Image Processing Dimension Error

Here is the Question I am working on. Below is also the matlab code I have written, but towards the end I get an error talking about how the "index in position 2 exceeds array bounds". Any ideas?

%* Part A *%
% Translation vector
translation = [10; -25; 40];

% Euler angles representing the orientation (REPLACE THESE ANGLES)
theta_x = -1; % Angle around X-axis in radians
theta_y = 0.7; % Angle around Y-axis in radians
theta_z = -0.5; % Angle around Z-axis in radians

% Compute the rotation matrices
Rx = [1, 0, 0; 0, cos(theta_x), -sin(theta_x); 0, sin(theta_x), cos(theta_x)];
Ry = [cos(theta_y), 0, sin(theta_y); 0, 1, 0; -sin(theta_y), 0, cos(theta_y)];
Rz = [cos(theta_z), -sin(theta_z), 0; sin(theta_z), cos(theta_z), 0; 0, 0, 1];

% Combine the translation and rotation matrices
cW_H = [Rx * Ry * Rz, translation; 0, 0, 0, 1];

% Display the transformation matrix
disp("Part A")

Part A

cW_H

cW_H = 4×4

0.6712 0.3667 0.6442 10.0000 -0.7348 0.2143 0.6436 -25.0000 0.0980 -0.9053 0.4132 40.0000 0 0 0 1.0000

%* Part B *%
% Compute the inverse transformation matrix
wC_H = inv(cW_H);

% Display the inverse transformation matrix
disp("Part B")

Part B

wC_H

wC_H = 4×4

0.6712 -0.7348 0.0980 -28.9996 0.3667 0.2143 -0.9053 37.9032 0.6442 0.6436 0.4132 -6.8822 0 0 0 1.0000

%* Part C *%
% Image size
image_width = 256;
image_height = 170;

% Focal length in pixels
focal_length = 400;

% Image center coordinates
image_center_x = image_width / 2;
image_center_y = image_height / 2;

% Intrinsic camera calibration matrix K
K = [focal_length, 0, image_center_x; 0, focal_length, image_center_y; 0, 0, 1];

% Display the intrinsic matrix
disp("Part C")

Part C

K

K = 3×3

400 0 128 0 400 85 0 0 1

%*Part D *%
% Create blank image
image = zeros(image_height, image_width);

% Project the 7 points onto the image
points_world = [6.8158 -35.1954 43.0640; 
                7.8493 -36.1723 43.7815; 
                9.9579 -25.2799 40.1151;
                8.8219 -38.3767 46.6153;
                9.5890 -28.8402 42.2858;
                10.8082 -48.8164 56.2858;
                13.2690 -58.0988 59.1422;]

points_world = 7×3

6.8158 -35.1954 43.0640 7.8493 -36.1723 43.7815 9.9579 -25.2799 40.1151 8.8219 -38.3767 46.6153 9.5890 -28.8402 42.2858 10.8082 -48.8164 56.2858 13.2690 -58.0988 59.1422

points_world2 = transpose(points_world)

points_world2 = 3×7

6.8158 7.8493 9.9579 8.8219 9.5890 10.8082 13.2690 -35.1954 -36.1723 -25.2799 -38.3767 -28.8402 -48.8164 -58.0988 43.0640 43.7815 40.1151 46.6153 42.2858 56.2858 59.1422

points_camera = cW_H(1:3, 1:3) * points_world2 + cW_H(1:3, 4)

points_camera = 3×7

29.4118 30.2095 33.2570 31.8796 33.1022 35.6147 35.7028 -9.8336 -10.3405 -11.9156 -9.7036 -11.0104 -7.1761 -9.1348 90.3273 91.6095 80.4397 94.8716 84.5238 108.5139 118.3390

for i = 1:size(points_camera, 2)
    point_camera = points_camera(:, i);
    projected_point = K * point_camera;
    projected_point = round(projected_point ./ projected_point(3));
    x = abs(projected_point(1));
    y = abs(projected_point(2));
    image(y, x) = 255;  % Set pixel value to white
end

% Display the image with white dots
imshow(image);

% Define point indices for drawing lines
point_indices = [1, 2; 2, 3; 3, 4; 4, 1; 5, 6; 6, 7; 7, 8; 8, 5];

% Draw lines between the points
for i = 1:size(point_indices, 1)
    point1 = points_camera(:, point_indices(i, 1));
    point2 = points_camera(:, point_indices(i, 2));
    projected_point1 = K * point1;
    projected_point2 = K * point2;
    projected_point1 = round(projected_point1 ./ projected_point1(3));
    projected_point2 = round(projected_point2 ./ projected_point2(3));
    line_points = [projected_point1(1:2)'; projected_point2(1:2)'];
    image = insertShape(image, 'Line', line_points, 'LineWidth', 1, 'Color', 'white');
end

Index in position 2 exceeds array bounds. Index must not exceed 7.

% Show the resulting image
imshow(image);

Answer 1

[KSSV]

This line:

point_indices = [1, 2; 2, 3; 3, 4; 4, 1; 5, 6; 6, 7; 7, 8; 8, 5];

should have indices/ values which should be less than or equal to size(points_camera). Note that the dimesnions of size_camera are 3x7. Here in the lines

    point1 = points_camera(:, point_indices(i, 1));
    point2 = points_camera(:, point_indices(i, 2));

When you extract 7, 8 indices an error will be throws because there is no 8th index in points_camera.

[Zahryn Martinez]

Here is the updated code, but I am still getting the same error:

% Part A
% Translation vector
translation = [10; -25; 40]; 

% Euler angles representing the orientation (REPLACE THESE ANGLES)
theta_x = -1; % Angle around X-axis in radians
theta_y = 0.7; % Angle around Y-axis in radians
theta_z = -0.5; % Angle around Z-axis in radians 

% Compute the rotation matrices
Rx = [1, 0, 0; 0, cos(theta_x), -sin(theta_x); 0, sin(theta_x), cos(theta_x)];
Ry = [cos(theta_y), 0, sin(theta_y); 0, 1, 0; -sin(theta_y), 0, cos(theta_y)];
Rz = [cos(theta_z), -sin(theta_z), 0; sin(theta_z), cos(theta_z), 0; 0, 0, 1]; 

% Combine the translation and rotation matrices
cW_H = [Rx * Ry * Rz, translation; 0, 0, 0, 1]; 

% Display the transformation matrix
disp("Part A")
disp(cW_H)

% Part B
% Compute the inverse transformation matrix
wC_H = inv(cW_H); 

% Display the inverse transformation matrix
disp("Part B")
disp(wC_H)

% Part C
% Image size
image_width = 256;
image_height = 170; 

% Focal length in pixels
focal_length = 400; 

% Image center coordinates
image_center_x = image_width / 2;
image_center_y = image_height / 2; 

% Intrinsic camera calibration matrix K
K = [focal_length, 0, image_center_x; 0, focal_length, image_center_y; 0, 0, 1]; 

% Display the intrinsic matrix
disp("Part C")
disp(K)

% Part D
% Create blank image
image = zeros(image_height, image_width); 

% Project the 7 points onto the image
points_world = [6.8158, -35.1954, 43.0640; 
                7.8493, -36.1723, 43.7815; 
                9.9579, -25.2799, 40.1151;
                8.8219, -38.3767, 46.6153;
                9.5890, -28.8402, 42.2858;
                10.8082, -48.8164, 56.2858;
                13.2690, -58.0988, 59.1422];
points_camera = (cW_H(1:3, 1:3) * points_world' + cW_H(1:3, 4))';

for i = 1:size(points_camera, 1)
    point_camera = points_camera(i, :);
    projected_point = K * point_camera';
    projected_point = round(projected_point ./ projected_point(3));
    x = projected_point(1);
    y = projected_point(2);
    image(y, x) = 255;  % Set pixel value to white
end 

% Display the image with white dots
disp("Part D")
imshow(image); 

% Part E
% Define point indices for drawing lines
point_indices = [1, 2; 2, 3; 3, 4; 4, 1; 5, 6; 6, 7; 7, 8; 8, 5]; 

% Draw lines between the points
for i = 1:size(point_indices, 1)
    point1 = points_camera(point_indices(i, 1), :);
    point2 = points_camera(point_indices(i, 2), :);
    projected_point1 = K * point1';
    projected_point2 = K * point2';
    projected_point1 = round(projected_point1 ./ projected_point1(3));
    projected_point2 = round(projected_point2 ./ projected_point2(3));
    line_points = [projected_point1(1:2)'; projected_point2(1:2)'];
    image = insertShape(image, 'Line', line_points, 'LineWidth', 1, 'Color', 'white');
end 

% Show the resulting image
disp("Part E")
imshow(image);