[SOLVED] Cs 270: digital image processing assignment 2

(a) Apply the 3 × 3 Sobel kernels (x-direction and y-direction) on Figure 1.tif to sharpen the image.
Since the Sobel kernels are separable, you should implement this by the combination of simple kernels.
Show the Sobel kernels and the corresponding processed images. (Implement your own convolution
operator.) (10 points)(b) Perform Gaussian Highpass filtering D0 = 100 on ’Figure 1.tif’ in the frequency domain. Show the
Gaussian Highpass filter and the results (You can use fft2(), ifft2() and fftshift(), but not the built-in
filtering function such as imfilter(), filter(), and filter2()). (15 points)Implement Homomorphic filtering on ’PET-scan.tif’ with the best paramters you think to improve the
contrast of the subjet’s limbs. Show the Homomorphic filter and filtered results. The preferable condition
is that the variance of pixel values within the white box exceeds 3 × 10−4
, when the image is normalized
to 0–1. (20 points)Convert ’PeppersRGB.tif’ from RGB to HSI color space, and then convert it back. Show the image in
HSI space and the recovered result in RGB space (Hint: you need to normalize all channels to [0,1] in
HSI space).(20 points)In the process of image acquisition, the image blur caused by the relative movement between the acquisition device and target at the moment of exposure is called motion blur. In the spatial domain, the
degenerate function model of motion blur can be expressed as:
g(x, y) = h(x, y)⋆f(x, y) + n(x, y)Here, g(x, y) represents the output image, h(x, y) represents the degradation function, f(x, y) represents
the input image, and n(x, y) represents the noise. The model in frequency domain can be expressed as:
G(x, y) = H(x, y)F(x, y) + N(x, y)We can use PSF= fspecial(’motion’,L,theta) to simulate the convolution kernel h(x, y). Here, theta
refers to the angle between the direction of motion and the horizontal direction, which is called the
direction of motion blur. L refers to the distance the pixel moves in the direction of motion, which is
called the motion blur distance.Restore the blurred.tif following:
(a) Calculate the spectrum of the image, shift the zero frequency to the center of the spectrum. Display
the spectrum logarithmically. You can use fft2().(5 points)(b) Estimate the parameters L and theta for blurred.tif (with a shape of N × N, N = 640).
Motion blur will produce periodic bright and dark stripes in the spectrogram. As shown in the example
picture, theta is the angle between the stripe and the vertical direction, d represents the distance between
two similar dark stripes (the distance between the two dark stripes near the center is 2d), then L=N/d.You can use the Radon transform to estimate the angle theta, and then rotate it 180-theta degree
counterclockwise. Vertical projection of the rotated spectrogram can be used to estimate L, L=N/d. Show
the estimated parameters in your report. (15 points)(c) Implement Wiener filtering with the estimated parameters, and choose the best K you think. You can
obtain H(u, v) through the psf2otf() function. (15 points)