DIGITAL IMAGE PROCESSING ASSIGNMENT

Transcription

1 DIGITAL IMAGE PROCESSING ASSIGNMENT Submitted by Kishore A. B6EC Michael George B64EC Mrinmay Kalita B633EC

2 . Filtering Using simple averaging masks. a. Code function y = mask(x,h) M_H N_H M_X N_X = = = = length(h(:,)); length(h(,:)); length(x(:,)); length(x(,:)); x=double(x); for i = :M_X for j = :N_X temp = double(); for k = :M_H for l = :N_H if i floor(m_h/)+k > && j floor(n_h/)+l > && i floor(m_h/)+k <= M_X && j floor(n_h/)+l <= N_X temp = temp + x(i-floor(m_h/)+k-,j-floor(n_h/ )+l-)*h(k,l); y(i,j) = temp; return moon=imread('pirate.tif'); imshow(moon) % 5 X 5 8 bit image. fil=[ ; ; ; ; ]/5; moon=mask(moon,fil); moon=uint8(moon); figure,imshow(moon) b. Masks 3 X 3 spatial smoothing filter /9

3 5 X 5 spatial smoothing filter /5 3 X 3 weighted averaging filter 4 /6 c. Images Original (Pirate image) 3 X 3 smoothing filtered 3

4 5 X 5 smoothing filtered 3 X 3 weighted averaging filtered Median Filtering. a. Code function y = medianmask(x,filsize) M_X = length(x(:,)); N_X = length(x(,:)); for i = :M_X for j = :N_X h=zeros(,filsize^); z=; for k = :filsize for l = :filsize if i-floor(filsize/)+k- > && jfloor(filsize/)+l-> && i-floor(filsize/)+k- <= M_X && jfloor(filsize/)+l-<= N_X h(,z)=x(i-floor(filsize/)+k-,jfloor(filsize/)+l-); z=z+; y(i,j) = median(h); return moon=imread('pirate.tif'); imshow(moon) filsize=3; % 5 X 5 8 bit image. % 3 X 3 median filtering. 4

5 moon=medianmask(moon,filsize); moon=uint8(moon); figure,imshow(moon) b. Images Original (Pirate image) 3 X 3 median filtered 5 X 5 median filtered 7 X 7 median filtered 5

6 Gaussian Filtering. a. Code moon=imread('pirate.tif'); imshow(moon) [m n]=size(moon); % 5 X 5 8 bit image. ft=fft(double(moon)); figure,imshow(uint8(abs(ft))) fts=fftshift(ft); % centering the spectrum figure,imshow(uint8(*log(+abs(fts)))) figure,imshow(uint8(ifft(ft))) moonft=zeros(m,n); m=floor(m/); n=floor(n/); DO=5; % sqrt of variance. for u=:m for v=:n moonft(u,v) = fts(u,v)*exp(-((u-m)^+(v-n)^)/(*do^)); figure,imshow(uint8(*log(+abs(moonft)))) moonft= ifftshift(moonft); % reversing the centering of the spectrum. figure,imshow(uint8(ifft(moonft))) b. Images Original (Pirate image) Dynamic range compressed centred Fourier spectrum. 6

7 Gaussian Low Pass filtered spectrum (with Do=5). Filtered image. Gaussian Low Pass filtered spectrum (with Do=5). Filtered image. Triangular Filters. a. Code moon=imread('pirate.tif'); imshow(moon) % 5 X 5 8 bit image. fil=[ 3 ; ; ; ; 3 ]/8; moon=mask(moon,fil); moon=uint8(moon); figure,imshow(moon) b. Masks 7

8 5 X 5 pyramidal filter /8 5 X 5 conical filter /5 c. Images Original (Pirate image) Pyramidal filtered image. 8

9 Conical filtered image. Comparison. (i) The weighted averaging and simple averaging masks produced similar blurring effect for the same order of filter mask. As the order of the filter mask increased, so did the blurring. (ii) The median filtered image encountered less smoothing than an average mask filtered image for the same filter size. The filtered image had a cartoonised blurred appearance, which increased as the order of the filter increased. (iii) The Gaussian low pass filtered image experienced increased blurring as the variance (Do) of the Gaussian low pass filter (used in the frequency domain) decreased. This is because as the variance decreased, more and more high frequency components were eliminated. (iv) The pyramidal filter mask produced more blurring than the conical filter mask but it produced less blurring than the averaging and the median filter masks(for the same order of filter mask).. Noise removal Simple addition. a. Code moon=imread('pirate.tif'); imshow(moon) moon=imdouble(moon); nrmoon =zeros(size(moon)); % 5 X 5 8 bit image. 9

10 for i=:3 moonoise=imnoise(moon,'gaussian',,.); if(rem(i,)==) figure,imshow(moonoise) nrmoon=nrmoon+moonoise; nrmoon=nrmoon/3; figure,imshow((nrmoon)) b. Images Original (Pirate image). Gaussian noise affected image (var =.). Another noise affected image. Adding 3 such images and averaging.

11 Adding only 3 such images and averaging. Adding 3 images (var=) and averaging. Adding 3 images (var=) and averaging. Using simple averaging masks. a. Code moon=imread('pirate.tif'); % 5 X 5 8 bit image. imshow(moon) moon=imdouble(moon); moonoise=imnoise(moon,'gaussian',,);

12 figure,imshow((moonoise)) moonoise=imnoise(moonoise,'salt & pepper',); figure,imshow(moonoise) fil=[ ; ; ]/9; moon=mask(moon,fil); figure,imshow(moon) b. Images Original (Pirate image) Gaussian and S&P noise affected image 3X 3 Filtered image. Filtered image. 5X5

13 Median Filtering. a. Code moon=imread('pirate.tif'); % 5 X 5 8 bit image. imshow(moon) moon=imdouble(moon); filsize=3; % 3 X 3 median filtering. moonoise=imnoise(moon,'salt & pepper',.); figure,imshow(moonoise) moon=medianmask(moonoise,filsize); figure,imshow(moon) b. Images Original (Pirate image) Salt & Pepper noise affected. 3

14 3 X 3 median filtered 5 X 5 median filtered Gaussian Filtering. a. Code (Gaussian noise affected image.) moon=imread('pirate.tif'); % 5 X 5 8 bit image. imshow(moon) [m n]=size(moon); moon=imnoise(moon,'gaussian',,.); figure,imshow((moon)) ft=fft(double(moon)); figure,imshow(uint8(abs(ft))) fts=fftshift(ft); % centering the spectrum figure,imshow(uint8(*log(+abs(fts)))) figure,imshow(uint8(ifft(ft))) moonft=zeros(m,n); m=floor(m/); n=floor(n/); DO=5; % sqrt of variance. for u=:m for v=:n moonft(u,v) = fts(u,v)*exp(-((u-m)^+(v-n)^)/(*do^)); figure,imshow(uint8(*log(+abs(moonft)))) moonft= ifftshift(moonft); % reversing the centering of the spectrum. figure,imshow(uint8(ifft(moonft))) b. Images Original (Pirate image). Gaussian noise affected image. 4

15 Gaussian Low Do=5). filtered (with Pass filtered (with Gaussian Low Pass Do=). Gaussian Low Pass filtered (with Do=5). c. Code (Salt and pepper noise affected image.) moon=imread('pirate.tif'); % 5 X 5 8 bit image. imshow(moon) [m n]=size(moon); moonoise=imnoise(moon,'salt & pepper',); figure,imshow(moonoise) ft=fft(double(moon)); figure,imshow(uint8(abs(ft))) fts=fftshift(ft); % centering the spectrum 5

16 figure,imshow(uint8(*log(+abs(fts)))) figure,imshow(uint8(ifft(ft))) moonft=zeros(m,n); m=floor(m/); n=floor(n/); DO=; % sqrt of variance. for u=:m for v=:n moonft(u,v) = fts(u,v)*exp(-((u-m)^+(v-n)^)/(*do^)); figure,imshow(uint8(*log(+abs(moonft)))) moonft= ifftshift(moonft); % reversing the centering of the spectrum. figure,imshow(uint8(ifft(moonft))) d. Images Original (Pirate image). Salt and Pepper noise affected image. 6

17 Spectrum of noise affected image. Gaussian Low Pass filtered (with Do=). Triangular Filters. a. Code moon=imread('pirate.tif'); % 5 X 5 8 bit image. imshow(moon) moon=imdouble(moon); moonoise=imnoise(moon,'gaussian',,); figure,imshow((moonoise)) moonoise=imnoise(moonoise,'salt & pepper',); figure,imshow(moonoise) fil=[ 3 ; ; ; ; 3 ]/8; moon=mask(moon,fil); figure,imshow(moon) b. Images Original (Pirate image) Gaussian and S&P noise affected image. 7

18 (ii) (iii) (iv) (v) Pyramidal filtered image. Conical filtered image. Comparison. (i) Noise reduction achieved by simple addition of several Gaussian noise affected images followed by averaging resulted in reduction of the noise effect. The resultant image had a washed out appearance. As the variance of the Gaussian noise was increased washed out appearance of the resultant image increased. Also as the number of noise affected images added and averaged was increased, the effect of noise decreased. Noise reduction using simple averaging masks had the capability to reduce the effect of severely noise affected images, specifically it was capable of reducing the effect of both Gaussian noise as well as Salt & Pepper noise. But as the order of the averaging mask was increased the blurring effect also increased. The median filtered is capable of reducing the effect of Salt &Pepper noise. But the noise reduction capability of the median filter is much less compared to the simple averaging masks. As the order of the median filter was increased the reduction in noise was better but the blurring increased. The Gaussian low pass filter is not capable of removing Gaussian noise, but it is capable of reducing the effect of Salt & Pepper noise in severely noise affected images. As the variance (Do) of the Gaussian filter was increased the blurring effect was found to be reduced as higher frequency components were passed. The triangular filters were found to have the capability to reduce the effect of both Salt & Pepper as well as Gaussian noise in severely noise affected images. The pyramidal filter mask produced more blurring than the conical filter mask of the same order. 3. Image Sharpening Gradient operator. a. Code (using Prewitt operator) 8

19 moon=imread('pirate.tif'); imshow(moon) % 5 X 5 8 bit image. fil=[- - -; ; ]; moon=mask(moon,fil); moon=uint8(moon); figure,imshow(moon) fil=[- ;- ;- ]; moon=mask(moon,fil); moon=uint8(moon); figure,imshow(moon) moonp=abs(moon)+abs(moon); figure,imshow(moonp) moons=moon+moonp; figure,imshow(moons) b. Masks 3 X 3 Prewitt masks. c. Images Original (Pirate image). Edges detected using Prewitt mask. 9

20 Sharpened image. d. Code (using Sobel operator) moon=imread('pirate.tif'); imshow(moon) % 5 X 5 8 bit image. fil=[- - -; ; ]; moon=mask(moon,fil); moon=uint8(moon); figure,imshow(moon) fil=[- ;- ;- ]; moon=mask(moon,fil); moon=uint8(moon); figure,imshow(moon) moonp=abs(moon)+abs(moon); figure,imshow(moonp) moons=moon+moonp; figure,imshow(moons) e. Masks 3 X 3 Sobel masks.

21 f. Images Original (Pirate image). using Sobel mask. Edges detected Sharpened image. Laplacian operator. a. Code (using composite laplacian mask) moon=imread('pirate.tif'); imshow(moon) % 5 X 5 8 bit image. fil=[ - ;- 5 -; - ]; %composite laplacian mask moon=mask(moon,fil); moon=uint8(moon); figure,imshow(moon)

22 moond=moon-moon; figure,imshow(moond) b. Masks 3 X 3 Composite lapalacian masks. 5 9 Mask Mask c. Images Original (Pirate image). Edges detected using mask (basic).

23 Sharpened image using mask. Edges detected using mask (basic). Sharpened image using mask. Comparison. (i) Gradient operator implemented using the Sobel operator resulted in a 3

24 (ii) sharpened image having thicker edges than a gradient operator implemented using a Prewitt operator. The Laplacian operator implemented using mask produced a more visually pleasing appearance compared to mask. Mask produced grainy appearance in the low frequency regions. Also more sharpness was obtained in case of Laplacian (which is second order) operator than gradient (which is first order) operator. Gradient operator resulted in thicker edges. 4. Bit plane slicing Natural image. a. Code moon=imread('pirate.tif'); imshow(moon) % 5 X 5 8 bit image. [m n]=size(moon); moon=zeros(m,n); moon=double(moon); for b=:8 for i=:m for j=:n moon(i,j)=bitget(moon(i,j),b); figure,imshow(moon) b. Images Original (Pirate image). Bit Bit 3 Bit 4

25 Bit 4 Bit 5 Bit 6 Bit 7 Bit 8 Computer generated image. a. Code moon=imread('compgen.tif'); % 34 X 4 8-bit image. imshow(moon) [m n p]=size(moon); moon=zeros(m,n); moon=double(moon); for b=:8 for i=:m for j=:n moon(i,j)=bitget(moon(i,j),b); figure,imshow(moon) 5

26 b. Images Original image ( D sine wave) Bit 3 Bit Bit 4 Bit 6 Bit Bit 5 Bit 7 Comparison. 6 Bit 8

27 Most of the information content in natural images were observed to reside in the bits 5 and above, while the computer generated image had an almost equal distribution of information content among the bits. 5. Basic transformations Image negative. a. Code moon=imread('kid.tif'); imshow(moon); [m n]= size(moon); mooneg=zeros(m,n); mooneg=uint8(mooneg); for i=:m for j=:n mooneg(i,j)=55-moon(i,j); figure,imshow(mooneg); b. Images 7

28 Original Image (kidney) Negative Power Law. a. Code moon=imread('ramp.tif'); imshow(moon); [m n]= size(moon); moon=double(moon); mpl=zeros(m,n); mpl=double(mpl); for i=:m for j=:n mpl(i,j)=*(moon(i,j)^(/.8)); % pixel-by-pixel power law transformation mpl=imuint8(matgray(mpl)); % matgray brings values in the range [,] and imuint8 brings it to [-55]. figure,imshow(mpl); b. Images 8

29 Gamma corrected for display on CRT Original Image Log. a. Code moon=imread('moon.tif'); imshow(moon); moon=double(moon); mfft=fft(moon); mfft=fftshift(mfft); figure,imshow(abs(mfft),[]) mfft=log(+abs(mfft)); % using logarithmic transformation to enhance details in the darker regions of the image. mfft=imuint8(matgray(mfft)); % matgray brings values in the range [,] and imuint8 brings it to [-55]. figure,imshow(mfft,[]) b. Images 9

30 Original Image (Moon) 6. Fourier spectrum Comparison. (i) The Negative gray level transformation is particularly suited for enhancing white or gray detail embedded in dark regions of an image, especially when the black areas are dominant in size. Thus negative transformation is used in medical image display and processing. (ii) The Power Law gray level transformation can be used for darkish image enhancement or whitish image enhancement deping on the value of gamma, the exponent in the power law equation. Cathode ray tubes used in computer monitors have an intensity to voltage response that is power law function with gamma varying from.8 to.5. To gain a better representation of an image, before displaying on the monitor the image can be gamma corrected with a gamma of approximately /.8. (iii) The Log gray level transformation can be used for dynamic range compression applications. Fourier spectrums can have values in the range to 6. Hence before displaying on monitor (that is usually scaled to 8 bits and hence the high values dominate the display) the dynamic range can be compressed by log transformation, to avoid lost visual detail in the lower intensity values of the spectrum. Piecewise Linear transformations Log transformed F.S. Contrast stretching. a. Code moon=imread('emc.tif'); imshow(moon) [m n]=size(moon); 3

31 moon=zeros(m,n); moon=double(moon); for i=:m for j=:n if (moon(i,j)<4) % contrast stretching moon(i,j)=.5*double(moon(i,j)); elseif (moon(i,j)>=4 && moon(i,j)<5) moon(i,j)=.8*double(moon(i,j))-9.4; else moon(i,j)=.5*double(moon(i,j))+7.5; moon=imuint8(matgray(moon)); % matgray brings values in the range [,] and imuint8 brings it to [-55]. figure,imshow(moon) image. % displaying the contrast stretched b. Images Original Image (Einstein) Contrast stretched image. Gray level slicing. 3

32 a. Code moon=imread('pirate.tif'); imshow(moon) [m,n]=size(moon); moon=uint8(zeros(m,n)); for i=:m for j=:n if (moon(i,j)>8) moon(i,j)= 9; else moon(i,j)=; moon=imuint8(moon); figure,imshow(moon) % Slicing % displaying the sliced image. b. Images Original Image (Pirate). Gray sliced image. Comparison. (i) The Contrast Stretching transformation can be used to increase the dynamic range of gray level values in the image being processed. Hence it is used to rectify low contrast images. (ii) The Gray level slicing transformation can be used to highlight specific 3

33 range of gray level values in an image. 7. Histogram Processing Histogram Equalization. a. Code function y=histogrameq(x) x = uint8(x); M = length(x(:,)); N = length(x(,:)); h(:56) = ; for i = :M for j = :N % finding histogram. h(x(i,j)+) = h(x(i,j)+)+; h = h/(m*n)*55; c() = h(); for i = :length(h) c(i) = c(i-)+h(i); % finding the c.d.f for i=:m for j=:n y(i,j)=c(x(i,j)+); return x=imread('pollen.tif'); figure,imshow(x) y=histogrameq(x); y=uint8(y); figure,imshow(y) b. Images 33

34 Original Image (Pollen). Histogram equalized image. Histogram Specification. a. Code function [y,t,g,z]=histogramspec(x,pz) % Pz should be normalized. x = uint8(x); M = length(x(:,)); N = length(x(,:)); Pr(:56) = ; for i = :M for j = :N Pr(x(i,j)+) = Pr(x(i,j)+)+; Pr = Pr/(M*N); T() = Pr(); for i = :length(pr) T(i) = T(i-)+Pr(i); G() = Pz(); for i = :length(pz) G(i) = G(i-)+Pz(i); for i = :length(t) j = ; while (G(j)-T(i))< && (j<55) j = j+; z(i) = j-; T = uint8(t*55); G = uint8(g*55); z = uint8(z); for i=:m for j=:n y(i,j)=z(x(i,j)+); y=uint8(y); return m=imread('pirate.tif'); n=imhist(m); [c d]=size(m); Pz=n/(c*d); x=imread('cameraman.tif'); [y T G z]=histogramspec(x,pz); imhist(x,56),figure,imshow(y);figure,imhist(y,56);figure,imhist(m,56) 34

35 b. Images Input Image (Cameraman)

36 Specified Histogram (Histogram of Pirate image). Histogram of input image Output image after Histogram Specification. 36

37 Histogram of output image. 37 5