Color Image Processing

1. Color Image Processing • Color simplifies object identification and extraction from a scene. • Humans can identify thousands of color shades and intensity compared to about only 25 shades of gray. • In full color image processing, we acquire image using full-color sensor such a color TV camera or color scanner. • In the case of pseudo color processing, we assign a color to a particular monochrome intensity or range of intensities.

2. Nature of Light and Color • According to Newton, when a beam of sunlight passes through a glass prism, it splits up into a continuous spectrum of colors varying from violet to red. (VIBGYOR). • The color perceived in an object are determined by the nature of the light reflected from the object. • If the light is achromatic (without color), its only attribute is its intensity or amount. • A chromatic light spans the electromagnetic spectrum from 400 to 700 nm. • 3 quantities are used to describe a light source. • They are: 1) Radiance – total amount of energy that flows from the light source and is measured in watts (W). • 2) Luminance – measures the amount of energy an observer perceives from a light source and is measured in lumens (lm). • 3) Brightness – a subjective descriptor and is impossible to measure.

3. Color Perception • Cones in our eye are responsible for color vision. • We have about 6 to 7 million cones in human eye 65% of cones are sensitive to red light, 33% are sensitive to green light and about 2% are sensitive to blue light. • Due to this, the colors are seen as combinations of the primary colors red (R), green (G) and blue (B). • The wavelength of blue is 435.8 nm, green is 546.1nm and red is 700nm. • When mixed in proper proportions, these colors can produce all visible colors.

4. Primary Colors • Primary colors can be added to produce the secondary colors of light – magenta (red plus blue), cyan (green plus blue) and yellow (red plus green). • Mixing these 3 primitives or a secondary with its opposite primary color, in right proportion gives white light.

5. Characteristics of a color • The characteristics used to distinguish one color from another are brightness, hue and saturation. • Brightness embodies the chromatic notion of intensity. • Hue is related with dominant wavelength in a mixture of light waves. • Hue represents dominant color perceived by an observer. • Saturation refers to the relative purity or amount of white light mixed with a hue. • The degree of saturation is inversely proportional to the amount of white light added.

6. Chromaticity • Hue and saturation together are called chromaticity. • The amounts of red, green and blue needed to form a color are called the tristimulus values and are denoted as X, Y and Z respectively. • A color is then specified by its trichromatic coefficients as: • X Y Z • x = -------------,y = ------------ z = -------------- • X + Y + Z X + Y + Z X + Y + Z • Here x + y + z = 1. • Another way of specifying colors is to use the CIE chromaticity diagram where each color is expressed as a function of x (red) and y (green). • We know, the value of z (blue) is obtained as: z = 1 – ( x + y).

7. Color Models • Color models are used to specify colors in some standard. • A color model uses a coordinate system and each color is represented by a single point. • Hardware oriented models (monitors, video cameras) use RGB model. • CMY (cyan, magenta, yellow) and CMYK (cyan, magenta, yellow, black) model are used for color printing. • HIS (hue, intensity, saturation) model closely resembles human color interpretation. • HIS decouples the color and ray-scale information in an image.

8. RGB Color Model • Here each color appears in its primary spectral components of red, green and blue. • It is based on Cartesian coordinate system. • We can imagine a cube in which RGB values are at 3 corners; • Cyan, magenta and yellow are at 3 other corners; • Black is at the origin and white is at the corner farthest from the origin. • Here gray scale extends from black to while along the line joining these 2 points. • Different colors in this model are points on or inside the cube and are defined by vectors extending from the origin. • Here all color values are normalized so that the cube is the unit cube.

9. Cube with RGB values are at 3 corners

10. clear all; close all; clc; vx = 10; vy = 10; vz = 4; vertices_matrix = [0 0 0; 0 0 1;0 1 0;0 1 1; 1 0 0;1 0 1;1 1 0;1 1 1]; faces_matrix = [1 5 6 2;1 3 7 5;1 2 4 3; 2 4 8 6;3 7 8 4;5 6 8 7]; colors = vertices_matrix; patch('Vertices', vertices_matrix,'Faces',faces_matrix, 'FaceVertexCData', colors,'FaceColor', 'interp','EdgeAlpha',0) axis off view([vx, vy, vz]) axis square

11. RGB Color Model • All R, G and B values are assumed to be in the range [0,1]. • The number of bits used to represent each pixel in RGB space is called the pixel depth. • The term full-color image is used to denote a 24 bit RGB color image. • It has 16,772,216 different colors. • A color image can be acquired by using 3 filters, sensitive to red, green and blue respectively. • A subset of colors can be reproduced faithfully, independent of viewer hardware capabilities. • These are called safe RGB colors or all-systems-safe colors

12. RGB Color Model • In internet applications we use safe Web Colors or safe browser colors. • Generally 256 colors are used here. • Of these 40 colors are processed differently by various operating systems. • The remaining 216 colors which are common to most systems are defined as safe colors. • Each of the 216 safe colors is formed from three RGB values, but each value can only be 0, 51, 102, 153, 204 or 255. • The RGB triplets of these values give us 63 = 216 possible values. • All values are here divisible by 3. • The 2 digit hexadecimal representations of these values are: • Hex 00 33 66 99 CC FF • Decimal 0 51 102 153 204 255

13. The CMY and CMYK Color Models • Cyan, Maganta and Yellow are secondary colors or light. • Color printers and copiers use this model. • They perform an RGB to CMY conversion internally as follows: • C = 1 - R • M = 1 - G • Y = 1 - B • Here all values are normalized to the range [0,1]. • The light reflected from a surface coated with pure cyan does not contain red. • Pure magenta does not reflect green and pure yellow does not reflect blue. • Combining these colors for printing produces a muddy-looking black. • To produce true black, a fourth color, black is added, giving us CMYK color model. • This leads to 4 color-printing.

14. HIS Color Model • This model decouples the intensity component from the color-carrying information (hue and saturation) in a color image. • We can do the conversion from RGB to HSI using the following formulae: • H = 0 if B ≤ G • = 360 – θ if B > G • (1/2)*[(R - G) + (R – B)] • θ = cos-1 ---------------------------------------- • [(R – G)2 + (R – B)(G – B)]1/2 • 3 • S = 1 - -------------[ min (R,G,B)] • ( R + G + B) • And I = (1/3)*( R + G + B).

15. Converting colors from HSI to RGB • Here we are given the HIS values, we try to find the RGB values. • We begin my multiplying H by 3600, which returns the hue to its original range of [ 00 , 3600]. • RG sector ([ 00 ≤ H < 1200): • When H is in this sector, the RGB components are given as: • B = I ( 1- S) • S cos H • R = I *[ 1 + ----------------] • Cos(600 – H) • G = 1 – ( R + B)

16. Converting colors from HSI to RGB • GB sector ([ 1200 ≤ H < 2400): • If the value of H is in this sector, we first subtract 1200 from it: • H = H - 1200 • R = I ( 1 – S) • S cos H • G = I *[ 1 +----------------] • Cos(600 – H) • B = 1 – ( R + G).

17. Converting colors from HSI to RGB • BR sector ([ 2400 ≤ H < 3600): • Here we subtract 2400 from it: • H = H - 2400 • G = I ( 1 – S) • S cos H • B = I *[ 1 + ----------------] • Cos(600 – H) • R = 1 – ( G + B)

21. clear all;close all; clc; f = imread('onion.png'); f = im2double(f); figure,imshow(f),title('Image') figure,imshow(f(:,:,1)),title('Red'); figure,imshow(f(:,:,2)),title('Green'); figure,imshow(f(:,:,3)),title('Blue'); f1 = 1-f; figure,imshow(f1(:,:,1)),title('Cyan'); figure,imshow(f1(:,:,2)),title('Magenta'); figure,imshow(f1(:,:,3)),title('Yellow'); h = rgb2hsi(f); figure,imshow(h(:,:,1)),title('Hue'); figure,imshow(h(:,:,2)),title('Saturation'); figure,imshow(h(:,:,3)),title('Intensity');

22. Histogram Equalization Using HSI image

23. clear all; close all; clc; • f = imread('Baboon24.png'); • f = imresize(f,[256,256]); • f1 = f(:,:,1); • f2 = f(:,:,2); • f3 = f(:,:,3); • h = rgb2hsi(f); • H = h(:,:,1); S = h(:,:,2); • I = h(:,:,3); • I1 = histeq(I); • res = cat(3,H,S,I1); • res1 = hsi2rgb(res); • figure,imshow(f),title('Original Image'); • figure,imshow(res1),title('Histogram Equalized');

24. Pseudocolor Image Processing • This is also called as false color. Here we assign colors to gray values based on a specified criterion. • Intensity Slicing • If an image is interpreted as a 3-D function, the method can be viewed as one of placing planes parallel to the coordinate plane of the image; • Each plane then “slices” the function in the area of intersection. • Let us slice the image function into 2 levels and assign different color to each side of the plane. • The pixels whose gray level is above the plane will be coded with one color and any pixel below the plane will be coded with the other. • Levels that lie on the plane are arbitrarily assigned to one of the two colors.

25. Intensity Slicing • Let [0, L-1] represent the gray scale, let level l0 represent black and level lL-1 represent white. Suppose that Plane s perpendicular to the intensity axis are defined at levels l1, l2, … lP. • Then assuming that 0 < P < L-1, the P planes partition the gray scale into P + 1 intervals, V1, V2, … VP+1. • Gray-level to color assignments are made according to the relation: • f ( x, y ) = ck if f(x,y) ξ Vk. • Here ck is the color associated with the kth intensity interval Vk defined by the partitioning planes at l = k -1 and l = k. • In general, gray scale is divided into intervals and a different color is assigned to each region, without regard for the meaning of the gray levels in the image.

27. clear all; close all; clc; f = imread('PIA02948.tif'); figure,imshow(f); %f = rgb2gray(f1); [m,n]=size(f); R(:,:,1)=zeros([m,n]); R(:,:,2)=zeros([m,n]); R(:,:,3)=zeros([m,n]); for i=1:m for j=1:n b = f(i,j); if b >= 200 R(i,j,3) = 200; elseif b >= 180 && b < 200 R(i,j,3) = 150; R(i,j,2) = 20; elseif b >= 160 && b < 180 R(i,j,3) = 50; R(i,j,2) = 10; R(i,j,3) = 150; elseif b >= 150 && b < 160 R(i,j,3) = 150; R(i,j,2) = 70; R(i,j,1) = 10; elseif b >= 120 && b < 150 R(i,j,3) = 10; R(i,j,2) = 70; R(i,j,1) = 150; elseif b >= 120 && b < 150 R(i,j,3) = 150; R(i,j,2) = 70; R(i,j,1) = 10; elseif b >= 100 && b < 120 R(i,j,3) = 50; R(i,j,2) = 200; R(i,j,1) = 150; elseif b >= 80 && b < 100 R(i,j,3) = 70; R(i,j,2) = 200; R(i,j,1) = 200; else R(i,j,3) = 70; R(i,j,2) = 200; R(i,j,1) = 20; end end end figure,imshow(uint8(R));

28. Gray level to color transformations • Here we perform three independent transformations on the gray level of any input pixel. • The three results are then fed separately into the red, green and blue channels. • The image is modulated by the nature of the transformation functions. • These functions act on gray levels of an image, not on its position.

29. Basics of full-color image processing • There are 2 approaches here. • In the first type, we process each component image individually and then form a composite processed color image from the individually processed components. • In second type, we work with color pixels directly.

30. Color Transformations • These techniques deal with processing the components of a color image within the context of a single color model, as opposed to the conversion of those components between models. • Here we model color transformations using the relation: • g(x,y) = T[f(x,y)] • where f(x,y) is a color input image, g(x,y) is the transformed color output image and T is an operator on f over a spatial neighborhood of (x,y). • Here pixel values are triplets or quartets from the color space chosen to represent the images

31. Color Transformations • The transformations are of the form: • si = Ti(r1,r2,…,rn), i = 1,2, …, n • Here ri and si are the variables denoting the color components of f(x,y) and g(x,y) at any point (x,y), n is the number of color components and Ti are the set of transformation or color mapping functions that operate. • Here the n transformations Ti combine to implement the single transformation function T. • For RGB color space, n =3 and ri values are red, green and blue components of an image.

32. Color Transformations • If we want to modify the intensity of the image, in the HSI color space only the intensity component r3 needs to be modified. • But in the RGB color space, all 3 components need to be transformed. • The HSI transformation involves fewest number of operations, but the computations need to convert an RGB or CMY(K) image to the HSI space often offsets the advantages. • But the output is the same.

33. Color Conversion

34. % RGB to CMYand YIQ conversion • % Read a RGB Color image and convert it into CMY and YIQ formats • f=imread('onion.png'); • f = im2double(f); • r=f(:,:,1); • g=f(:,:,2); • b=f(:,:,3); • c = 1-r; • m = 1-g; • y = 1-b; • CMY = cat(3,c,m,y); • figure,imshow(f); • figure,imshow(CMY); • Y = 0.3*r+0.59*g+0.11*b; • I = 0.6*r-0.28*g-0.32*b; • Q = 0.21*r-0.52*g+0.31*b; • YIQ =cat(3,Y,I,Q); • figure,imshow(YIQ);

35. Color Slicing • Highlighting a specific range of colors in an image is useful for separating objects from their surroundings. • A simple approach is to “slice” a color image to map the colors outside some range of interest to a nonprominent neutral color. • f the colors of interest are enclosed by a cube (or hypercube for n > 3) of width W and centered at a prototypical color with components (a1,a2, …, an), the transformation is: • si = 0.5 if | rj – aj | > (W/2) for any 1 ≤ j ≤ n • = ri otherwise for any i = 1,2, …, n • These transformations highlight the colors around the prototype by forcing all other colors to the midpoint of the reference color space.

36. Color Slicing • If a sphere is used to specify the colors of interest, then we have: • si = 0.5 if Σ ( rj – aj )2 > (R02) for 1 ≤ j ≤ n • = ri otherwise for any i = 1,2, …, n • Here R0 is the radius of the enclosing sphere and a1,a2, …, an are the components of its center.

37. Histogram processing • Color images are composed of multiple components. • It is unwise to histogram equalize the components of a color image independently. • This results in erroneous color. • A logical approach is to spread the color intensities uniformly, leaving the colors themselves (hues) unchanged. • The intensity equalization process did not alter the values of hue and saturation of the image, it did impact the overall color perception.

38. Color Image smoothing • Gray-scale image smoothing can be viewed as a spatial filtering operation in which the coefficients of the filtering mask are all 1’s. • As the mask is slid across the image to be smoothed, each pixel is replaced by the average of ht pixels in the neighborhood defined by the mask. • For a color image, we must deal with component vectors of the color image.

39. Color Image smoothing • The average of the RGB component vectors in this neighborhood is: • c’(x,y) = (1/K)* Σ c(x,y) • Also, c’(x,y) = (1/K)* Σ R(x,y) • (1/K)* Σ G(x,y) • (1/K)* Σ B(x,y) • Thus smoothing by neighborhood averaging can be obtained by per-color-plane basis.

40. Color Image sharpening • The Laplacian of a vector is defined as a vector whose components are equal to the Laplacian of the individual scalar components of the input vector. • In the RGB color system, the Laplacian vector is given as: • Λ2 R(x,y) • Λ2 [c(x,y)] = Λ2 G(x,y) • Λ2 B(x,y) • Thus we can compute the Laplacian of a full-color image by computing the Laplacian of each component image separately.

41. Color segmentation • Segmentation is the process of partitioning an image into regions. • Saturation is used as a masking image in order to isolate further regions of interest in the hue image. • The intensity image is less frequently used for segmentation of color images because it carries no color information.

42. Segmentation in RGB Vector space • HSI space is intuitive for many aspects of image processing. • But for segmentation, RGB color vectors give better results. • Let us say, we want to segment objects of a specified color range in an RGB image. • Given a set of sample color points of interest, we obtain the estimate of the “average” color that we want to segment. • Let us denote this average color by a vector a RGB vector a. • The aim of segmentation is to classify each RGB pixel in a given image as having a color in the specified range or not.

43. Segmentation in RGB Vector space • We use Euclidean distance for comparison. • Let z denotes an arbitrary point in the RGB space. • We say that z is similar to a if the distance between them is less than a specified threshold D0. • The Euclidean distance between z and a is given by: • D(z,a) = || z – a || • = [ ( z – a )T ( z – a ) ]1/2 • = [ (zR – aR )2 + (zG – aG )2 +(zB – aB )2 ]1/2 • Here the subscripts R, G and B denote the RGB components of vectors a and z. • The locus of point such that D(z,a) ≤ D0 is a solid sphere of radius D0. • Points contained within or on the surface of the sphere satisfy the specified color criterion; points outside do not. • Coding these two sets of points with black and white gives a binary segmented image.

44. Segmentation in RGB Vector space • The generalization of the distance measure is of the form: • D(z,a) = [ ( z – a )T C-1( z – a ) ]1/2 • Here C is the covariance matrix of the sample representative of the color we wish to segment. • The locus of the points such that D(z,a) ≤ D0 describes a solid 3-D elliptical body. • Its principal axes are oriented in the direction of maximum data spread. • When C = I, the 3 X 3 identity matrix, the above two equations become identical .

45. Segmentation in RGB Vector space • As distances are positive and monotonic, we work with the distance squared, and avoid root computations. • But implementing the above equation, is also computationally expensive. • We can use a box centered on a and its dimensions along each of the color axes can be chosen proportional to the standard deviation of the samples along each of the axis. • Standard deviations are done only once using sample color data. • Given an arbitrary color point, we segment it by finding whether or not it is on the surface or inside the box. • This computation is simpler than finding distance.

46. Color Edge Detection • The edge detection by gradient operators is not defined for vector quantities. • Computing the gradient on individual images and then using the results to form a color will lead to erroneous results. • Because gradient discussed so far is applicable to a scalar function f(x,y); • It is not applicable to vector functions. • We can extend the concept of a gradient to vector functions.

47. Color Edge Detection • Let r,g and b be unit vectors along the R, G and B axis of RGB color space and define the vectors • ∂R ∂G ∂B • u = --- r + ---- g + --- b • ∂x ∂x ∂x • ∂R ∂G ∂B • v = --- r + ---- g + --- b • ∂y ∂y ∂y

48. Color Edge Detection • Let the quantities gxx, gyy, and gxy, are defined in terms of the dot product of these vectors as: • gxx= u.u = uTu = |∂R/∂x |2 + |∂G/∂x |2 +|∂B/∂x |2 • gyy= v.v = vTv = |∂R/∂y |2 + |∂G/∂y |2 +|∂B/∂y |2 • gxy= u.v = uTv = (∂R/∂x)(∂R/∂y)+(∂G/∂x)(∂G/∂y) +(∂B/∂x)(∂B/∂y)

49. Color Edge Detection • Now the direction of maximum rate of change of c(x,y) is given by the angle • θ = (1/2) * tan-1( 2gxy / (gxx - gyy)) • The value of the rate of change at (x,y) in the direction of θ is given by • F(θ)={0.5*[(gxx + gyy)+(gxx-gyy)cos 2θ+2gxysin 2θ]}1/2 • Since F(θ) = F(θ + Π), F needs to be calculated only for values of θ in the half-open interval [ 0, Π). • The partial derivatives required here can be computed using the Sobel operator.

50. Color Edge