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- Consider the following 8-bit greyscale image: 12 12 12 59 179 254 254 254 12 12 12 59 179 254 254 254 12 12 12 59 179 254 254 254 12 12 12 59 179 254 254 254 Compress the image using Huffman coding. Hint: construct the Huffman table and encode the image scanlines using the table entries.The figure shown above is a binary images I in which white piİxels have values of one and black pixels have values of zero. First compute derivatives of the image intensities in the x and y directions following the numerical way to obtain Ix and Iy : Ix(i,j)= (I(i+1,j)-I(i-1,j))/2 and Iy(i,j) = (I(i,j+1)-I(i,j-1))/2. For the computation of Ix(i,j) on pixels in the first column Ix(i, j) = I(i+1,j) - I(i,j) or of Iy(i,j) on pixels in the first row Iy(i,j) = I(i,j+1) - I(i,j). For the computation of Ix(i,j) on pixels in the last column Ix(i,j) = I(i,j) - I(i-1,j) or of Iy(i,j) on pixels in the last row Iy(i,j) = I(i,j) - I(i,j-1). Calculate the response R of the Harris corner detector at each pixel based on Ix and ly, assuming (i) a value of k=0.05 in the calculation, (ii) that products of derivatives are summed over an equally weighted 3 by 3 pixel window around each pixel, (iii) that the image is padded with zeros when computing at pixels on the edge. ANSWER: R= (to 2 decimal places)Integral image is obtained by summing all the pixels before each pixel (Naively you can think of this as similar to the cumulative distribution function where a particular value is obtained by summing all the values before). Let's take an example to understand this. Suppose we have a 5x5 binary image as shown below. The integral image is shown on the right. 2, 1, 2, 2], 1, 1, 3, 3], 5, 5], 8], [1, 2, 2, 5, [2, 4, 4, 8, [ 3, 5, 5, 9, 10]]. Integral image All the pixels in the integral image are obtained by summing all the previous pixels. Previous here means all the pixels above and to the left of that pixel (inclusive of that pixel). For instance, the 3 (blue circle) is obtained by adding that pixel with the above and left pixels in the input image i.e. 1+0+0+1+0+0+0+1 = 3. [[1, 0, 0, 1, 0], [0, 0, 0, 1, 0], [0, 1, 0, 1, 0], [1, 1, 0, 1, 0], [1, 0, 0, 0, 1]] Original image [[1, 1, 1, [1, Write a function integral_image () that takes as parameter an image in the form of a nested list A…
- Perform histogram equalization on the following 6*6 image the gray scalelevel distribution of the image is given belowThe attatched image is the 2D profile of an image, showing I(x,y). True or False: The spatial frequency in the x direction (kx) is π; the spatial frequency in the y direction (ky) is π; and the inital phase is π. To create this 2D intensity, we need to add together multiple 2D sine waves. The Fourier transformation of this image will contain a single peak at a single frequency (not counting peaks at zero and the overtones) The wave in the 2D profile is plotted for 3 wavelengthsFollowing figure (next slide) shows the histograms of three different images, and three possible point functions. For each original image, which point operation can best equalize its histogram? Briefly explain your reasoning. h₁(f), a 0 g₁(f) + 255 128 0 64 128 255 f 192 255 f h₂(f) a 0 64 9₂(f)+ 255 128 0 128 192 255 h₂(f) 4 a 0 g3(f) + 255 128 0 128 255 f 128 255
- An 8-bit image has a perfectly normalized histogram. Suppose that each pixel value is ANDed with 1000 0000 , and is set to white if the result of ANDing is non-zero, otherwise is set to black if the result is zero. What is the normalized number of black pixels in the output image? Write the number with 2 decimal points in the box below.Given the above modified Euclid’s algorithm, how many iterations of the while loop are needed for the input (35, 110)? Please look at the attached image.Suppose images f(x,y) and g(x,y) have histograms h; and hg. Suppose you form image k(x,y) as the sum of these two images: k(x,y) = f(x,y) + g(x,y). (a) Under what conditions (on images f and g) can you determine the histogram hų of image k in terms of the histograms hf and hg? (That is, under what conditions can you determine hu if you are only given hj and he? Hint: this turns out to be fairly restrictive.) (b) Explain how you would derive hỵ in this case.
- Observe the following image matrix. Note that this is 4-bits grayscale image. Identify the following items: 11 10 12 13 10 11 15 15 15 11 15 12 10 10 12 12 10 13 11 15 15 12 12 10 11 12 11 15 11 15 14 12 10 14 11 12 10 11 10 11 12 11 10 12 14 13 10 10 11 11 11 11 12 12 14 14 11 11 11 11 14 14 13 13 14 13 11 11 10 13 15 15 11 13 12 15 14 10 12 11 10 14 14 14 11 11 11 11 15 15 11 11 11 15 11 11 11 15 (a) Intensity Level Resolution bits/pixel (b) Spatial Resolution pixel (c) Memory size required to store the image bits (d) Memory size of colour image (RGB) with the similar specification as the mentioned grayscale image bits 5N2N 45Computer Science Let C be a black circular disk in front of a white background. The circular disk is parallel to the image plane. This disk is projected on the image plane through a pinhole. What is the shape of the disk’s projection on the image plane? [Hint: A circular disk parallel to the image plane is described algebraically as all 3D points [X,Y,Z]T with (X-X0) 2 +(Y-Y0) 2 =R2 , Z=Z0, where [X0,Y0,Z0] T is the center of the disk and R is its radius.]For the given 4x4 RGB image below, apply uniform quantization algorithm and find the reduced 64-color palette image. (Hint: divide each color space into 8 regions.) 38,49,35 26,34,19 70,80,72 58,67,50 63,70,54 76,85,82 40,46,44 45,52,45 46,51,47 40,45,38 58,65,49 23,28,8 111,111,99 78,79,63 80,80,56 30,29,1