All codes

Author: cxy1997

Project 1/Problem1.pdf

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+clc;clear;
+%% Write a computer program for computing the histogram of an image.
+fig1 = imread('data/Fig1.jpg');
+fig2 = imread('data/Fig2.jpg');
+figure('Name', 'Original Histogram');
+set(gcf, 'position', [0 0 1024 512]);
+subplot(1, 2, 1);
+[L1 D1] = myImhist(fig1);
+title('Fig 1');
+subplot(1, 2, 2);
+[L2 D2] = myImhist(fig2);
+title('Fig 2');
+
+%% Implement the histogram equalization technique.
+figure('Name', 'Transformation of Fig. 1');
+set(gcf, 'position', [0 0 960 512]);
+subplot(1, 2, 1);
+imshow(fig1, []);
+R1 = myEqualization(L1, D1);
+for i = 1:size(fig1, 1)
+    for j = 1:size(fig1, 2)
+        fig1(i, j) = R1(fig1(i, j) + 1);
+    end
+end
+subplot(1, 2, 2);
+imshow(fig1, []);
+
+figure('Name', 'Transformation of Fig. 2');
+set(gcf, 'position', [0 0 1024 512]);
+subplot(1, 2, 1);
+imshow(fig2, []);
+R2 = myEqualization(L2, D2);
+for i = 1:size(fig2, 1)
+    for j = 1:size(fig2, 2)
+        fig2(i, j) = R2(fig2(i, j) + 1);
+    end
+end
+subplot(1, 2, 2);
+imshow(fig2, []);
+
+figure('Name', 'Transformation Function');
+subplot(1, 2, 1);
+plot(R1);
+subplot(1, 2, 2);
+plot(R2);
+
+figure('Name', 'Equalized Histogram');
+set(gcf, 'position', [0 0 1024 512]);
+subplot(1, 2, 1);
+[L1 D1] = myImhist(fig1);
+%title('Fig 1');
+subplot(1, 2, 2);
+[L2 D2] = myImhist(fig2);
+%title('Fig 2');

Project 1/src/Histogram_Equalization.m

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+function [ output_distribution ] = myEqualization( L, distribution )
+%MYEQUALIZATION equalizes the histogram
+%   It returns a mapping that equalizes the original distribution
+
+    output_distribution = distribution;
+    for i = 2:size(distribution);
+        output_distribution(i) = output_distribution(i-1) + distribution(i);
+    end
+    output_distribution = output_distribution * (L - 1) / sum(distribution(:));
+
+
+end
+

Project 1/src/data/Fig1.jpg

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+function [ L, distribution ] = myImhist( fig )
+%MYIMHIST creates the histogram of a given image.
+%   The function returns the number of pixels for each gray level, 
+%   and draws a figure automatically.
+    L = 8;
+    if L <= max(max(fig))
+        L = 256;
+    end
+    distribution = zeros(L, 1);
+    for i = 1:size(fig, 1)
+        for j = 1:size(fig, 2)
+            distribution(fig(i, j) + 1, 1) = distribution(fig(i, j) + 1, 1) + 1;
+        end
+    end
+    % distribution = table(:, 2);
+    distribution = distribution ./ size(fig, 1) ./ size(fig, 2)
+    s = size(distribution);
+    b = bar(distribution,'FaceColor', 'blue', 'EdgeColor', 'blue','LineWidth',0.6);
+    set(gca,'XLim',[0 L]);
+    set(gca,'XTick',[0:L/4:L]);
+    set(gca,'XTickLabel',[0:L/4:L]);
+    ylabel('Occurance');
+    colormap(gray);
+    c = colorbar('Location', 'southoutside', 'FontSize',10, 'Ticks', 0:64:256, 'TickLabels', {'0', '64', '128', '192', '256'});
+    c.Label.String = 'Intensity';
+    
+
+end
+

Project 1/src/data/Fig2.jpg

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+clc; clear;
+%% Read the original image
+% (a) The original image
+fig_original = double(imread('data/skeleton_orig.tif')) / 255;
+figure;
+subplot(2, 4, 1);
+imshow(fig_original);
+imwrite(fig_original, 'data/skeleton_orig.png');
+
+% (b) The Laplacian of the original image
+laplace_result = imfilter([-1 -1 -1; -1 8 -1; -1 -1 -1], fig_original);
+subplot(2, 4, 2);
+imshow(remap(laplace_result, 0, 1));
+imwrite(remap(laplace_result, 0, 1), 'data/laplace_result.png');
+
+% (c) The sharpened image using Laplacian
+sharpened_laplace_result = fig_original + laplace_result;
+subplot(2, 4, 3);
+imshow(sharpened_laplace_result);
+imwrite(sharpened_laplace_result, 'data/sharpened_laplace_result.png');
+
+% (d) The Sobel gradient of the original image
+sobel_grad = abs(imfilter([-1 -2 -1; 0 0 0; 1 2 1], fig_original)) + abs(imfilter([-1 0 1; -2 0 2; -1 0 1], fig_original));
+subplot(2, 4, 4);
+imshow(sobel_grad);
+imwrite(sobel_grad, 'data/sobel_grad.png');
+
+% (e) The smoothed Sobel gradient
+smoothed_sobel_grad = imfilter(ones(5)/25, sobel_grad);
+subplot(2, 4, 5);
+imshow(smoothed_sobel_grad);
+imwrite(smoothed_sobel_grad, 'data/smoothed_sobel_grad.png');
+
+% (f) Mask image formed by the product of (c) and (e)
+product_laplace_sobel = sharpened_laplace_result .* smoothed_sobel_grad;
+subplot(2, 4, 6);
+imshow(product_laplace_sobel);
+imwrite(product_laplace_sobel, 'data/product_laplace_sobel.png');
+
+% (g) Sharpened image obtained by the sum of (a) and (f)
+sharpened_image = max(fig_original + product_laplace_sobel, 0);
+subplot(2, 4, 7);
+imshow(sharpened_image);
+imwrite(sharpened_image, 'data/sharpened_image.png');
+
+% (h) Final result obtained by applying a powerlaw transformation to (g)
+final_result = power(sharpened_image, 0.5);
+subplot(2, 4, 8);
+imshow(final_result);
+imwrite(final_result, 'data/final_result.png');

Project 1/src/myEqualization.m

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+function [ g ] = imfilter( w, x )
+%IMFILTER conducts the filter operation given filter w and matrix x
+%   Paddings are automatically computered, with stepsize = 1.
+    [h_x, w_x] = size(x);
+    [h_w, w_w] = size(w);
+    h_w_half = (h_w - 1) / 2;
+    w_w_half = (w_w - 1) / 2;
+    g = zeros(h_x, w_x);
+    for i = 1 : h_x
+        for j = 1 : w_x
+            g(i, j) = 0;
+            for k = -h_w_half : h_w_half
+                for l = -w_w_half : w_w_half
+                    if i + k > 0 && i + k <= h_x && j + l > 0 && j + l <= w_x
+                        g(i, j) = g(i, j) + w(k + h_w_half + 1, l + w_w_half + 1) * x(i + k, j + l);
+                    end
+                end
+            end
+        end
+    end
+end
+

Project 1/src/myImhist.m

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+function [ output ] = remap( input, lb, ub )
+%REMAP remaps a matrix to the interval [lb, ub]
+%   lb = lower bound, ub = upper bound
+    if max(max(input)) ~= min(min(input))
+        output = (input - min(min(input))) / (max(max(input)) - min(min(input))) * (ub - lb) + lb;
+    else
+        output = input - input + (ub + lb) / 2;
+    end
+end
+

Project 2/problem2.pdf

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+function [ output ] = butterworth_highpass_filter( m, n, D0, N )
+%BUTTERWORTH_HIGHPASS_FILTER The Butterworth highpass filter
+%   H(u, v) = 1 - (1 / (1 + (D(u, v) / D0)^2n))
+    u = [0:(m-1) -m:-1];
+    v = [0:(n-1) -n:-1];
+    [V, U] = meshgrid(v, u);
+    D = sqrt((V.^2 + U.^2));
+    output = 1 - (1 ./ (1 + (D ./ D0).^(2 * N)));
+end
+

Project 2/src/data/final_result.png

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+function [ output ] = butterworth_lowpass_filter( m, n, D0, N )
+%BUTTERWORTH_LOWPASS_FILTER The Butterworth lowpass filter
+%   H(u, v) = 1 / (1 + (D(u, v) / D0)^2n)
+    u = [0:(m-1) -m:-1];
+    v = [0:(n-1) -n:-1];
+    [V, U] = meshgrid(v, u);
+    D = sqrt((V.^2 + U.^2));
+    output = 1 ./ (1 + (D ./ D0).^(2 * N));
+end
+