Given the following 4 times 4 image A, we wish to resample it to produce a 5 times 5 image B. A = [30 68 53 250 42 217 118 239 105 231 106 16 140 87 28 120] a. Using zeroth-order interpolation (also called nearest neighbor interpolation), what is image B? Show the full matrix with all values rounded to integers. b. Using first-order (bilinear) interpolation, what is image B? Show the full matrix with all values rounded to integers. For problems 2 and 3, there are several grayscale images available on BBLearn. To keep things simple, use zeroth-order (nearest neighbor) interpolation as needed. The original image data is 8-bit grayscale, so your output image should also be 8-bit grayscale and properly quantized to the nearest integer value. Write your own source code and do not share code with others! In Matlab, write a function g = imgRotate(f, theta, mode) for performing image rotation about the center of the image, f is the original grayscale image, theta is the rotation angle in degrees, with positive angles going counterclockwise. If mode = ‘crop’, the rotated image should be cropped (about its center) to the same size as the input image. This should be the default. If mode = ‘full’, the output image should be the smallest size capable of containing the full rotated input image for the given angle. The background of the rotated image should be black. To test your function, rotate a test image (one of those on BBLearn) by 30 degrees, -45 degrees, and 110 degrees. Use full mode, but include at least one test using crop mode. Show your results. Include your Matlab source code in your homework submission. In Matlab, write a function g = imgShear(f, sv, sh) for performing image shear, f is the original grayscale image, sv and sh are the vertical and horizontal shearing factors, which can be any real numbers. Output image g must be the same size as input image f. The background of the sheared image should be black. To test your function, shear a test image (one of those on BBLearn) using the following combinations of values for (sv, sh): (0.5, 0), (0, -0.75), and (0.5, -0.75). Show your results. Include your Matlab source code in your homework submission.