[Frontiers of Computer Science] Chapter 5 Answers 2022 - Image Processing

Chapter 5

5.1 Image Pixels and Colors

5.1.1 Picture display

fig() + image(img_gray, cmap='gray')

5.1.2 Image data structure analysis

print(type(img_gray))
print(img_gray.shape)
printMat2D(img_gray)

5.1.3 Pixel - single pixel readout

val = img_gray[18, 16]
print(val)

5.1.4 Pixel - single pixel modification

img_gray_copy = image_copy(img_gray)
img_gray_copy[18, 16] = 255
fig() + image(img_gray_copy, cmap='gray')

5.1.5 Pixel-line modification

img_gray_copy = image_copy(img_gray)
img_gray_copy[18:25, 16] = 255
fig() + image(img_gray_copy, cmap='gray')

5.1.6 Pixel-area modification

img_gray_copy = image_copy(img_gray)
img_gray_copy[18:25, 16:25] = 255
fig() + image(img_gray_copy, cmap='gray')

5.1.7 Pixel-area modification shorthand

img_gray_copy = image_copy(img_gray)
img_gray_copy[8:25, 8:25] = 255
fig() + image(img_gray_copy, cmap='gray')

5.1.8 Exercise - Flower Border

img_gray_copy = image_copy(img_gray)
img_gray_copy[3:23, 22] = 255
img_gray_copy[2:23, 7] = 255
img_gray_copy[23, 7:23] = 255
img_gray_copy[2, 8:23] = 255
fig() + image(img_gray_copy, cmap='gray')

5.1.9 Color pictures

fig() + image(img_shibe)
print(img_shibe.shape)

5.1.10 Color Channel Splitting

red, green, blue = color_split(img_shibe)
fig(1, 3) + [image(red, cmap='Reds'), image(green, cmap='Greens'), image(blue, cmap='Blues')]

merged_img = color_merge(red, green, blue)
fig() + image(merged_img)

5.1.11 Color Channel Splitting - Another Approach

r = img_shibe[:, :, 0]
g = img_shibe[:, :, 1]
b = img_shibe[:, :, 2]
fig(1, 3) + [image(r, cmap='Reds'), image(g, cmap='Greens'), image(b, cmap='Blues')]

5.2 Image color transformation

5.2.1 Color transformation warm-up 1 - channel swap

fig() + image(img_raw)
img_bgr = image_copy(img_raw)

tmp = image_copy(img_bgr[:, :, 0])
img_bgr[:, :, 0] = img_bgr[:, :, 2]
img_bgr[:, :, 2] = tmp

fig() + image(img_bgr)

5.2.2 Color transformation warm-up 2 - warm color system

img_warm = image_copy(img_raw)

img_warm = image_int2float(img_warm)
img_warm[:, :, 2] = img_warm[:, :, 2] / 2
img_warm = image_float2int(img_warm)

fig() + image(img_warm)

5.2.3 Matrix Form - Channel Swap

mat = [
    [0, 0, 1],
    [0, 1, 0],
    [1, 0, 0]
]

img_bgr = image_copy(img_raw)
img_bgr = map_color_space(img_bgr, mat)
fig() + image(img_bgr)

5.2.4 Exercise - Realize Warm Color System in Matrix Form

mat = [[0, 0, 1],
     [0, 1, 0], 
     [1, 0, 0]]

img_bgr = image_copy(img_raw)
img_bar_warm = image_int2float(img_bgr)
img_bar_warm[:, :, 2] /= 2
img_bar_warm = image_float2int(img_bar_warm)

fig() + image(img_bar_warm)

5.2.5 Matrix Form - Vintage Effect

mat = [
    [0.393, 0.769, 0.189],
    [0.349, 0.686, 0.168],
    [0.272, 0.534, 0.131]
]

img_retro = image_copy(img_raw)
img_retro = image_int2float(img_retro)
img_retro = map_color_space(img_retro, mat)
img_retro = bound(img_retro, 0, 255)
img_retro = image_float2int(img_retro)
fig() + image(img_retro)

5.2.6 Matrix Form - Red-Green Blindness Simulation

rgb2lms_mat = [
    [17.8824, 43.5161, 4.11935],
    [3.45565, 27.1554, 3.86714],
    [0.0299566, 0.184309, 1.46709]
]

lms2rgb_mat = [
    [8.09444479e-02, -1.30504409e-01, 1.16721066e-01],
    [-1.02485335e-02, 5.40193266e-02, -1.13614708e-01],
    [-3.65296938e-04, -4.12161469e-03, 6.93511405e-01]
]

lms_mix_mat = [
    [0, 2.02344, -2.52581],
    [0, 1, 0],
    [0, 0, 1]
]

img_cb = image_copy(img_raw)
img_cb = image_int2float(img_cb)

img_cb = map_color_space(img_cb, rgb2lms_mat)
img_cb = map_color_space(img_cb, lms_mix_mat)
img_cb = map_color_space(img_cb, lms2rgb_mat)

img_cb = bound(img_cb, 0, 255)
img_cb = image_float2int(img_cb)

fig() + image(img_raw)
fig() + image(img_cb)

5.2.7 Exercise - Design your own transformation

import itertools
import random
mat = [
    [],
    [],
    []
]

for item, _ in itertools.product(mat, range(3)):
    item.append(random.random())

img_retro = image_copy(img_raw)
img_retro = image_int2float(img_retro)
img_retro = map_color_space(img_retro, mat)
img_retro = bound(img_retro, 0, 255)
img_retro = image_float2int(img_retro)
fig() + image(img_retro)

5.2.8 From linear transformation to nonlinear transformation - wood carving effect

img_woodcut = image_copy(img_wzj)
img_woodcut = rgb2gray(img_woodcut)
img_woodcut = binary_threshold(img_woodcut, 170, 0, 255)
fig() + image(img_woodcut, cmap='gray')

5.3 Production of image special effects

5.3.1 Frosted glass effects

def groundglass_code(img, k=3):
    res = image_copy(img)
    H, W = get_image_size(img)
    
    for i in range(H):
        for j in range(W):
            offset_i = random_int(-k, k)
            offset_j = random_int(-k, k)
            
            src_i = i + offset_i
            src_j = j + offset_j
            
            src_i = bound(src_i, 0, H - 1)
            src_j = bound(src_j, 0, W - 1)
            
            res[i, j, :] = img[src_i, src_j, :]
            return res
        
img_groundglass = groundglass(img_sand,3)
fig() + image(img_sand)
fig() + image(img_groundglass)

5.3.2 Frosted glass expansion - adjust parameters

img_groundglass_ex = groundglass(img_sand,8)
fig() + image(img_sand)
fig() + image(img_groundglass_ex)

5.3.3 Oil painting effects

def oil_painting_code(img, num_bin=2, region_size =4):
    H, W = get_image_size(img)
    res = image_copy(img)
    bin_assignment = compute_bin_assignment(img, num_bin)
    for i in range(0, H):
        for j in range(0, W):
            bb = get_bounding_box(i, j, region_size, H, W)
            y1, y2, x1, x2 = bb
            
            img_region = img[y1:y2, x1:x2, :]
            bin_assignment_region = bin_assignment[y1:y2, x1:x2]  
            region_r, region_g, region_b = get_most_frequent_color(img_region, bin_assignment_region)
            
            res[y1:y2, x1:x2, 0] = region_r
            res[y1:y2, x1:x2, 1] = region_g
            res[y1:y2, x1:x2, 2] = region_b
            return res
  
img_painting = oil_painting(img_sand,3,4)
fig() + image(img_sand)
fig() + image(img_painting)

5.3.4 Oil painting effect extension - adjust parameters

img_painting = oil_painting(img_sand,20,4)
fig() + image(img_sand)
fig() + image(img_painting)

5.4 Image Distortion

5.4.1 Mapping function formula:

Recall the mapping function formula for image warping:
$$u,v=T(x,y)$$

T() corresponds the (x, y) of the original image to the (u, v) pixel of the new image. However, when implemented by a computer, this process is reversed: for a pixel on the new image, we hope to find its corresponding source point on the original image. Therefore, when writing a program, the mapping function formula should actually be written as:

$$x,y=T^{-1}(u,v)$$

5.4.2 Global Warp 1 - Collapse Mapping Function

Collapse mapping function:
$$x^{\prime }=x\ast (1-p\ast r)/(1-p)$$

$$y^{\prime }=y\ast (1-p\ast r)/(1-p)$$

$$r=\sqrt{x^2+y^2}$$

def warp1(x, y):
    p = 0.4
    r = (x**2 + y**2)**0.5
    xp = x * (1 - p*r) / (1 - p)
    yp = y * (1 - p*r) / (1 - p)
    return xp, yp

img_anchor_warp = global_len_warp(img_anchor, warp1)

fig() + image(img_anchor)
fig() + image(img_anchor_warp)

5.4.3 Global Warp 1 - Collapse Warp Effect

def warp1(x, y):
    p = 0.4
    r = (x**2 + y**2)**0.5
    xp = x * (1 - p*r) / (1 - p)
    yp = y * (1 - p*r) / (1 - p)
    return xp, yp

img_warp_boy = global_len_warp(img_boy, warp1)
fig() + image(img_boy)
fig() + image(img_warp_boy)

5.4.4 Global Distortion 1 - Collapse Exercise

def warp1_ex(x, y):
    p = 0.2
    r = (x**2 + y**2)**0.5
    xp = x * (1 - p*r) / (1 - p)
    yp = y * (1 - p*r) / (1 - p)
    return xp, yp

img_warp_boy_ex = global_len_warp(img_boy, warp1_ex)

fig() + image(img_boy)
fig() + image(img_warp_boy_ex)

5.4.5 Global Warp 2 - Prism Warp Function

Prism warp function:
$$x^{\prime }=sin(x)\ast x^2$$

$$y^{\prime }=without\left(and\right)\_\ast y^2$$

def warp2(x, y):
    xp = sin(x) * x**2
    yp = sin(y) * y**2
    return xp, yp

img_warp_anchor_ex2 = global_len_warp(img_anchor, warp2)
fig() + image(img_warp_anchor_ex2)

5.4.6 Global Distortion 2 - Prism Distortion Effect

def warp2(x, y):
    xp = sin(x) * x**2
    yp = sin(y) * y**2
    return xp, yp

img_warp_boy2 = global_len_warp(img_boy, warp2)
fig() + image(img_warp_boy2)

5.4.7 Global Warp - Crazy Mode

def warp_ex(x, y):
    xp = sin(x) * x
    yp = sin(y) * y    
    return xp, yp

img_warp_boy_insane = global_len_warp(img_boy, warp_ex)
fig() + image(img_warp_boy_insane)

5.4.8 Local Twist - Stretch Twist Function

warp_params = [(125, 125), (0, 80), 120]
img_warp_local_anchor = local_warp_image(img_anchor, warp_params)

warp_params = [(125, 125), (0, 80), 60]
img_warp_local_anchor2 = local_warp_image(img_anchor, warp_params)

fig() + image(img_warp_local_anchor)
fig() + image(img_warp_local_anchor2)

5.4.9 Local Distortion - Stretch Distortion Effect

warp_params = [(100, 100), (0, 20), 50]
img_warp_local_boy = local_warp_image(img_boy, warp_params)

fig() + image(img_warp_local_boy)

5.5 Face key point detection

5.5.1 Face key points

In a series of studies on faces, scientists found that the positioning of some important position coordinates of the face is very important for subsequent tasks, such as face alignment, segmentation, etc. These points are called face key points. Going up in precision, there are 68, 104, and 240 points. The following figure shows the distribution of 68 points:

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5.5.2 Face key point detection

points = detect_keypoints(img_boy)
print(points)

5.5.3 Visualization of facial key points

img_boy_with_points = draw_points(img_boy, points)
fig() + image(img_boy_with_points)

5.5.4 Application of Key Points in the Coming Year - find out the positions of the corners of the mouth and the center of the eyebrows

mouth_left = points[48]
mouth_right = points[54]

left_eyebrow = points[19]
right_eyebrow = points[24]

cust_points = [mouth_left, mouth_right, left_eyebrow, right_eyebrow]
img_boy_cust = draw_points(img_boy, cust_points)
fig() + image(img_boy_cust)

5.5.5 Exercise - outline the eyes and mouth

left_eye = points[36:42]
right_eye = points[42:48]
mouth = points[48:60]

img_boy_face = draw_points(img_boy, left_eye + right_eye + mouth)
fig() + image(img_boy_face)

5.5.6 Exercise - Calculating the Center of the Mouth Using Key Points

mouth_up = points[51]
mouth_down = points[57]

mouth_center_y = int((mouth_up[0] + mouth_down[0] + mouth_left[0] + mouth_right[0]) / 4)

mouth_center_x = int((mouth_up[1] + mouth_down[1] + mouth_left[1] + mouth_right[1]) / 4)
mouth_center = (mouth_center_y, mouth_center_x)

img_boy_mouth = draw_points(img_boy, mouth_center)
fig() + image(img_boy_mouth)

5.6 Making dynamic emoticons

5.6.1. Detect keypoints

points = detect_keypoints(img_wzj)
img_with_points = draw_points(img_wzj, points)
fig() + image(img_with_points)

5.6.2 Visual expression control points

mouth_left = points[48]
mouth_right = points[54]
left_eyebrow = points[19]
right_eyebrow = points[24]

cust_points = [mouth_left, mouth_right, left_eyebrow, right_eyebrow]
img_with_points = draw_points(img_wzj, cust_points)
fig() + image(img_with_points)

5.6.3. Set the stretching function and make emoticons

warp_params = [
    [left_eyebrow, (0, -5), 35],
    [right_eyebrow, (0, -5), 35],
    [mouth_left, (-5, -5), 40],
    [mouth_right, (5, -5), 40]
]

sticker = make_sticker(img_wzj, warp_params)
fig() + gif(sticker)

5.6.4 Upload pictures and make your own emoticons

You can do this yourself, in fact, you don’t have to write it, just a url of a network map will do.

url = "https://xxxxx"
img_url = imread(url)