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Background The purpose of this assignment is to practice building, inspecting, and modifying multi-dimensional lists effectively. This often requires nested for-loops, but not always. It involves thinking of the structure like an MxN matrix of labeled spots, each with a row and column index, or a higher dimensional structure like a 3D matrix that has indexes for height, width and depth. Multi-dimensional lists aren't conceptually more difficult than single-dimension lists, but in practice the nested loops, aliasing, and more complex traversals and interactions merit some extra practice and thought. Scenario We want to implement a set of functions that are very common in image processing tools and form the basis for all the advanced features one finds in tools like Photoshop, GIMP, etc. Definitions A digital image with dimensions HxW is represented with a matrix of pixels that has H rows and W columns. In Python we can store this matrix in a list of lists [ [. . .], [. . .], [. . .] . . . . . [. . .] ]. The length of the outer list equals the number of rows H, while the length of each nested list (it’s the same for all of them) equals the number of columns W. In grayscale images, each pixel is an integer that takes values from 0-255 (i.e. 1 byte). A value of zero corresponds to the black color and a value of 255 corresponds to the white color. Everything in between is a tone of gray; the darker the gray the closer to 0, the lighter the gray the closer to 255. Figure 1a depicts a zoom-in on a 16x12 grayscale image. In Figure 1b you can see the values of each pixel superimposed on the image. And in Figure 1c you can see the matrix representation of this grayscale image. a b c Figure 1 (grayscale image) 1 In color images, each pixel consists of a list of 3 integers that each takes values from 0-255. The first number corresponds to Red, the second number corresponds to Green, and the third number corresponds to Blue. Any color can be represented with the proper combination of the RGB values. Figure 2 (color image) Therefore, a color image in Python will be a list of lists of lists and will look like this: [ [. . . , [90,0,53], . . .] , . . . , [. . . , [249,215,203], . . .] , . . . , [. . . , [213,60,67], . . .], . . . ] Restrictions  You are not allowed to import anything. It’s ok to import modules for debugging purposes and/ or for experimenting with the provided helper code but make sure you remove all imports when you submit your work.  You are not allowed to use recursion, classes, exceptions, and list comprehensions  From the built-in functions, you are allowed to use: range(), len(), sorted(), int(), sum()  From list methods, you are allowed to use: append(), extend(), insert(), copy(), sort(), remove(), pop()  You are allowed to use the del keyword Assumptions You may assume that: • The types of the function arguments are the proper ones, you don’t have to validate them. • Image dimensions and the range of tones/colors are according to the specification, no validation is required 2 Functions The following are the functions you must implement. The signature of each one is provided, do not make any changes to them otherwise the tester will not work properly. Keep in mind that you do not have to write a main body for your program in this project. histogram(image) Description: It creates and returns a histogram of a grayscale image. A histogram provides a summary of the image by counting the number of pixels for each tonal value. The list of counters are ordered based on the pixel value (i.e. from 0 to 255). Input image should not be altered in any way. Parameters: image (2D list of int) is the grayscale image Return value: A list of int with 256 values Example: histogram([[1,1,2,2,5,2], [3,4,4,5,9,5]]) → [0, 2, 3, 1, 2, 3, 0, 0, 0, 1, 0 . . . 0] flip(image, orientation) Description: It takes a grayscale image and flips its content either horizontally or vertically. No image is returned, all changes occur in place. Parameters: image (a 2D list of int) is the input image, orientation (string) is either 'horizontal' or 'vertical' Return value: None Examples: flip([ [1,2,3,4,5,6], [ [6,5,4,3,2,1], [7,8,9,0,4,1] ], 'horizontal') → [1,4,0,9,8,7] ] flip([ [1,2,3,4,5,6], [ [7,8,9,0,4,1], [7,8,9,0,4,1] ], 'vertical') → [1,2,3,4,5,6] ] rotate(image) Description: It takes a square grayscale image and rotates its content by 90 degrees clockwise. No image is returned, all changes occur in place. Parameters: image (a 2D list of int) is the input image Return value: None Example: rotate([[1,2,3], [[7,4,1], [4,5,6], [8,5,2], [7,8,9]]) → [9,6,3]] 4 crop(image, origin, height, width) Description: It returns a cropped tile out of a color image without altering the input in any way. Parameters: image (a 3D list of int) is the original image, origin (tuple of int) is a pair of coordinates (row, column) for top left corner where the cropping will begin, height (int) is the height of the cropped tile, width (int) is the width of the cropped tile Return value: The cropped image that is a 3D list of int Example: crop([ [[1,1,1], [2,2,2],[3,3,3]], [[4,4,4], [5,5,5],[6,6,6]], [[7,7,7], [8,8,8],[9,9,9]] ], (0,0), 1, 2) → [[[1,1,1], [2,2,2]]] color2gray(image) Description: It takes a color image (3D list) and returns a new grayscale image (2D list) where each pixel will take the average value of the three color components truncated to integer. Input image should not be altered in any way. Parameters: image (3D list of int) is the color image Return value: The grayscale image that is a 2D list of int Example: color2gray([ [[1,1,2], [2,5,2]], [[1, 3], [[3,4,4], [5,9,5]] ]) → [3, 6]] extract_layer(image, color) Description: It extracts a single color out of the RGB values of the color image and returns this layer as a grayscale image. Input image should not be altered in any way. Parameters: image (3D list of int) is the color image, color (string) is either 'red' or 'green' or 'blue' Return value: A 2D list of int Example: extract_layer([ [[1,0,4], [8,0,9],[3,1,3]], [[7,4,9], [4,5,9],[7,6,0]], [[0,0,6], [2,8,3],[5,4,3]] ], 'red') → [[1,8,3], [7,4,7], [0,2,5]] 5 scale(image, factor) Description: It scales a grayscale image by some factor. If the factor is positive it scales the image up by filling in all the extra pixels with the same value as the original. If the factor is negative it scales the image down by just deleting the extra pixels (in this case assume that the dimensions of the image are divided exactly by the factor). The scaling happens in place, nothing is returned. Parameters: image (2D list of int) is the grayscale image, factor (int) is a number either greater than 1 or less than -1 Return value: None Examples: scale([ [1,7,2,5], [ [1,1,7,7,2,2,5,5], [3,4,4,9] ], 2) → [1,1,7,7,2,2,5,5], [3,3,4,4,4,4,9,9], [3,3,4,4,4,4,9,9] ] scale([ [1,2,3,4], [5,6,7,8], [9,8,7,6], [ [1,3], [9, 7] ] [5,4,3,2] ], -2) → compress(image) Description: It compresses a grayscale image and returns a data structure (list of lists) that holds a summary of the content, based on the following algorithm: First, we construct from the original image a black and white bitmap – values less than 128 are mapped to black and the rest are mapped to white. Then, we encode each row of this bitmap as a list containing the lengths of the alternating black and white sequences. Last, we package all these lists in an outer list. You can think of the encoding of each row as the process of counting the length of the consecutive black and white pixels (starting always with the black pixels) and adding these values in a list in the same order as we encounter the alternating black and white sequences. Obviously, each row, depending on its content, will have a different number of alternating sequences, so the full data structure will most probably be a list of variable-size sublists. Parameters: image (2D list of int) is the grayscale image Return value: A list of lists that summarizes the image Example: compress([[100,170,200,111,250,128], [223,244,255,115,127,105], [100,100,100,120,120,120]]) → [ [1, 2, 1, 2], [0, 3, 3], [6] ] 6 median_filter(image) Description: It applies a 3x3 median filter on a grayscale image and returns the filtered image as a new grayscale image. A median filter replaces the value of a certain pixel with the median value of the 9 pixels that belong to its 3x3 neighborhood. Because the border pixels don’t have a full 3x3 neighborhood, the filtered image will have 2 fewer pixels in each dimension. Parameters: image (2D list of int) is the grayscale image Return value: A grayscale image (2D list of int) Example: median_filter([[1,2,3,4], [8,7,6,5], [9,8,7,5], [[7,5], [9,9,4,1]]) → [8,6]] Extra credit – the following function is optional and gives 5pts extra credit This function is more challenging, but still only uses the same skills as before. fill(image, tone, seed) Description: It fills in a grayscale image with a certain tone of gray and returns the result as a new image. The input image should not be modified in any way. The filling starts at location defined by seed and spreads all around (check all 8 neighbors) until a different/boundary tone is hit. All the pixels that are replaced (i.e. filled-in) must have the same value as the initial pixel at seed, any other value is considered a boundary. The tone is a color that does not exist in the image before filling. You’re not allowed to use recursion. Parameters: image (2D list of int) is the grayscale image, tone (int) is the replacement tone of gray, seed (tuple of int) is a pair of coordinates (row, column) Return value: A grayscale image (2D list of int) Example: fill([[0,9,6,0,0,0], [[0,9,6,2,2,2], [0,7,4,0,0,0], [0,7,4,2,2,2], [1,3,0,7,8,0], [1,3,2,7,8,2], [0,9,5,1,0,1],], 2, (0,3)) → [0,9,5,1,2,1]]

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"""
It creates and returns a histogram of a grayscale image.
A histogram provides a summary of the image by counting the number of pixels for each tonal value.
The list of counters are ordered based on the pixel value (i.e. from 0 to 255).
Input image should not be altered in any way.
"""


def histogram(image):
    pixels = []
    for i in range(256):
       pixels.append(0)
    for i in range(len(image)):
       for j in range(len(image[0])):
            pixels[image[i][j]] += 1
    return pixels


"""
It takes a grayscale image and flips its content either horizontally or vertically.
No image is returned, all changes occur in place.
"""
def flip(image, orientation):
    if orientation == 'horizontal':
       for i in range(len(image)):
            itm = image[i]
            j = 0
            k = len(itm) - 1
            while j < k:
                tmp = itm[j]
                itm[j] = itm[k]
                itm[k] = tmp
                j += 1
                k -= 1
    elif orientation == 'vertical':
       for i in range(len(image[0])):
            j = 0
            k = len(image) - 1
            while j < k:
                tmp = image[j][i]
                image[j][i] = image[k][i]
                image[k][i] = tmp
                j += 1
                k -= 1


"""
It takes a square grayscale image and rotates its content by 90 degrees clockwise.
No image is returned, all changes occur in place.
"""
def rotate(image):
    n = len(image)
    for i in range(int(n / 2)):
       for j in range(i, n - i - 1):
            temp = image[i][j]
            image[i][j] = image[n - 1 - j][i]
            image[n - 1 - j][i] = image[n - 1 - i][n - 1 - j]
            image[n - 1 - i][n - 1 - j] = image[j][n - 1 - i]
            image[j][n - 1 - i] = temp


"""
It returns a cropped tile out of a color image without altering the input in any way.
"""
def crop(image, origin, height, width):
    result = []
    for i in range(origin[0], origin[0] + height):
       res = []
       for j in range(origin[1], origin[1] + width):
            res.append(image[i][j])
       result.append(res)
    return result



"""
It takes a color image (3D list) and returns a new grayscale image (2D list)
where each pixel will take the average value of the three color components truncated to integer.
Input image should not be altered in any way.
"""
def color2gray(image):
    result = []
    for i in range(len(image)):
       res = []
       for j in range(len(image[0])):
            avg = int(sum(image[i][j]) / len(image[i][j]))
            res.append(avg)
       result.append(res)
    return result...

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