Winter 2013 EECS 332 Digital Image Analysis Machine Problem 1 Connect Component Analysis

Transcription

1 Winter 2013 EECS 332 Digital Image Analysis Machine Problem 1 Connect Component Analysis Jiangtao Gou Department of Statistics, Northwestern University Instructor: Prof. Ying Wu 22 January Introduction In this report, I applied the sequential algorithm for connect component labelling which was introduced in class on January 15th, There are four programs: CCL.m, E table.m, size filter.m, and show result.m. 2 Algorithm Description In CCL.m, I realized the sequential solution which was described on slide 9 and 10, Lecture Binary Image Analysis II. Basically I followed the pseudocodes provided by professor, scanned the image from left to right and from top to bottom. There is one trick which I used. Suppose that the size of image is m n, then I add one zero-column to the left and one zero-row on the top to expand the size of image to (m + 1) (n + 1), in the end, I transferred the image to the original size. This trick is necessary when any component touched the edges of the image. In E table.m, I used an array to store the equivalent table. It is the simplest way to realize the equivalent table as professor suggested. If neither the index of upper pixel nor the index of left pixel has been changed, we only need to make these two indices equal. Otherwise, we need to go over the whole equivalent table to update all indices. In size filter.m, when the area of one region is less than a pre-determined parameter, we treat this area as noises, and change this area to background. In show result.m, I showed the result of component detection by using a grey figure. 1

2 3 Results analysis I applied my program onto three test file, with and without size filter. The results are presented in Figure 1 and 2. I also drew one graph to test the algorithm, which is shown in Figure 3. Figure 1: test.bmp and face.bmp Figure 2: gun.bmp (Left: without filter, Right: with filter, threshold = 50) 4 MATLAB codes 1 function MP1 main 2 % Jiangtao Gou 3 % f i l e n a m e = f a c e ; 2

3 Figure 3: My own test image file 5 f i l e n a m e = t e s t ; 6 f i l e n a m e = gun ; 7 f i l e n a m e = china ; 8 img = imread ( [ filename,.bmp ] ) ; % For gun. bmp, use s m a l l e s t s i z e = % 10 [ label i m g, num ] = CCL( img ) ; 11 % 12 s m a l l e s t s i z e = 5 0 ; 13 [ label i m g, num ] = s i z e f i l t e r ( label img, num, s m a l l e s t s i z e ) ; 14 % 15 s h o w r e s u l t ( l a b e l img, num, f i l e n a m e ) ; 1 function [ l a bel i m g, num ] = CCL( img ) 2 % % Jiangtao Gou 4 i m g s i z e = size ( img ) ; 5 temp img = zeros ( i m g s i z e + [ 1, 1 ] ) ; 6 temp img ( 2 : 1 : ( i m g s i z e ( 1, 1 ) +1), 2 : 1 : ( i m g s i z e ( 1, 2 ) +1) ) = img ; % Add one zero row on the top and one zero colum on the l e f t. 7 temp label img = zeros ( i m g s i z e + [ 1, 1 ] ) ; 8 l a b e l i m g = zeros ( i m g s i z e ) ; 9 l a b e l v e c s i z e = 1000; 3

4 10 l a b e l v e c = 1 : 1 : l a b e l v e c s i z e ; 11 num = 0 ; 12 l a b e l = 0 ; 13 for u = 2 : 1 : ( i m g s i z e ( 1, 1 ) +1) 14 for v = 2 : 1 : ( i m g s i z e ( 1, 2 ) +1) 15 i f temp img (u, v ) == 1 16 u p p e r l a b e l = temp label img (u 1,v ) ; % Upper l a b e l 17 l e f t l a b e l = temp label img (u, v 1) ; % L e f t l a b e l 18 i f ( u p p e r l a b e l == l e f t l a b e l ) && ( u p p e r l a b e l = 0) && ( l e f t l a b e l = 0) % The same l a b e l 19 temp label img (u, v ) = u p p e r l a b e l ; 20 e l s e i f ( u p p e r l a b e l = l e f t l a b e l ) && ( u p p e r l a b e l && l e f t l a b e l ) % E i t h e r i s 0 21 temp label img (u, v ) = max( u p p e r l a b e l, l e f t l a b e l ) ; 22 e l s e i f ( u p p e r l a b e l = l e f t l a b e l ) && ( u p p e r l a b e l > 0) && ( l e f t l a b e l > 0) % Both 23 temp label img (u, v ) = min( u p p e r l a b e l, l e f t l a b e l ) ; 24 l a b e l v e c = E table ( l a b e l, l a b e l v e c, u p p e r l a b e l, l e f t l a b e l ) ; 25 else 26 l a b e l = l a b e l + 1 ; 27 temp label img (u, v ) = l a b e l ; 28 i f l a b e l > l a b e l v e c s i z e 29 error ( The S i z e o f Equivalent Table i s NOT big enough. Please I n c r e a s e i t. ) ; 30 end 31 end 32 end 33 end 34 end 35 l a b e l i m g = temp label img ( 2 : 1 : ( i m g s i z e ( 1, 1 ) +1), 2 : 1 : ( i m g s i z e ( 1, 2 ) +1) ) ; 36 l a b e l v e c = l a b e l v e c ( 1 : 1 : l a b e l ) ; 37 u n i q u e l a b e l = unique ( l a b e l v e c ) ; 38 for u = 1 : 1 : i m g s i z e ( 1, 1 ) 39 for v = 1 : 1 : i m g s i z e ( 1, 2 ) 40 i f img (u, v ) == 1 41 l a b e l i m g (u, v ) = l a b e l v e c ( l a b e l i m g (u, v ) ) ; % Merger Regions 42 l a b e l i m g (u, v ) = find ( u n i q u e l a b e l == l a b e l i m g (u, v ) ) ; % Use 1, 2, 3,... as the region numbers. 43 end 44 end 4

5 45 end 46 num = length ( u n i q u e l a b e l ) ; 1 function l a b e l v e c = E table ( l a b e l, l a b e l v e c, L u, L l ) 2 % % Jiangtao Gou 4 min L = min( l a b e l v e c ( L u ), l a b e l v e c ( L l ) ) ; 5 i f ( l a b e l v e c ( L u ) == L u ) && ( l a b e l v e c ( L l ) == L l ) % Neither o f i n d e x e s has been changed 6 l a b e l v e c ( L u ) = min L ; 7 l a b e l v e c ( L l ) = min L ; 8 else 9 for i =1:1: l a b e l 10 i f ( l a b e l v e c ( i ) == l a b e l v e c ( L u ) ) ( l a b e l v e c ( i ) == l a b e l v e c ( L l ) ) 11 l a b e l v e c ( i ) = min L ; 12 end 13 end 14 end 1 function [ l a bel i m g, num ] = s i z e f i l t e r ( label img, num, s m a l l e s t s i z e ) 2 % % Jiangtao Gou 4 i m g s i z e = size ( l a b e l i m g ) ; 5 p i x e l p o i n t c o u n t e r = zeros ( 1,num) ; 6 for i =1:1:num 7 p i x e l p o i n t c o u n t e r ( i ) = length ( find ( l a b e l i m g == i ) ) ; 8 end 9 i f sum( p i x e l p o i n t c o u n t e r < s m a l l e s t s i z e ) 10 n o t n o i s e l a b e l = ( p i x e l p o i n t c o u n t e r >= s m a l l e s t s i z e ) ; 11 n o t n o i s e l a b e l l o c = find ( n o t n o i s e l a b e l > 0) ; 12 for u = 1 : 1 : i m g s i z e ( 1, 1 ) 13 for v = 1 : 1 : i m g s i z e ( 1, 2 ) 14 i f l a b e l i m g (u, v ) > 0 15 i f n o t n o i s e l a b e l ( l a b e l i m g (u, v ) ) == 0 16 l a b e l i m g (u, v ) = 0 ; 17 else 18 l a b e l i m g (u, v ) = find ( n o t n o i s e l a b e l l o c == l a b e l i m g (u, v ) ) ; 19 end 20 end 21 end 22 end 23 else 5

6 24 n o t n o i s e l a b e l l o c = ones ( size ( p i x e l p o i n t c o u n t e r ) ) ; 25 end 26 num = length ( n o t n o i s e l a b e l l o c ) ; 1 function s h o w r e s u l t ( l a b el img, num, f i l e n a m e ) 2 % % Jiangtao Gou 4 i m g s i z e = size ( l a b e l i m g ) ; 5 gray img = l a b e l i m g ; 6 for u = 1 : 1 : i m g s i z e ( 1, 1 ) 7 for v = 1 : 1 : i m g s i z e ( 1, 2 ) 8 i f l a b e l i m g (u, v ) > 0 9 gray img (u, v ) = round( l a b e l i m g (u, v ) /num 255) ; 10 end 11 end 12 end 13 imshow ( gray img, [ ] ) ; 14 set ( gcf, p a p e r s i z e, [ 5 5 ] ) ; 15 picname = [ mp1, filename,. eps ] ; 16 saveas ( gcf, picname, epsc ) ; 17 eps2pdf ( picname ) ; 6

7 Winter 2013 EECS 332 Digital Image Analysis Machine Problem 2 Morphological Operators Jiangtao Gou Department of Statistics, Northwestern University Instructor: Prof. Ying Wu 24 January Introduction In this report, I realized some basic morphological operators which were introduction on January 17th. By following slides Binary Image Analysis III by Prof Wu, and Jain, Kasturi and Schunck s Machine Vision (1995), page 61-69, the following morphological operators are defined below. Erosion A B = {p B p A}. (1) Dilation Opening Closing Boundary A B = bi BA bi. (2) A B = (A B) B. (3) A B = (A B) B. (4) β B (A) = A (A B). (5) In order to get clear boundary, I tried to combine those morphological operators above. In the end, this one below worked well, and I called it Clear Boundary, as shown below. Clear Boundary γ B (A) = (A B) (A B). (6) Meanwhile, in order to get rid of the noise, I used the techniques in Machine Problem 1, where I labelled different component, and treated the small components as noise. 1

8 2 Algorithm Description For erosion and dilation, I went through the whole picture, and decided the output image. For opening, closing, boundary, and clear boundary, I simply used the combination of erosion and dilation. In order to get rid of the noise, I ran the size filter at first, then I ran clear boundary function. The threshold need to be specified ahead. 3 Results analysis First, I tried to apply a 3 by 3 square structure element (Figure 1) on gun.bmp. Figure 1: Structure Element: 3 by 3 Square As shown in Figure 2, function clear boundary works well, except some noises. By using size filter, we can achieve better boundary, as shown in Figure 3. Second, I tried to apply a 5 by 5 square structure element on gun.bmp. As shown in Figure 5, function clear boundary works well, except some noises. By using size filter, we can achieve better boundary, as shown in Figure 6. Third, I tried to apply a 3 by 3 square structure element (Figure 1) on palm.bmp. As shown in Figure 7, function clear boundary works well, except some noises. It looks that the boundary in Figure 7 for Palm was not very clear. We will see by change the structure element, we will get a clear boundary. 2

9 Figure 2: Structure Element: 3 by 3 Square. Erosion (top left), Dilation (top right), Opening (middle left), Closing (middle right), Boundary (bottom left), Clear Boundary (bottom right) 3

10 Figure 3: Structure Element: 3 by 3 Square. Clear Boundary after Filtering. Threshold = 9 (left), Threshold = 100 (right) Figure 4: Structure Element: 5 by 5 Square 4

11 Figure 5: Structure Element: 5 by 5 Square. Erosion (top left), Dilation (top right), Opening (middle left), Closing (middle right), Boundary (bottom left), Clear Boundary (bottom right) 5

12 Figure 6: Structure Element: 5 by 5 Square. Clear Boundary after Filtering. Threshold = 9 (left), Threshold = 100 (right) 8. By using size filter, we can achieve better boundary, as shown in Figure Fourth, I tried to apply a 5 by 9 rectangle structure element on palm.bmp. As shown in Figure 10, function clear boundary works well, except some noises. By using size filter, we can achieve better boundary, as shown in Figure MATLAB codes 1 function MP2 main 2 % Jiangtao Gou 3 % f i l e n a m e = palm ; 5 img in = imread ( [ filename,.bmp ] ) ; 6 SE = ones ( 5, 9 ) ; 7 % SE = [ 0, 1, 0 ; 1, 1, 1 ; 0, 0, 0 ] ; 8 % 9 img out = Erosion ( img in, SE) ; 10 imshow ( img out, [ 0 1 ] ) ; 11 set ( gcf, p a p e r s i z e, [ 4 4 ] ) ; 12 picname = [ e r o s i o n, filename,. eps ] ; 13 saveas ( gcf, picname, epsc ) ; 14 eps2pdf ( picname ) ; 6

13 Figure 7: Structure Element: 3 by 3 Square. Erosion (top left), Dilation (top right), Opening (middle left), Closing (middle right), Boundary (bottom left), Clear Boundary (bottom right) 7

14 Figure 8: Structure Element: 3 by 3 Square. Clear Boundary after Filtering. Threshold = 5 (left), Threshold = 10 (right) Figure 9: Structure Element: 5 by 9 rectangle 8

15 Figure 10: Structure Element: 5 by 9 rectangle. Erosion (top left), Dilation (top right), Opening (middle left), Closing (middle right), Boundary (bottom left), Clear Boundary (bottom right) 9

16 Figure 11: Structure Element: 5 by 9 rectangle. Clear Boundary after Filtering. Threshold = % 16 img out = D i l a t i o n ( img in, SE) ; 17 imshow ( img out, [ 0 1 ] ) ; 18 set ( gcf, p a p e r s i z e, [ 4 4 ] ) ; 19 picname = [ d i l a t i o n, filename,. eps ] ; 20 saveas ( gcf, picname, epsc ) ; 21 eps2pdf ( picname ) ; 22 % 23 img out = Opening ( img in, SE) ; 24 imshow ( img out, [ 0 1 ] ) ; 25 set ( gcf, p a p e r s i z e, [ 4 4 ] ) ; 26 picname = [ opening, filename,. eps ] ; 27 saveas ( gcf, picname, epsc ) ; 28 eps2pdf ( picname ) ; 29 % 30 img out = Closing ( img in, SE) ; 31 imshow ( img out, [ 0 1 ] ) ; 32 set ( gcf, p a p e r s i z e, [ 4 4 ] ) ; 33 picname = [ c l o s i n g, filename,. eps ] ; 34 saveas ( gcf, picname, epsc ) ; 35 eps2pdf ( picname ) ; 36 % 37 img out = Boundary ( img in, SE) ; 38 imshow ( img out, [ 0 1 ] ) ; 39 set ( gcf, p a p e r s i z e, [ 4 4 ] ) ; 40 picname = [ boundary, filename,. eps ] ; 41 saveas ( gcf, picname, epsc ) ; 10

17 42 eps2pdf ( picname ) ; 43 % 44 img temp = D i l a t i o n ( img in, SE) ; 45 img out = Boundary ( img temp, SE) ; 46 imshow ( img out, [ 0 1 ] ) ; 47 set ( gcf, p a p e r s i z e, [ 4 4 ] ) ; 48 picname = [ clearboundary, filename,. eps ] ; 49 saveas ( gcf, picname, epsc ) ; 50 eps2pdf ( picname ) ; 51 % 52 % F i l t e r i n g at f i r s t 53 img = imread ( [ filename,.bmp ] ) ; % For gun. bmp, use s m a l l e s t s i z e = [ label i m g, num ] = CCL( img ) ; 55 s m a l l e s t s i z e = 1 00; 56 [ label i m g, num ] = s i z e f i l t e r ( label img, num, s m a l l e s t s i z e ) ; 57 s i z e i m g = size ( l a b e l i m g ) ; 58 img in = l a b e l i m g 59 for i = 1 : 1 : s i z e i m g ( 1, 1 ) 60 for j = 1 : 1 : s i z e i m g ( 1, 2 ) 61 i f l a b e l i m g ( i, j ) > 0 62 img in ( i, j ) = 1 ; 63 end 64 end 65 end 66 img temp = D i l a t i o n ( img in, SE) ; 67 img out = Boundary ( img temp, SE) ; 68 imshow ( img out, [ 0 1 ] ) ; 69 set ( gcf, p a p e r s i z e, [ 4 4 ] ) ; 70 picname = [ f i l t e r B o u n d a r y, filename,. eps ] ; 71 saveas ( gcf, picname, epsc ) ; 72 eps2pdf ( picname ) ; 1 function img out = Erosion ( img in, SE) 2 % Note : SEs s i d e l e n g t h s should be odd numbers, e. g., 3by3, 1by3, 5 by % Jiangtao Gou 4 % s i z e S E = size (SE) ; 6 extenderr = ( s i z e S E ( 1, 2 ) 1) / 2 ; 7 extenderc = ( s i z e S E ( 1, 1 ) 1) / 2 ; 8 s i z e i m g = size ( img in ) ; 9 img out = zeros ( size ( img in ) ) ; 10 for i = ( extenderc +1) : 1 : ( s i z e i m g ( 1, 1 ) extenderc ) 11 for j = ( extenderr+1) : 1 : ( s i z e i m g ( 1, 2 ) extenderr ) 11

18 12 i f sum(sum( img in ( ( i extenderc ) : 1 : ( i+extenderc ), ( j extenderr ) : 1 : ( j+extenderr ) ). SE) ) == sum(sum(se) ) 13 img out ( i, j ) = 1 ; 14 else 15 img out ( i, j ) = 0 ; 16 end 17 end 18 end 19 % Test data 20 % img in = [ 0, 0, 1, 0, 0 ; 0, 1, 1, 1, 0 ; 0, 0, 1, 0, 0 ; 0, 1, 1, 1, 1 ; 0, 0, 0, 0, 0 ] ; 21 % SE = [ 1, 1, 1 ] ; 1 function img out = D i l a t i o n ( img in, SE) 2 % Note : SEs s i d e l e n g t h s should be odd numbers, e. g., 3by3, 1by3, 5 by % Jiangtao Gou 4 % s i z e S E = size (SE) ; 6 extenderr = ( s i z e S E ( 1, 2 ) 1) / 2 ; 7 extenderc = ( s i z e S E ( 1, 1 ) 1) / 2 ; 8 s i z e i m g = size ( img in ) ; 9 img out temp = zeros ( size ( img in ) +[2 extenderc, 2 extenderr ] ) ; 10 for i = ( extenderc +1) : 1 : ( s i z e i m g ( 1, 1 )+extenderc ) 11 for j = ( extenderr+1) : 1 : ( s i z e i m g ( 1, 2 )+extenderr ) 12 i f img in ( i extenderc, j extenderr ) == 1 13 for k1 = 1 : 1 : s i z e S E ( 1, 1 ) 14 for k2 = 1 : 1 : s i z e S E ( 1, 2 ) 15 i f SE( k1, k2 ) == 1 16 img out temp ( i+k1 extenderc 1, j+k2 extenderr 1) = 1 ; 17 end 18 end 19 end 20 end 21 end 22 end 23 img out = img out temp ( ( extenderc +1) : 1 : ( s i z e i m g ( 1, 1 )+extenderc ), ( extenderr+1) : 1 : ( s i z e i m g ( 1, 2 )+extenderr ) ) ; 1 function img out = Opening ( img in, SE) 2 % Note : SEs s i d e l e n g t h s should be odd numbers 3 % Jiangtao Gou 4 % img temp = Erosion ( img in, SE) ; 6 img out = D i l a t i o n ( img temp, SE) ; 12

19 1 function img out = Closing ( img in, SE) 2 % Note : SEs s i d e l e n g t h s should be odd numbers 3 % Jiangtao Gou 4 % img temp = D i l a t i o n ( img in, SE) ; 6 img out = Erosion ( img temp, SE) ; 1 function img out = Boundary ( img in, SE) 2 % Note : SEs s i d e l e n g t h s should be odd numbers 3 % Jiangtao Gou 4 % img temp = Erosion ( img in, SE) ; 6 img out = img in img temp ; 13

20 Winter 2013 EECS 332 Digital Image Analysis Machine Problem 3 Histogram Techniques Jiangtao Gou Department of Statistics, Northwestern University Instructor: Prof. Ying Wu 27 January Introduction In this report, I implied the histogram equalization and the lighting correction to adjust the gray scale of pictures, and made it easy to be distinguished by human eyes. Histogram equalization is a technique to stretch the histogram of the pixels grayscale, and make the histogram as uniform as possible. In statistics, when a p-value is used as a test statistic for a simple null hypothesis, then for any continuously distributed test statistic, the p-value is uniformly distributed between 0 and 1 if the null hypothesis is true. Similarly, histogram equalization normalizes the original grayscale histogram at first, then uses the distribution function as the new variables, and scales the new variable between 0 and 255 to form a new histogram. This histogram is approximately uniformly distribution. A new picture is got correspondingly. Lighting correction is used to set the brightness all over a certain picture to a nearly same level. By treating the grayscale as a function of the position of pixels, a plan and quadratic surface can be estimated as the background. By submitting the background from the original picture, we will get a lighting correction. In application, I added the median of the estimated background surface back, and then either used truncation technique, where I set all number bigger than 255 as 255 and all number smaller than 0 as 0, or used scale technique, where I set the biggest number as 255 and smallest number as 0, then all other number were determined linearly by linear interpolation. 1

21 2 Algorithm Description Code in HistoEqualization.m is for histogram equalization, where a histogram of original picture is constructed at first, then the grayscale is stretched in order to make the new histogram approximately uniform. Code in LightingCorrection.m calls either LightingCorrectionLinear.m or LightingCorrectionQuadratic.m. Code in LightingCorrectionLinear.m applies a linear lighting correction. First a plane is estimated by using the least square estimation to estimate a, b and const. Then get the correction CG p (R, C) this way. P (R, C) = ar + bc + const. (1) CG p (R, C) = G(R, C) P (R, C) + median R,C (P (R, C)). (2) In the end, either a truncated version 0, if CG p (R, C) < 0, CG pt (R, C) = CG p (R, C), if 0 CG p (R, C) 255, 255, if CG p (R, C) > 255, or a scaled version CG ps (R, C) = 255 CG p (R, C) min CG p (R, C) max CG p (R, C) min CG p (R, C) gives the corrected pictures. Similarly, code in LightingCorrectionQuadratic.m applies a quadratic lighting correction. First a quadratic surface is estimated by using the least square estimation to estimate a, b, c, d, e and const. S(R, C) = ar 2 + brc + cc 2 + dr + ec + const. (5) Then get the correction CG s (R, C) by using the formula below. CG s (R, C) = G(R, C) S(R, C) + median R,C (S(R, C)). (6) In the end, either a truncated version 0, if CG s (R, C) < 0, CG st (R, C) = CG s (R, C), if 0 CG s (R, C) 255, 255, if CG s (R, C) > 255, 2 (3) (4) (7)

22 or a scaled version CG ss (R, C) = 255 CG s (R, C) min CG s (R, C) max CG s (R, C) min CG s (R, C) (8) gives the pictures after correction. 3 Results analysis Figure 1 shows the original moon.bmp and its Histogram Density Gray Scale Figure 1: The original moon.bmp and its Histogram. Figure 2 represents the distribution function and the transformation of moon.bmp. Figure 3 shows the equalized moon.bmp and its Histogram. By comparing with Figure 1, a lot of details can be got from this picture. Figure 4 shows the background plane of linear Lighting Correction of moon.bmp. Figure 5 shows the results of linear Lighting Correction of moon.bmp. Figure 6 shows the background quadratic surface of quadratic Lighting Correction of moon.bmp. Figure 7 shows the results of quadratic Lighting Correction of moon.bmp. 3

23 Distribution Function Gray Scale Figure 2: Distribution Function and the Transformation of moon.bmp Density Gray Scale Figure 3: The equalized moon.bmp and its Histogram. 4

24 Figure 4: Linear Lighting Correction of moon.bmp: the background plane. Figure 5: Truncated Version (left) and Scaled Version (right): Linear Lighting Correction of moon.bmp. 5

25 Figure 6: Quadratic Lighting Correction of moon.bmp: the background surface. Figure 7: Truncated Version (left) and Scaled Version (right): Quadratic Lighting Correction of moon.bmp. 6

26 By comparing with Figure 3, pictures in Figure 5 and Figure 7 have more uniformly distributed grayscales. I also computed an additional example, the original picture is from http: //info.cndsi.com/html/ / html, which was about Fighter-10 in China Air Force. By applying histogram equalization and lighting correction, more details were discovered, especially the runway Density Gray Scale Figure 8: The original nightfighter.jpg and its Histogram Density Gray Scale Figure 9: The equalized nightfighter.jpg and its Histogram. 7

27 Figure 10: Linear Lighting Correction of nightfighter.jpg: the background plane. 8

28 Figure 11: Truncated Version (top) and Scaled Version (bottom): Linear Lighting Correction of nightfighter.jpg. 9

29 Figure 12: Quadratic Lighting Correction of nightfighter.jpg: the background plane. 10

30 Figure 13: Truncated Version (top) and Scaled Version (bottom): Quadratic Lighting Correction of nightfighter.jpg. 11

31 4 MATLAB codes 1 function MP3 main 2 % Jiangtao Gou 3 % f i l e n a m e = moon ; 5 img in = rgb2gray ( imread ( [ filename,.bmp ], bmp ) ) ; 6 img out = H i s t o E q u a l i z a t i o n ( img in ) ; 7 imshow ( img out, [ 0, ] ) ; 8 set ( gcf, p a p e r s i z e, [ 5 5 ] ) ; 9 picname = [ filename, e q u a l i z e d. eps ] ; 10 saveas ( gcf, picname, epsc ) ; 11 eps2pdf ( picname ) ; 12 % L i g h t i n g Correction 13 img in = img out ; 14 method = 2 ; 15 [ img out truncated, i m g o u t s c a l e d ] = L i g h t i n g C o r r e c t i o n ( img in, method ) ; 16 imshow ( img out truncated, [ 0, ] ) ; 17 set ( gcf, p a p e r s i z e, [ 5 5 ] ) ; 18 picname = [ filename, truncated method,num2str( method ),. eps ] ; 19 saveas ( gcf, picname, epsc ) ; 20 eps2pdf ( picname ) ; 21 imshow ( i m g o u t s c a l e d, [ 0, ] ) ; 22 set ( gcf, p a p e r s i z e, [ 5 5 ] ) ; 23 picname = [ filename, scaled method,num2str( method ),. eps ] ; 24 saveas ( gcf, picname, epsc ) ; 25 eps2pdf ( picname ) ; 1 function img out = H i s t o E q u a l i z a t i o n ( img in ) 2 % Jiangtao Gou 3 % plotsgn = 1 ; % Whether p l o t or not 5 histplotsgn1 = 1 ; % Whether p l o t histgram or not 6 histplotsgn2 = 1 ; % Whether p l o t d i s t r i b u t i o n or not 7 histplotsgn3 = 0 ; 8 histplotsgn4 = 0 ; 9 histplotsgn5 = 1 ; % Whether p l o t histgram or not 10 i m g s i z e = size ( img in ) ; 11 R = i m g s i z e ( 1, 1 ) ; 12 C = i m g s i z e ( 1, 2 ) ; 13 % Construct a Histogram 14 h = zeros ( 1, ) ; 15 for r = 1 : 1 :R 16 for c = 1 : 1 :C 12

32 17 h ( img in ( r, c ) +1) = h ( img in ( r, c ) +1)+1; 18 end 19 end 20 x = 0 : 1 : ; 21 y1 = h ; 22 y2 = 1/sum( h ) h ; 23 i f plotsgn && h i s t PlotSgn1 24 plot ( x, y2, k, LineWidth, 3 ) ; 25 axis ( [ ] ) ; 26 xlabel ( Gray S c a l e, f o n t s i z e,16) ; 27 ylabel ( Density, f o n t s i z e,16) ; 28 set ( gcf, p a p e r s i z e, [ 5 8 ] ) ; 29 picname = [ h i s t o r i g i n a l. eps ] ; 30 saveas ( gcf, picname, epsc ) ; 31 eps2pdf ( picname ) ; 32 end 33 %x = reshape ( img in, R C, 1 ) ; [ f, x i ] = k s d e n s i t y ( x ) ; p l o t ( xi, f ) ; 34 y3 = zeros ( size ( y2 ) ) ; 35 y3 ( 1 ) = y2 ( 1 ) ; 36 for i =2:1: length ( h ) 37 y3 ( i ) = y3 ( i 1)+y2 ( i ) ; 38 end 39 i f plotsgn && h i s t PlotSgn2 40 plot ( x, y3, k, LineWidth, 3 ) ; 41 axis ( [ ] ) ; 42 xlabel ( Gray S c a l e, f o n t s i z e,16) ; 43 ylabel ( D i s t r i b u t i o n Function, f o n t s i z e,16) ; 44 set ( gcf, p a p e r s i z e, [ 5 8 ] ) ; 45 picname = [ d i s t r o r i g i n a l. eps ] ; 46 saveas ( gcf, picname, epsc ) ; 47 eps2pdf ( picname ) ; 48 end 49 x2 = round( y3 255) ; 50 i f plotsgn && h i s t PlotSgn3 51 plot ( x2, y2, r, LineWidth, 3 ) ; 52 axis ( [ ] ) ; 53 xlabel ( Gray S c a l e, f o n t s i z e,16) ; 54 ylabel ( Density, f o n t s i z e,16) ; 55 set ( gcf, p a p e r s i z e, [ 5 8 ] ) ; 56 picname = [ h i s t e q u a l i z e d t r y. eps ] ; 57 saveas ( gcf, picname, epsc ) ; 58 eps2pdf ( picname ) ; 59 end 60 i f plotsgn && h i s t PlotSgn4 61 plot ( x2, y3, r, LineWidth, 3 ) ; 13

33 62 axis ( [ ] ) ; 63 xlabel ( Gray S c a l e, f o n t s i z e,16) ; 64 ylabel ( D i s t r i b u t i o n Function, f o n t s i z e,16) ; 65 set ( gcf, p a p e r s i z e, [ 5 8 ] ) ; 66 picname = [ d i s t r e q u a l i z e d. eps ] ; 67 saveas ( gcf, picname, epsc ) ; 68 eps2pdf ( picname ) ; 69 end 70 for r = 1 : 1 :R 71 for c = 1 : 1 :C 72 img out ( r, c ) = x2 ( img in ( r, c ) +1) ; 73 end 74 end 75 % Construct an E q u a l i z e d Histogram 76 hh = zeros ( 1, ) ; 77 for r = 1 : 1 :R 78 for c = 1 : 1 :C 79 hh ( img out ( r, c ) +1) = hh ( img out ( r, c ) +1)+1; 80 end 81 end 82 yy1 = hh ; 83 yy2 = 1/sum( hh ) hh ; 84 i f plotsgn && h i s t PlotSgn5 85 plot ( x, yy2, k, LineWidth, 3 ) ; 86 axis ( [ ] ) ; 87 xlabel ( Gray S c a l e, f o n t s i z e,16) ; 88 ylabel ( Density, f o n t s i z e,16) ; 89 set ( gcf, p a p e r s i z e, [ 5 8 ] ) ; 90 picname = [ h i s t e q u a l i z e d. eps ] ; 91 saveas ( gcf, picname, epsc ) ; 92 eps2pdf ( picname ) ; 93 end 1 function [ img out truncated, i m g o u t s c a l e d ] = L i g h t i n g C o r r e c t i o n ( img in, method ) 2 % img in i s an e q u a l i z e d image 3 % Jiangtao Gou 4 % switch method 6 case 1 7 [ img out truncated, i m g o u t s c a l e d ] = L i g h t i n g C o r r e c t i o n L i n e a r ( img in ) ; 8 case 2 9 [ img out truncated, i m g o u t s c a l e d ] = L i g h t i n g C o r r e c tionquadratic ( img in ) ; 14

34 10 o t h e r w i s e 11 error ( Only Linear method and Quadratic method are a v a i l a b l e t e m p o r arily. ) 12 end 1 function [ img out truncated, i m g o u t s c a l e d ] = L i g h t i n g C o r r e c t i o n L i n e a r ( img in ) 2 % Jiangtao Gou 3 % imgsgn = 1 ; 5 i m g s i z e = size ( img in ) ; 6 R = i m g s i z e ( 1, 1 ) ; 7 C = i m g s i z e ( 1, 2 ) ; 8 xyz = zeros (R C, 3 ) ; 9 for r = 1 : 1 :R 10 for c = 1 : 1 :C 11 xyz ( ( r 1) C+c, 1 ) = r ; 12 xyz ( ( r 1) C+c, 2 ) = c ; 13 xyz ( ( r 1) C+c, 3 ) = img in ( r, c ) ; 14 end 15 end 16 x = xyz ( :, 1 ) ; 17 y = xyz ( :, 2 ) ; 18 z = xyz ( :, 3 ) ; 19 const = ones ( size ( xyz ( :, 1 ) ) ) ; % Vector o f ones f o r constant term 20 C o e f f i c i e n t s = [ x y const ] \ z ; % Find the c o e f f i c i e n t s 21 XCoeff = C o e f f i c i e n t s ( 1 ) ; % X c o e f f i c i e n t 22 YCoeff = C o e f f i c i e n t s ( 2 ) ; % X c o e f f i c i e n t 23 CCoeff = C o e f f i c i e n t s ( 3 ) ; % constant term 24 xx = ( 1 : 1 :R) ones ( 1,C) ; 25 yy = ones (R, 1 ) ( 1 : 1 :C) ; 26 %[ yy, xx ] = meshgrid ( 1 : 1 :C, 1 : 1 :R) ; % Generating a r e g u l a r g r i d f o r p l o t t i n g 27 zz = XCoeff xx + YCoeff yy + CCoeff ; 28 i f imgsgn == 1 29 surf ( xx, yy, zz ) % P l o t t i n g the s u r f a c e 30 t i t l e ( sprintf ( P l o t t i n g plane z=(%f ) x+(%f ) y+(%f ), XCoeff, YCoeff, CCoeff ) ) ; 31 xlabel ( Row Number ( x ) ) ; ylabel ( Column Number ( y ) ) ; zlabel ( Gray S c a l e ( z ) ) ; 32 set ( gcf, p a p e r s i z e, [ 5 6 ] ) ; 33 picname = [ LinearPlane. eps ] ; 34 saveas ( gcf, picname, epsc ) ; 35 eps2pdf ( picname ) ; 36 end 15

35 37 % 38 zzround = round( zz ) ; 39 i f imgsgn == 1 40 imshow ( zzround, [ 0, ] ) ; 41 set ( gcf, p a p e r s i z e, [ 5 5 ] ) ; 42 picname = [ LinearPlaneGray. eps ] ; 43 saveas ( gcf, picname, epsc ) ; 44 eps2pdf ( picname ) ; 45 end 46 img plane = zz ; 47 midpoint = median(median( img plane ) ) ; 48 img out = midpoint + img in img plane ; 49 img out truncated = round( img out ) ; 50 % imshow ( i m g o u t t r u ncated, [ 0, ] ) ; 51 for r = 1 : 1 :R 52 for c = 1 : 1 :C 53 i f img out truncated ( r, c ) > img out truncated ( r, c ) = 255; 55 e l s e i f img out truncated ( r, c ) < 0 56 img out truncated ( r, c ) = 0 ; 57 end 58 end 59 end 60 graymax = max(max( img out ) ) ; 61 graymin = min(min( img out ) ) ; 62 i m g o u t s c a l e d = round(255/( graymax graymin ) ( img out graymin ones ( size ( img out ) ) ) ) ; 1 function [ img out truncated, i m g o u t s c a l e d ] = L i g h t i n g C o r r e c t i o n Q u adratic ( img in ) 2 % Jiangtao Gou 3 % imgsgn = 1 ; 5 i m g s i z e = size ( img in ) ; 6 R = i m g s i z e ( 1, 1 ) ; 7 C = i m g s i z e ( 1, 2 ) ; 8 xyz = zeros (R C, 3 ) ; 9 for r = 1 : 1 :R 10 for c = 1 : 1 :C 11 xyz ( ( r 1) C+c, 1 ) = r ; 12 xyz ( ( r 1) C+c, 2 ) = c ; 13 xyz ( ( r 1) C+c, 3 ) = img in ( r, c ) ; 14 end 15 end 16 x = xyz ( :, 1 ) ; 16

36 17 y = xyz ( :, 2 ) ; 18 z = xyz ( :, 3 ) ; 19 xy = x. y ; 20 xsquare = x. x ; 21 ysquare = y. y ; 22 const = ones ( size ( xyz ( :, 1 ) ) ) ; % Vector o f ones f o r constant term 23 C o e f f i c i e n t s = [ xsquare xy ysquare x y const ] \ z ; % Find the c o e f f i c i e n t s 24 xsquarecoeff = C o e f f i c i e n t s ( 1 ) ; 25 xycoeff = C o e f f i c i e n t s ( 2 ) ; 26 ysquarecoeff = C o e f f i c i e n t s ( 3 ) ; 27 XCoeff = C o e f f i c i e n t s ( 4 ) ; % X c o e f f i c i e n t 28 YCoeff = C o e f f i c i e n t s ( 5 ) ; % X c o e f f i c i e n t 29 CCoeff = C o e f f i c i e n t s ( 6 ) ; % constant term 30 xx = ( 1 : 1 :R) ones ( 1,C) ; 31 yy = ones (R, 1 ) ( 1 : 1 :C) ; 32 %[ yy, xx ] = meshgrid ( 1 : 1 :C, 1 : 1 :R) ; % Generating a r e g u l a r g r i d f o r p l o t t i n g 33 zz = zeros (R,C) ; 34 for r = 1 : 1 :R 35 for c = 1 : 1 :C 36 zz ( r, c ) = xsquarecoeff xsquare ( ( r 1) C+c, 1 ) + xycoeff xy ( ( r 1) C+c, 1 ) + ysquarecoeff ysquare ( ( r 1) C+c, 1 ) + XCoeff x ( ( r 1) C+c, 1 ) + YCoeff y ( ( r 1) C+c, 1 ) + CCoeff ; 37 end 38 end 39 %z z = xsquarecoeff xsquare + xycoeff xy + ysquarecoeff ysquare + XCoeff xx + YCoeff yy + CCoeff ; 40 i f imgsgn == 1 41 surf ( xx, yy, zz ) % P l o t t i n g the s u r f a c e 42 t i t l e ( sprintf ( P l o t t i n g Quadratic Surface ) ) ; 43 xlabel ( Row Number ( x ) ) ; ylabel ( Column Number ( y ) ) ; zlabel ( Gray S c a l e ( z ) ) ; 44 set ( gcf, p a p e r s i z e, [ 5 6 ] ) ; 45 picname = [ QuadraticPlane. eps ] ; 46 saveas ( gcf, picname, epsc ) ; 47 eps2pdf ( picname ) ; 48 end 49 % 50 zzround = round( zz ) ; 51 i f imgsgn == 1 52 imshow ( zzround, [ 0, ] ) ; 53 set ( gcf, p a p e r s i z e, [ 5 5 ] ) ; 54 picname = [ QuadraticPlaneGray. eps ] ; 17

37 55 saveas ( gcf, picname, epsc ) ; 56 eps2pdf ( picname ) ; 57 end 58 img plane = zz ; 59 midpoint = median(median( img plane ) ) ; 60 img out = midpoint + img in img plane ; 61 img out truncated = round( img out ) ; 62 % imshow ( i m g o u t t r u ncated, [ 0, ] ) ; 63 for r = 1 : 1 :R 64 for c = 1 : 1 :C 65 i f img out truncated ( r, c ) > img out truncated ( r, c ) = 255; 67 e l s e i f img out truncated ( r, c ) < 0 68 img out truncated ( r, c ) = 0 ; 69 end 70 end 71 end 72 graymax = max(max( img out ) ) ; 73 graymin = min(min( img out ) ) ; 74 i m g o u t s c a l e d = round(255/( graymax graymin ) ( img out graymin ones ( size ( img out ) ) ) ) ; 75 %% Test Example 76 % img in = [ 0, 1 0 0, ; 5 0, 2 5 5, ] ; 18

38 Winter 2013 EECS 332 Digital Image Analysis Machine Problem 4 Color Models and Color Segmentation Jiangtao Gou Department of Statistics, Northwestern University Instructor: Prof. Ying Wu 31 January Introduction In this report, I applied Histogram methods based on RGB, N-RGB, HSI systems. Meanwhile, I applied Gaussian methods based on HSI systems as well. The first step is to collect flesh tone training data. My flesh tone training data were collected from the 19 pictures which were shown in Figure 1. I took 2 rectangular patches from each picture by using MATLAB imcrop() function. I got 100,725 pixels in total. The second step is to choose a color space among all three choices which we mentioned in class. For HSI system, I applied MATLAB functions rgb2hsv() and hsv2rgb(). Finally we either use histogram method or Gaussian method. 2 Algorithm Description For histogram method, basically there are two parameters need to be tuned. The first one is the grid of histogram, I used grid up to The second one is the threshold of percentage. I assume the top 90%, 95% or 99% pixels should represent the skin color. After I decided these two parameters, I could got whether one point in a color space belongs skin color or not. Then we use this criteria to find the skin in our test examples. For Gaussian method, it is easier to program than histogram method. 1

39 Figure 1: My Flesh Tone Training DataBase 2

40 Note there is a typo in lecture slides. (c µ) T Σ 1 (c µ) > t (1) should conclude that c(u, v) is not a skin color. I first estimated µ and Σ, then for each point, I compute its (c µ) T Σ 1 (c µ), and compared it with t. I used t = 2, t = 3, and t = 4. 3 Results analysis Let me try histogram method and Gaussian method on gun1.bmp at first. First, I tried RGB system. By using RGB system, I think taking threshold 99%, and using grid for histogram is a good choice for gun1.bmp. Second, I tried N-RGB system. From Figure 5, we noted that the histogram concentrated at three corners. I tried several parameters and thresholds, but N-RGB could not give good results. One result was shown in Figure 5. Third, I tried HSI system. For gun1.bmp, when using histogram method and based on my training data, it seem that RGB > HSI >> NRGB. (2) Fourth, I tried to apply Gaussian Model on HSI system. Estimated parameters are shown below. µ = [ , ] (3) ( ) Σ = (4) The results in Figure 9 look better than the results by histogram method. Then I tried joy1.bmp and pointer1.bmp, as shown in Figure Note the wedding bind on the hand. 4 MATLAB codes 3

41 Figure 2: R-G Histogram based on RGB. Top: 8 by 8, Middle, 16 by 16, Bottom Left, 32 by 32, Bottom Right 64 by 64. 4

42 Figure 3: Skin Regions of gun1.bmp based on RGB by using n n bins 2-D histogram. Threshold 95%. Top Left: n=8, Top Right: n=16, Middle Left: n=32, Middle Right: n=64, Bottom Left: n=128, Bottom Right: n=256. 5

43 Figure 4: Skin Regions of gun1.bmp based on RGB by using n n bins 2-D histogram. Threshold 99%. Left: n=32, Right: n=256. Figure 5: NR-NG Histogram based on N-RGB. Skin Regions of gun1.bmp based on N-RGB. 6

44 Figure 6: H-S Histogram based on HSI. Grid: 64 by function t h r e s h o l d h i s t = bisectionmp4 ( t h r e s h o l d p e r c e n t, leftend, rightend, nhistn ) 2 % Jiangtao Gou 3 % a = leftend ; 5 b = rightend ; 6 c =(a+b ). / 2 ; 7 p = t h r e s h o l d p e r c e n t ; 8 sizen = size ( nhistn ) ; 9 f a = sum(sum( nhistn. ( nhistn>=a ) ) ) ; 10 fb = sum(sum( nhistn. ( nhistn>=b ) ) ) ; 11 f c = sum(sum( nhistn. ( nhistn>=c ) ) ) ; 12 cc = 0 ; 13 while abs ( fb f a )>1e 3 14 cc = cc + 1 ; 15 i f ( fc p ) ( fb p )<0 16 a = c ; 17 f a = f c ; 18 else 19 b = c ; 20 fb = f c ; 21 end 7

45 Figure 7: Skin Regions of gun1.bmp based on HSI by using bins 2-D histogram. Threshold 90% (Top), 95% (Middle), 99% (Bottom). 8

46 HSI Gaussian S H Figure 8: H-S Gaussian Distribution based on HSI. 22 c = ( a+b ) / 2 ; 23 f c = sum(sum( nhistn. ( nhistn>=c ) ) ) ; 24 x = c ; 25 i f cc > break ; 27 end 28 end 29 t h r e s h o l d h i s t = x ; 1 function FleshToneCollector 2 % Jiangtao Gou 3 % PicNum = 1 9 ; 5 SelectTime = 2 ; 6 for i = 1 : 1 : PicNum 7 picname = [ num2str( i ),. jpg ] ; 8 I = imread ( picname ) ; 9 for j = 1 : 1 : SelectTime 10 picname = [ s k i n,num2str( i ),, num2str( j ),. jpg ] ; 11 I2 = imcrop ( I ) ; 12 imwrite ( I2, picname, jpg ) ; 13 end 9

47 Figure 9: Gaussian Method: Skin Regions of gun1.bmp based on HSI. Threshold t = 2 (Top), 3 (Middle), 4 (Bottom). 10

48 Figure 10: Skin Regions of joy1.bmp and pointer1.bmp based on RGB. Grid 64 64, threshold = 99%. 11

49 Figure 11: Skin Regions of joy1.bmp and pointer1.bmp based on HSI. Grid 64 64, threshold = 99%. 12

50 Figure 12: Gaussian Method: Skin Regions of joy1.bmp and pointer1.bmp based on HSI. Threshold t = 4. 13

51 14 end 1 function t h r e s h o l d p e r c e n t = verifybisectionmp4 ( t h r e s h o l d h i s t, nhistn ) 2 % Jiangtao Gou 3 % t = t h r e s h o l d h i s t ; 5 t h r e s h o l d p e r c e n t = sum(sum( nhistn. ( nhistn>=t ) ) ) ; 1 function colorspacedata = c o l o r S p a c e D a t a C o l l e c t o r ( spacetype ) 2 % Jiangtao Gou 3 % switch spacetype 5 case 1 6 colorspacedata = colorspacedatacollectorrgb ; 7 case 2 8 colorspacedata = colorspacedatacollectornrgb ; 9 case 3 10 colorspacedata = colorspacedatacollectorhsi ; 11 o t h e r w i s e 12 error ( Only RGB, nrgb, HSI are a v a i l a b l e t emporarily. ) 13 end 1 function colorspacedata = colorspacedatacollectorrgb 2 % Jiangtao Gou 3 % PicNum = 1 9 ; 5 SelectTime = 2 ; 6 colorspacedata = [ ] ; 7 for i = 1 : 1 : PicNum 8 for j = 1 : 1 : SelectTime 9 picname = [ s k i n,num2str( i ),, num2str( j ),. jpg ] ; 10 J = imread ( picname ) ; 11 s i z e J = size ( J ) ; 12 % A Faster way 13 mat2d1 = J ( :, :, 1 ) ; 14 mat2d2 = J ( :, :, 2 ) ; 15 mat1d1 = reshape (mat2d1, s i z e J ( 1, 1 ) s i z e J ( 1, 2 ), 1 ) ; 16 mat1d2 = reshape (mat2d2, s i z e J ( 1, 1 ) s i z e J ( 1, 2 ), 1 ) ; 17 colorspacedata = [ colorspacedata ; [ mat1d1, mat1d2 ] ] ; 18 % A Slower way 19 % f o r k1 = 1 : 1 : s i z e J (1,1) 20 % f o r k2 = 1 : 1 : s i z e J (1,2) 21 % colorspacedata = [ colorspacedata ; [ J ( k1, k2, 1 ), J ( k1, k2, 2 ) ] ] ; 14

52 22 % end 23 % end 24 end 25 end 26 colorspacedata = double ( colorspacedata ) ; 27 %% Test 28 % mat3d ( :, :, 1 ) = [ 1, 3, 5, 6 ; 2, 8, 4, 9 ] ; 29 % mat3d ( :, :, 2 ) = [ 1 7, 3 7, 5 7, 6 7 ; 2 7, 8 7, 4 7, 9 7 ] ; 30 % mat2d1 = mat3d ( :, :, 1 ) ; 31 % mat2d2 = mat3d ( :, :, 2 ) ; 32 % mat1d1 = reshape (mat2d1, prod ( s i z e (mat2d1) ),1) ; 33 % mat1d2 = reshape (mat2d2, prod ( s i z e (mat2d2) ),1) ; 34 % mat1d = [ mat1d1, mat1d2 ] ; 1 function colorspacedata = colorspacedatacollectornrgb 2 % Jiangtao Gou 3 % PicNum = 1 9 ; 5 SelectTime = 2 ; 6 colorspacedata = [ ] ; 7 for i = 1 : 1 : PicNum 8 for j = 1 : 1 : SelectTime 9 picname = [ s k i n,num2str( i ),, num2str( j ),. jpg ] ; 10 J = imread ( picname ) ; 11 s i z e J = size ( J ) ; 12 mat2dsum = J ( :, :, 1 )+J ( :, :, 2 )+J ( :, :, 3 ) ; 13 mat2d1 = J ( :, :, 1 ). / mat2dsum ; 14 mat2d2 = J ( :, :, 2 ). / mat2dsum ; 15 mat1d1 = reshape (mat2d1, s i z e J ( 1, 1 ) s i z e J ( 1, 2 ), 1 ) ; 16 mat1d2 = reshape (mat2d2, s i z e J ( 1, 1 ) s i z e J ( 1, 2 ), 1 ) ; 17 colorspacedata = [ colorspacedata ; [ mat1d1, mat1d2 ] ] ; 18 end 19 end 20 colorspacedata = double ( colorspacedata ) ; 1 function colorspacedata = colorspacedatacollectorhsi 2 % Jiangtao Gou 3 % PicNum = 1 9 ; 5 SelectTime = 2 ; 6 colorspacedata = [ ] ; 7 for i = 1 : 1 : PicNum 8 for j = 1 : 1 : SelectTime 9 picname = [ s k i n,num2str( i ),, num2str( j ),. jpg ] ; 10 J = imread ( picname ) ; 15

53 11 rgb image = J ; 12 hsv image = rgb2hsv ( rgb image ) ; 13 J = hsv image ; 14 s i z e J = size ( J ) ; 15 mat2d1 = J ( :, :, 1 ) ; 16 mat2d2 = J ( :, :, 2 ) ; 17 mat1d1 = reshape (mat2d1, s i z e J ( 1, 1 ) s i z e J ( 1, 2 ), 1 ) ; 18 mat1d2 = reshape (mat2d2, s i z e J ( 1, 1 ) s i z e J ( 1, 2 ), 1 ) ; 19 colorspacedata = [ colorspacedata ; [ mat1d1, mat1d2 ] ] ; 20 end 21 end 22 colorspacedata = double ( colorspacedata ) ; 1 function n h i s t = h i s t P l o t 1 ( colorspacedata, nbins ) 2 % From MATLAB h i s t 3 B i v a r i a t e histogram 3 % Jiangtao Gou 4 % dat = colorspacedata ; 6 kk = 256/ nbins ; 7 %h i s t 3 ( dat, [ nbins nbins ], FaceAlpha,. 6 5 ) ; % Draw histogram in 2 D 8 h i s t 3 ( dat, { 0 : kk :255 0 : kk : }, FaceAlpha,. 6 5 ) ; 9 hold on ; 10 xlabel ( R ) ; 11 ylabel ( G ) ; 12 %n = h i s t 3 ( dat, [ nbins nbins ], FaceAlpha,. 6 5 ) ; % Extract histogram data ; 13 n= h i s t 3 ( dat, { 0 : kk :255 0 : kk : }, FaceAlpha,. 6 5 ) ; 14 n1 = n ; 15 n1 ( size (n, 1 ) + 1, size (n, 2 ) + 1 ) = 0 ; 16 % Generate g r i d f o r 2 D p r o j e c t e d view o f i n t e n s i t i e s 17 xb = linspace (min( dat ( :, 1 ) ),max( dat ( :, 1 ) ), size (n, 1 ) +1) ; 18 yb = linspace (min( dat ( :, 2 ) ),max( dat ( :, 2 ) ), size (n, 1 ) +1) ; 19 % Make a p s e u d o c o l o r p l o t on t h i s g r i d 20 h = pcolor ( xb, yb, n1 ) ; 21 % Set the z l e v e l and colormap o f the d i s p l a y e d g r i d 22 set (h, zdata, ones ( size ( n1 ) ) max(max( n ) ) ) 23 colormap ( hot ) % heat map 24 t i t l e ( RGB ) ; 25 zlabel ( Count ) ; 26 set ( gcf, r e n d e r e r, opengl ) ; 27 grid on 28 % Display the d e f a u l t 3 D p e r s p e c t i v e view 29 view ( 3 ) ; 30 hold o f f ; 16

54 31 n h i s t = n ; 32 %% 33 set ( gcf, p a p e r s i z e, [ 5 8 ] ) ; 34 picname = [ h i s t. eps ] ; 35 saveas ( gcf, picname, epsc ) ; 36 eps2pdf ( picname ) ; 1 function n h i s t = h i s t P l o t 2 ( colorspacedata, nbins ) 2 % Jiangtao Gou 3 % dat = colorspacedata ; 5 kk = 1/ nbins ; 6 %h i s t 3 ( dat, [ nbins nbins ], FaceAlpha,. 6 5 ) ; % Draw histogram in 2 D 7 h i s t 3 ( dat, { 0 : kk : 1 0 : kk : 1 }, FaceAlpha,. 6 5 ) ; 8 hold on ; 9 xlabel ( NR ) ; 10 ylabel ( NG ) ; 11 %n = h i s t 3 ( dat, [ nbins nbins ], FaceAlpha,. 6 5 ) ; % Extract histogram data ; 12 n= h i s t 3 ( dat, { 0 : kk : 1 0 : kk : 1 }, FaceAlpha,. 6 5 ) ; 13 n1 = n ; 14 n1 ( size (n, 1 ) + 1, size (n, 2 ) + 1 ) = 0 ; 15 % Generate g r i d f o r 2 D p r o j e c t e d view o f i n t e n s i t i e s 16 xb = linspace (min( dat ( :, 1 ) ),max( dat ( :, 1 ) ), size (n, 1 ) +1) ; 17 yb = linspace (min( dat ( :, 2 ) ),max( dat ( :, 2 ) ), size (n, 1 ) +1) ; 18 % Make a p s e u d o c o l o r p l o t on t h i s g r i d 19 h = pcolor ( xb, yb, n1 ) ; 20 % Set the z l e v e l and colormap o f the d i s p l a y e d g r i d 21 set (h, zdata, ones ( size ( n1 ) ) max(max( n ) ) ) 22 colormap ( hot ) % heat map 23 t i t l e ( N RGB ) ; 24 zlabel ( Count ) ; 25 set ( gcf, r e n d e r e r, opengl ) ; 26 grid on 27 % Display the d e f a u l t 3 D p e r s p e c t i v e view 28 view ( 3 ) ; 29 hold o f f ; 30 n h i s t = n ; 31 %% 32 set ( gcf, p a p e r s i z e, [ 5 8 ] ) ; 33 picname = [ h i s t n. eps ] ; 34 saveas ( gcf, picname, epsc ) ; 35 eps2pdf ( picname ) ; 17

55 1 function n h i s t = h i s t P l o t 3 ( colorspacedata, nbins ) 2 % Jiangtao Gou 3 % dat = colorspacedata ; 5 minh = min( dat ( :, 1 ) ) ; 6 maxh = max( dat ( :, 1 ) ) ; 7 mins = min( dat ( :, 2 ) ) ; 8 maxs = max( dat ( :, 2 ) ) ; 9 kh = (maxh minh) / nbins ; 10 ks = ( maxs mins ) / nbins ; 11 %h i s t 3 ( dat, [ nbins nbins ], FaceAlpha,. 6 5 ) ; % Draw histogram in 2 D 12 h i s t 3 ( dat, { minh : kh :maxh mins : ks : maxs}, FaceAlpha,. 6 5 ) ; 13 hold on ; 14 xlabel ( H ) ; 15 ylabel ( S ) ; 16 %n = h i s t 3 ( dat, [ nbins nbins ], FaceAlpha,. 6 5 ) ; % Extract histogram data ; 17 n= h i s t 3 ( dat, { minh : kh :maxh mins : ks : maxs}, FaceAlpha,. 6 5 ) ; 18 n1 = n ; 19 n1 ( size (n, 1 ) + 1, size (n, 2 ) + 1 ) = 0 ; 20 % Generate g r i d f o r 2 D p r o j e c t e d view o f i n t e n s i t i e s 21 xb = linspace (min( dat ( :, 1 ) ),max( dat ( :, 1 ) ), size (n, 1 ) +1) ; 22 yb = linspace (min( dat ( :, 2 ) ),max( dat ( :, 2 ) ), size (n, 1 ) +1) ; 23 % Make a p s e u d o c o l o r p l o t on t h i s g r i d 24 h = pcolor ( xb, yb, n1 ) ; 25 % Set the z l e v e l and colormap o f the d i s p l a y e d g r i d 26 set (h, zdata, ones ( size ( n1 ) ) max(max( n ) ) ) 27 colormap ( hot ) % heat map 28 t i t l e ( HSI ) ; 29 zlabel ( Count ) ; 30 set ( gcf, r e n d e r e r, opengl ) ; 31 grid on 32 % Display the d e f a u l t 3 D p e r s p e c t i v e view 33 view ( 3 ) ; 34 hold o f f ; 35 n h i s t = n ; 36 %% 37 set ( gcf, p a p e r s i z e, [ 5 8 ] ) ; 38 picname = [ h i s t h s. eps ] ; 39 saveas ( gcf, picname, epsc ) ; 40 eps2pdf ( picname ) ; 1 function [ r e s u l t P i c, r e s u l t P i c C o l o r ] = skinregionsearcherrgb ( 18

56 picname, sgnhist, nbins ) 2 % Jiangtao Gou 3 % k = 256/ nbins ; 5 sgnrgb = kron ( sgnhist, ones ( k, k ) ) ; 6 % picname = gun1. bmp ; 7 SK = imread ( picname ) ; 8 r e s u l t P i c C o l o r = SK; 9 sizesk = size (SK) ; 10 r e s u l t P i c = zeros ( sizesk ( 1, 1 ), sizesk ( 1, 2 ) ) ; 11 for i = 1 : 1 : sizesk ( 1, 1 ) 12 for j = 1 : 1 : sizesk ( 1, 2 ) 13 i f sgnrgb(sk( i, j, 1 ) +1,SK( i, j, 2 ) +1) == 1 14 r e s u l t P i c ( i, j ) = 1 ; 15 else 16 r e s u l t P i c ( i, j ) = 0 ; 17 r e s u l t P i c C o l o r ( i, j, 1 ) = 0 ; 18 r e s u l t P i c C o l o r ( i, j, 2 ) = 0 ; 19 r e s u l t P i c C o l o r ( i, j, 3 ) = 0 ; 20 end 21 end 22 end 1 function [ r e s u l t P i c, r e s u l t P i c C o l o r ] = skinregionsearchernrgb ( picname, sgnhist, nbins ) 2 % Jiangtao Gou 3 % k = 1/ nbins ; 5 % picname = gun1. bmp ; 6 SK = imread ( picname ) ; 7 SKsum = SK ( :, :, 1 )+SK ( :, :, 2 )+SK ( :, :, 3 ) ; 8 SKN1 = SK ( :, :, 1 ). /SKsum ; 9 SKN2 = SK ( :, :, 2 ). /SKsum ; 10 r e s u l t P i c C o l o r = SK; 11 sizesk = size (SK) ; 12 r e s u l t P i c = zeros ( sizesk ( 1, 1 ), sizesk ( 1, 2 ) ) ; 13 for i = 1 : 1 : sizesk ( 1, 1 ) 14 for j = 1 : 1 : sizesk ( 1, 2 ) 15 xx = c e i l (SKN1( i, j ) /k ) ; 16 yy = c e i l (SKN2( i, j ) /k ) ; 17 i f xx == 0 18 xx = 1 ; 19 end 20 i f yy == 0 21 yy = 1 ; 19

57 22 end 23 i f sgnhist ( xx, yy ) == 1 24 r e s u l t P i c ( i, j ) = 1 ; 25 else 26 r e s u l t P i c ( i, j ) = 0 ; 27 r e s u l t P i c C o l o r ( i, j, 1 ) = 0 ; 28 r e s u l t P i c C o l o r ( i, j, 2 ) = 0 ; 29 r e s u l t P i c C o l o r ( i, j, 3 ) = 0 ; 30 end 31 end 32 end 1 function [ r e s u l t P i c, r e s u l t P i c C o l o r ] = skinregionsearcherhsi ( picname, sgnhist, nbins, colorspacedata ) 2 % Jiangtao Gou 3 % dat = colorspacedata ; 5 minh = min( dat ( :, 1 ) ) ; 6 maxh = max( dat ( :, 1 ) ) ; 7 mins = min( dat ( :, 2 ) ) ; 8 maxs = max( dat ( :, 2 ) ) ; 9 kh = (maxh minh) / nbins ; 10 ks = ( maxs mins ) / nbins ; 11 % picname = gun1. bmp ; 12 SK = imread ( picname ) ; 13 rgb image = SK; 14 hsv image = rgb2hsv ( rgb image ) ; 15 SK = hsv image ; 16 r e s u l t P i c C o l o r = SK; 17 sizesk = size (SK) ; 18 r e s u l t P i c = zeros ( sizesk ( 1, 1 ), sizesk ( 1, 2 ) ) ; 19 for i = 1 : 1 : sizesk ( 1, 1 ) 20 for j = 1 : 1 : sizesk ( 1, 2 ) 21 hh = c e i l ( (SK( i, j, 1 ) minh) /kh) ; 22 s s = c e i l ( (SK( i, j, 2 ) mins ) /ks ) ; 23 i f (SK( i, j, 1 ) >= maxh) ( SK( i, j, 1 ) <= minh) ( SK( i, j, 2 ) >= maxs) ( SK( i, j, 2 ) <= mins ) 24 r e s u l t P i c ( i, j ) = 0 ; 25 r e s u l t P i c C o l o r ( i, j, 1 ) = 0 ; 26 r e s u l t P i c C o l o r ( i, j, 2 ) = 0 ; 27 r e s u l t P i c C o l o r ( i, j, 3 ) = 0 ; 28 e l s e i f sgnhist ( hh, s s ) == 0 29 r e s u l t P i c ( i, j ) = 0 ; 30 r e s u l t P i c C o l o r ( i, j, 1 ) = 0 ; 31 r e s u l t P i c C o l o r ( i, j, 2 ) = 0 ; 20

58 32 r e s u l t P i c C o l o r ( i, j, 3 ) = 0 ; 33 else 34 r e s u l t P i c ( i, j ) = 1 ; 35 end 36 end 37 end 38 r e s u l t P i c C o l o r = hsv2rgb ( r e s u l t P i c C o l o r ) ; 1 function r e s u l t P i c C o l o r = skinregionsearchergaussian ( picname,mu, sigma, colorspacedata, c ) 2 % For HSI only 3 % Jiangtao Gou 4 % SK = imread ( picname ) ; 6 rgb image = SK; 7 hsv image = rgb2hsv ( rgb image ) ; 8 SK = hsv image ; 9 r e s u l t P i c C o l o r = SK; 10 sizesk = size (SK) ; 11 for i = 1 : 1 : sizesk ( 1, 1 ) 12 for j = 1 : 1 : sizesk ( 1, 2 ) 13 vec = [SK( i, j, 1 ) ; SK( i, j, 2 ) ] mu ; 14 normdev = vec inv ( sigma ) vec ; 15 i f normdev > c 16 r e s u l t P i c C o l o r ( i, j, 1 ) = 0 ; 17 r e s u l t P i c C o l o r ( i, j, 2 ) = 0 ; 18 r e s u l t P i c C o l o r ( i, j, 3 ) = 0 ; 19 end 20 end 21 end 22 r e s u l t P i c C o l o r = hsv2rgb ( r e s u l t P i c C o l o r ) ; 1 function MP4 main 2 % Jiangtao Gou 3 % FleshToneCollector ; 5 % 1 RGB, 2 nrgb, 3 HSI 6 colorspacedata = c o l o r S p a c e D a t a C o l l e c t o r ( 1 ) ; 7 nbins = 6 4 ; 8 n h i s t = h i s t P l o t 1 ( colorspacedata, nbins ) ; 9 nhistn = 1/sum(sum( n h i s t ) ) n h i s t ; 10 leftend = min(min( nhistn ) ) ; 11 rightend = max(max( nhistn ) ) / 4 ; 12 t h r e s h o l d p e r c e n t = ; 21

59 13 t h r e s h o l d h i s t = bisectionmp4 ( t h r e s h o l d p e r c e n t, leftend, rightend, nhistn ) ; 14 % 15 t h r e s h o l d p e r c e n t = verifybisectionmp4 ( t h r e s h o l d h i s t, nhistn ) ; 16 % 17 sgnhist = ( nhistn >= t h r e s h o l d h i s t ) ; 18 % 19 picname1 = p o i n t e r 1.bmp ; 20 f i l e n a m e 1 = p o i n t e r 1 ; 21 [ r e s u l t P i c, r e s u l t P i c C o l o r ] = skinregionsearcherrgb ( picname1, sgnhist, nbins ) ; 22 %imshow ( r e s u l t P i c, [ 0, 1 ] ) ; 23 imshow ( r e s u l t P i c C o l o r ) ; 24 f i l e n a m e = f i l e n a m e 1 ; 25 set ( gcf, p a p e r s i z e, [ 5 6 ] ) ; 26 picname = [ filename,. eps ] ; 27 saveas ( gcf, picname, epsc ) ; 28 eps2pdf ( picname ) ; 1 function MP4 main 2 2 % Jiangtao Gou 3 % % 1 RGB, 2 nrgb, 3 HSI 5 colorspacedata = c o l o r S p a c e D a t a C o l l e c t o r ( 2 ) ; 6 nbins = 1 6 ; 7 n h i s t = h i s t P l o t 2 ( colorspacedata, nbins ) ; 8 nhistn = 1/sum(sum( n h i s t ) ) n h i s t ; 9 leftend = min(min( nhistn ) ) ; 10 rightend = max(max( nhistn ) ) ; 11 t h r e s h o l d p e r c e n t = ; 12 t h r e s h o l d h i s t = bisectionmp4 ( t h r e s h o l d p e r c e n t, leftend, rightend, nhistn ) ; 13 % 14 t h r e s h o l d p e r c e n t = verifybisectionmp4 ( t h r e s h o l d h i s t, nhistn ) ; 15 % 16 sgnhist = ( nhistn >= t h r e s h o l d h i s t ) ; 17 % 18 picname1 = gun1. bmp ; 19 f i l e n a m e 1 = gun1 n ; 20 [ r e s u l t P i c, r e s u l t P i c C o l o r ] = skinregionsearchernrgb ( picname1, sgnhist, nbins ) ; 21 %imshow ( r e s u l t P i c, [ 0, 1 ] ) ; 22 imshow ( r e s u l t P i c C o l o r ) ; 23 f i l e n a m e = f i l e n a m e 1 ; 24 set ( gcf, p a p e r s i z e, [ 5 6 ] ) ; 22

60 25 picname = [ filename,. eps ] ; 26 saveas ( gcf, picname, epsc ) ; 27 eps2pdf ( picname ) ; 1 function MP4 main 3 2 % Jiangtao Gou 3 % % 1 RGB, 2 nrgb, 3 HSI 5 colorspacedata = c o l o r S p a c e D a t a C o l l e c t o r ( 3 ) ; 6 nbins = 6 4 ; 7 n h i s t = h i s t P l o t 3 ( colorspacedata, nbins ) ; 8 % 9 nhistn = 1/sum(sum( n h i s t ) ) n h i s t ; 10 leftend = min(min( nhistn ) ) ; 11 rightend = max(max( nhistn ) ) ; 12 t h r e s h o l d p e r c e n t = ; 13 t h r e s h o l d h i s t = bisectionmp4 ( t h r e s h o l d p e r c e n t, leftend, rightend, nhistn ) ; 14 % 15 t h r e s h o l d p e r c e n t = verifybisectionmp4 ( t h r e s h o l d h i s t, nhistn ) ; 16 % 17 sgnhist = ( nhistn >= t h r e s h o l d h i s t ) ; 18 % 19 picname1 = joy1. bmp ; 20 f i l e n a m e 1 = j o y 1 h s ; 21 [ r e s u l t P i c, r e s u l t P i c C o l o r ] = skinregionsearcherhsi ( picname1, sgnhist, nbins, colorspacedata ) ; 22 %imshow ( r e s u l t P i c, [ 0, 1 ] ) ; 23 imshow ( r e s u l t P i c C o l o r ) ; 24 f i l e n a m e = f i l e n a m e 1 ; 25 set ( gcf, p a p e r s i z e, [ 5 6 ] ) ; 26 picname = [ filename,. eps ] ; 27 saveas ( gcf, picname, epsc ) ; 28 eps2pdf ( picname ) ; 1 function MP4 main Gaussian 2 % For HSI only 3 % Jiangtao Gou 4 % colorspacedata = colorspacedatacollectorhsi ; 6 mu = mean( colorspacedata ) ; 7 sigma = cov ( colorspacedata ) ; 8 % 9 c = 4 ; 10 picname1 = p o i n t e r 1.bmp ; 23

61 11 f i l e n a m e 1 = p o i n t e r 1 g a u s s i a n ; 12 r e s u l t P i c C o l o r = skinregionsearchergaussian ( picname1,mu, sigma, colorspacedata, c ) ; 13 imshow ( r e s u l t P i c C o l o r ) ; 14 f i l e n a m e = f i l e n a m e 1 ; 15 set ( gcf, p a p e r s i z e, [ 5 6 ] ) ; 16 picname = [ filename,. eps ] ; 17 saveas ( gcf, picname, epsc ) ; 18 eps2pdf ( picname ) ; 19 % 20 minhs = min( colorspacedata ) ; 21 maxhs = max( colorspacedata ) ; 22 x = minhs ( 1 ) : ( ( maxhs( 1 ) minhs ( 1 ) ) /10) : maxhs( 1 ) ; 23 y = minhs ( 2 ) : ( ( maxhs( 2 ) minhs ( 2 ) ) /10) : maxhs( 2 ) ; 24 [X,Y]=meshgrid ( x, y ) ; 25 p=mvnpdf ( [X( : ),Y( : ) ],mu, sigma ) ; 26 P=reshape (p, size (X) ) ; 27 surf (X,Y,P) 28 shading f l a t 29 xlabel ( H ) ; 30 ylabel ( S ) ; 31 t i t l e ( HSI Gaussian ) ; 32 set ( gcf, p a p e r s i z e, [ 5 8 ] ) ; 33 picname = [ g a u s s i a n h s. eps ] ; 34 saveas ( gcf, picname, epsc ) ; 35 eps2pdf ( picname ) ; 36 % 24

62 Winter 2013 EECS 332 Digital Image Analysis Machine Problem 5 Canny Edge Detector Jiangtao Gou Department of Statistics, Northwestern University Instructor: Prof. Ying Wu 26 February Introduction In this report, I implemented the Canny edge detector by using MATLAB. 2 Algorithm Description The first step is to use Gaussian smoothing as a filter to get rid of image noise by using Gaussian kernel. When the picture is relatively smooth, I compute the image gradient by Sobel operators, which used 3 by 3 grid to compute, and should give better results than Robert Cross operators, which used 2 by 2 grid. Then I choose high and low thresholds. As Professor suggested, I choose high threshold to achieve 80% above, and choose low threshold as half of high threshold. The fourth step is to supress non-maxima. In the following I linked the edges by using the recursive algorithm, where I randomly choose the start point, and link edges. Parameter N and σ were changed to see the different effects. 3 Results analysis Some computation could be slow. The results are shown in those pictures below. 1

63 I tested my edge detector on all four pictures which provided by professor. Meanwhile, I use the whole body picture of Lena as the case of my own to test this edge detector. The results are presented in these pictures. 4 MATLAB codes 1 function E=EdgeLinking ( Mag low, Mag high ) 2 3 [ row, c o l ]= find ( Mag high >0) ; 4 for t =1:1: size ( c o l ) 5 i f ( row ( t )<size ( c o l ) & c o l ( t )<size ( c o l ) ) 6 i f ( Mag low ( row ( t ) +1, c o l ( t ) ) >0) 7 Mag high ( row ( t ) +1, c o l ( t ) ) =1; 8 Mag low ( row ( t ) +1, c o l ( t ) ) =0; 9 end 10 i f ( Mag low ( row ( t ), c o l ( t ) +1)>0) 11 Mag high ( row ( t ), c o l ( t ) +1)=1; 12 Mag low ( row ( t ), c o l ( t ) +1)=0; 13 end 14 i f ( Mag low ( row ( t ) +1, c o l ( t ) +1)>0) 15 Mag high ( row ( t ) +1, c o l ( t ) +1)=1; 16 Mag low ( row ( t ) +1, c o l ( t ) +1)=0; 17 end 18 i f ( Mag low ( row ( t ) 1, c o l ( t ) 1)>0) 19 Mag high ( row ( t ) 1, c o l ( t ) 1)=1; 20 Mag low ( row ( t ) 1, c o l ( t ) 1)=0; 21 end 22 i f ( Mag low ( row ( t ) +1, c o l ( t ) 1)>0) 23 Mag high ( row ( t ) +1, c o l ( t ) 1)=1; 24 Mag low ( row ( t ) +1, c o l ( t ) 1)=0; 25 end 26 i f ( Mag low ( row ( t ) 1, c o l ( t ) +1)>0) 27 Mag high ( row ( t ) 1, c o l ( t ) +1)=1; 28 Mag low ( row ( t ) 1, c o l ( t ) +1)=0; 29 end 30 i f ( Mag low ( row ( t ) 1, c o l ( t ) ) >0) 31 Mag high ( row ( t ) 1, c o l ( t ) ) =1; 32 Mag low ( row ( t ) 1, c o l ( t ) ) =0; 33 end 34 i f ( Mag low ( row ( t ), c o l ( t ) 1)>0) 35 Mag high ( row ( t ), c o l ( t ) 1)=1; 36 Mag low ( row ( t ), c o l ( t ) 1)=0; 2

64 Figure 1: Result: N=3, Sigma=3, PercentageOfNonEdge=

65 Figure 2: Result: N=3, Sigma=3, PercentageOfNonEdge=

66 Figure 3: Result: N=3, Sigma=3, PercentageOfNonEdge= end 38 end 39 end 40 E=Mag high ; 1 function [ T low, T high ]= FindThreshold (Mag, percentageofnonedge ) 2 [ n,m]= size (Mag) ; 3 binnum=64; 4 counts=i mhist (Mag, binnum) ; 5 6 maxv=max(mag ( : ) ) ; 7 %minimum v a l u e i s zero 8 minv =0; 9 T high = ( find (cumsum( counts ) > percentageofnonedge m n, 1, f i r s t ) / (binnum 1) ) (maxv minv )+minv ; 10 T low =0.5 T high ; 1 function s=gausssmoothing ( I, N, sigma ) 2 %N=3 3 %Sigma=3 5

67 Figure 4: Result: N=3, Sigma=5, PercentageOfNonEdge= Gmask=f s p e c i a l ( g aussian, [N,N], sigma ) ; 5 s=conv2( I, Gmask, same ) ; 1 function [ Mag, Theta]= ImageGradient ( s ) 2 % S o b e l f i l t e r 3 [ n,m]= size ( s ) ; 4 Theta=zeros (n,m) ; 5 h = [ ; 0 0 0; 1 2 1]; 6 op = h / 8 ; % S o b e l approximation to d e r i v a t i v e 7 x mask = op ; % g r a d i e n t in the X d i r e c t i o n 8 y mask = op ; 9 10 % compute t he g r a d i e n t in x and y d i r e c t i o n 11 bx = i m f i l t e r ( s, x mask, r e p l i c a t e ) ; 12 by = i m f i l t e r ( s, y mask, r e p l i c a t e ) ; 13 % compute t he magnitude and d i r e c t i o n 14 Mag = sqrt ( bx. bx + by. by ) ; Theta ( find ( by =0) )=atan ( bx ( find ( by =0) ). / by ( find ( by =0) ) ) ; 17 Theta ( find ( by==0)) =3.14/2; 6

68 Figure 5: Result: N=5, sigma=5, PercentageOfNonEdge= % Get t he i n i t i a l image lena. g i f 2 f i l e n a m e = gun1 ; 3 %binary 4 img in = rgb2gray ( imread ( [ filename,.bmp ], bmp ) ) ; 5 figure ; 6 colormap ( gray ) ; 7 % s u b p l o t (2,3,1) ; 8 imagesc ( img in ) ; 9 t i t l e ( O r i g i n a l image ) 10 %Gaussian smooth with two parameters N and sigma 11 N=5; 12 sigma =5; 13 s=gausssmoothing ( img in, N, sigma ) ; 14 figure ; 15 colormap ( gray ) ; 16 % s u b p l o t (2,3,2) ; 17 imagesc ( s ) ; 18 t i t l e ( Gaussian smoothing ) 19 %c a l c u l a t i n g image g r a d i e n t with S obel 20 [ Mag, Theta]= ImageGradient ( s ) ; 7

69 Figure 6: Result: The image right after gaussian smoothing. 21 %f i n d maximum v a l u e 22 maxv=max(mag ( : ) ) ; 23 %normalize v a l u e s 24 Mag=Mag/maxv ; 25 figure ; 26 colormap ( gray ) ; 27 % s u b p l o t (2,3,3) ; 28 imagesc (Mag) ; 29 t i t l e ( C a l c u l a t i n g image g r a d i e n t by Sobel ) 30 %f i n d two t h r e s h o l d s with one parameter percentageofnonedge 31 percentageofnonedge = 0. 6; 32 [ T low, T high ]= FindThreshold (Mag, percentageofnonedge ) ; 33 %s u p r e s s i n g nonmaxima 34 Mag supress=nonmaximasupress (Mag, Theta ) ; 35 figure ; 36 colormap ( gray ) ; 37 % s u b p l o t (2,3,4) ; 38 imagesc ( Mag supress ) ; 39 t i t l e ( Non maxima s u p r e s s i n g ) % Applying T high 8

70 Figure 7: Result: N=3, Sigma=3, PercentageOfNonEdge=

71 Figure 8: Result: N=3, Sigma=3, PercentageOfNonEdge=

72 Figure 9: Result: N=3, Sigma=3, PercentageOfNonEdge=

73 Figure 10: Result: N=3, Sigma=3, PercentageOfNonEdge=

74 Figure 11: Result: N=3, Sigma=3, PercentageOfNonEdge=

75 Figure 12: Result: N=3, Sigma=3, PercentageOfNonEdge=

76 Figure 13: Result: N=3, Sigma=3, PercentageOfNonEdge=

77 Figure 14: Result: N=3, Sigma=3, PercentageOfNonEdge=

78 42 Mag high=mag supress ; 43 Mag high ( find ( Mag supress<t high ) ) =0; 44 Mag high ( find ( Mag supress>=t high ) ) =1; 45 figure ; 46 colormap ( gray ) 47 % s u b p l o t (2,3,5) ; 48 imagesc ( Mag high ) ; 49 t i t l e ( Applying T high ) ; % Applying T low 52 Mag low=mag supress ; 53 Mag low ( find ( Mag supress<t low ) ) =0; 54 Mag low ( find ( Mag supress>=t low ) ) =1; 55 figure ; 56 colormap ( gray ) 57 % s u b p l o t (2,3,6) ; 58 imagesc ( Mag low ) 59 t i t l e ( Applying T low ) ; 60 %Edge l i n k i n g 61 E=EdgeLinking ( Mag low, Mag high ) ; 62 figure 63 colormap ( gray ) 64 imagesc (E) ; 65 t i t l e ( f i n a l Canny ) ; figure 68 edge ( img in, s o b e l ) 69 t i t l e ( s o b e l by MATLAB f u n c t i o n edge ) 70 figure 71 edge ( img in, r o b e r t s ) 72 t i t l e ( r o b e r t s by MATLAB f u n c t i o n edge ) 73 figure 74 edge ( img in, z e r o c r o s s ) 75 t i t l e ( z e r o c r o s s by MATLAB f u n c t i o n edge ) 76 figure 77 edge ( img in, canny ) 78 t i t l e ( canny by MATLAB f u n c t i o n edge ) t t =1; 1 function Mag supress=nonmaximasupress (Mag, Theta ) 2 %s u p r e s s i n g nonmaxima by the i n t e r p o l a t i o n method 3 [ n,m]= size (Mag) ; 4 for i =2:n 1, 5 for j =2:m 1, 17

79 6 7 X=[ 1,0,+1; 1,0,+1; 1,0,+1]; 8 Y=[ 1, 1, 1;0,0,0;+1,+1,+1]; 9 Z=[Mag( i 1, j 1),Mag( i 1, j ),Mag( i 1, j +1) ; 10 Mag( i, j 1),Mag( i, j ),Mag( i, j +1) ; 11 Mag( i +1, j 1),Mag( i +1, j ),Mag( i +1, j +1) ] ; 12 XI=[ sin ( Theta ( i, j ) ), sin ( Theta ( i, j ) ) ] ; 13 YI=[cos ( Theta ( i, j ) ), cos ( Theta ( i, j ) ) ] ; ZI=interp2 (X,Y, Z, XI, YI ) ; 16 i f Mag( i, j ) >= ZI ( 1 ) & Mag( i, j ) >= ZI ( 2 ) 17 Mag supress ( i, j )=Mag( i, j ) ; 18 else 19 Mag supress ( i, j ) =0.0; 20 end end 23 end 18

80 Winter 2013 EECS 332 Digital Image Analysis Machine Problem 6 Hough Transform: Line Detection Jiangtao Gou Department of Statistics, Northwestern University Instructor: Prof. Ying Wu 4 March Introduction In this report, I implemented Hough transform, which is an algorithm for line detection. My main references are Prof. Wu s lecture notes Hough Transform and Jain, Kasturi and Schunck s book Machine Vision, section 6.8.4, Hough Transform. For Hough Transform itself, I basically followed Algorithm 6.4 Hough Transform Algorithm, which is described on page 220 of the book Machine Vision. The basic idea is to use the dual space, where points and lines are dual elements to each other. For line detection, we can either use rectangular coordinate system or polar system. In this report, I use polar system (ρ, θ). 2 Algorithm Description The first step is edge detection. We can either use the programs in Machine Problem 5 last time or use edge(), which is a MATLAB function. Here I directly use edge(). For each edge point (x, y) in original image (size R C), I will use ρ = x cos θ + y sin θ to transform the point (x, y) to a curve in ρ-θ space, where ρ ( R 2 + C 2, R 2 + C 2 ) and θ ( π/2, π/2). Accumulators will count how many times each point has satisfied the curve equation. In the third step, I will choose a threshold, choose the points in ρ-θ space which have large count numbers. 1

81 Finally, I transform these points in ρ-θ space back to several lines in x-y space. x = ρ y sin θ. cos θ It is really a very smart idea to use dual elements. 3 Results analysis In this report, without special claim, I use a picture as my ρ-θ picture. In the plot of significant intersections, I enlarged each intersection in order to make each point easy to be observed. 3.1 Picture test.bmp For Picture test.bmp, I used canny as the edge detector, and the accumulator got 119 as the maximal count. 3.2 Picture test2.bmp For Picture test2.bmp, I used canny as the edge detector, and the accumulator got 122 as the maximal count. 3.3 Picture input.bmp For Picture input.bmp, when I used canny as the edge detector, and the accumulator got 54 as the maximal count. The results by using Canny edge detector as a pre-processor were presented in Figure 5 and 6. We could see that it was OK to detect the paper, but it is relatively difficult to detect the finger (or you need to bring in a lot of noise lines). We need to change the edge detector. Now I used sobel as the edge detector, and the accumulator got 56 as the maximal count. The results by using Sobel edge detector as a pre-processor were presented in Figure 7 and 8. 2

82 Figure 1: Original picture test.bmp, edge detected picture, curves in parameter space. 3

83 Figure 2: Top-down: threshold 90, 85, 80, 60, significant intersections and detected lines. 4

84 Figure 3: Original picture test2.bmp, edge detected picture, curves in parameter space. 5

85 Figure 4: Top-down: threshold 80, 75, 70, 60, significant intersections and detected lines. 6

86 Figure 5: Original picture input.bmp, edge detected picture, curves in parameter space. (Canny Edge Detection) 7

87 Figure 6: Top-down: threshold 38, 30, significant intersections and detected lines. (Canny Edge Detection) 8

88 By using Sobel edge detector, detecting finger is still not easy, but we can observe that Sobel edge detector achieved better result than Canny edge detector. I also tried different quantization scheme. I tried , , , and I felt that gave the best results. So neither using too coarse nor too fine quantization achieve good result Nissan Altima 2.5 SV I got a picture from I used sobel as the edge detector, and the accumulator got 244 as the maximal count, as shown in Figure 12. By setting the threshold as 195, we got the detected lines, as shown in Figure 13. The result looks good. We can observe that the edges of windshield, the edge of front door, the edge of shift selector area and the edge of glove box are all detected. 4 MATLAB codes 1 % main MP6 2 f i l e n a m e = altima i n t 2 ; 3 picname = [ filename,. jpg ] ; 4 % 5 I1 = imread ( picname ) ; 6 I2 = rgb2gray ( I1 ) ; 7 % 8 imshow ( I2, [ 0, ] ) ; 9 set ( gcf, p a p e r s i z e, [ 5 5 ] ) ; 10 picname = [ filename, 1. eps ] ; 11 saveas ( gcf, picname, epsc ) ; 12 eps2pdf ( picname ) ; 13 % 14 % BW = edge ( I2, canny ) ; 15 BW = edge ( I2, s o b e l ) ; 16 % 17 imshow (BW, [ 0, 1 ] ) ; 18 set ( gcf, p a p e r s i z e, [ 5 5 ] ) ; 19 picname = [ filename, 2. eps ] ; 9

89 Figure 7: Original picture input.bmp, edge detected picture, curves in parameter space. (Sobel Edge Detection) 10

90 Figure 8: Top-down: threshold 30, 20, significant intersections and detected lines. (Sobel Edge Detection) 11

91 Figure 9: Parameter space, Significant intersections, Detected lines, Sobel detector, picture as the ρ-θ picture. Maxima 71, threshold

92 Figure 10: Parameter space, Significant intersections, Detected lines, Sobel detector, picture as the ρ-θ picture. Maxima 117, threshold

93 Figure 11: Parameter space, Significant intersections, Detected lines, Sobel detector, picture as the ρ-θ picture. Maxima 200, threshold

94 Figure 12: Original picture altima-int2.jpg, and edge detected picture (Sobel). 15

95 Figure 13: Line Detection of altima-int2.jpg. 16