a 1 if it has at least i neighbor with value, else it leaves p(k,j) unchanged.

KEY POINTS Swell operator is an iterative operation for smoothening of images. i th Swell operator is monotonic in nature. Swell operator converges in finite steps. It fills small inlets or removes holes from a foreground object area. It is dual of shrink operator.

STEPS IN IMAGE ANALYSIS 1. Apply threshold to a gray scale image. 2. Binary scale image segmented into background and foreground areas is obtained. 3. Iterative shrink (i) operator is applied for some I>4. 4. Shrink operator converges when total foreground area remains the same after last application.

STEPS CONTINUED… 5. Similar to shrink operator, swell operator is applied till convergence occurs. 6. Smoothed, distinct foreground regions are labeled. 7. Moments are calculated for each region R. 8. Using the moments. Area, centroid and the principal angle are calculated.

Euler’s Number The Euler Number of an image is defined as number of parts minus the number of holes. EulerNumber = #Objects - #Holes

Examples

Parts and Holes A part is a connected foreground region. A hole is am isolated background region enclosed by part.

Properties Eulers numbers follows the additive set property.

Is Euler Number a good Shape Descriptor ?? The Eulers numbers is not a good shape descriptor. Characterize the connected components by describing the edges.

Applications Vast applications in the areas of machine vision, automatic borders detection and image understading. Fast easy and reliable method of calculating eulers numbers can increase the performance of the system.

Perspective Transformation Perspective Projection Two types Direct perspective transformation Inverse perspective transformation

Perspective Projection Projection is actually a term used when you’re changing the dimension of something. Perspective is something that refers to the way an object’s size is affected by distance. The farther away an object moves, the smaller it gets: that’s the effect of perspective

Transformation With the two definitions by your side, you can probably tell that when I say “perspective projection transformation”, I’ve talking about a transformation that will do both at the same time. i.e- “Given the coordinates of the object with respect to camera frame, to find the coordinates of its image with respect to camera frame, the transformation technique used is called perspective transformation.

Inverse perspective transformation “Given the coordinates of image with respect to camera frame, to find the coordinates of the object with respect to camera frame, the transformation technique used is called inverse perspective transformation.” Inverse Perspective Transformation is more useful than perspective Transformation –As the robotic controller uses inverse transformation to find the coordinates of object itself w.r.t to the camera frame.