Various fixes and improvements

Assignment_2/Image2Graph.m

@@ -11,9 +11,12 @@ function myAffinityMat = Image2Graph (imIn)
     imageHeight = size(imIn, 1);
     imageChannels = size(imIn, 3);
     
+    % Produces the matrix
     singleLineTransform = reshape(imIn, 1, [], imageChannels);
-    diff = repmat(singleLineTransform, imageWidth * imageHeight, 1, 1) - ...
+    myAffinityMat = 1 ./ exp( ...
-        permute(singleLineTransform, [2 1 3]);
+        sum((   ...
-    dist = sum(diff .^ 2, 3) .^ 0.5;
+        repmat(singleLineTransform, imageWidth * imageHeight, 1, 1) - ...
-    myAffinityMat = 1 ./ exp(dist);
+        permute(singleLineTransform, [2 1 3])) ...
+        .^ 2, 3) ...
+        .^ 0.5);
 end

Assignment_2/calculateNcut.m

@@ -1,8 +1,8 @@
 function nCutValue = calculateNcut (anAffinityMat , clusterIdx)
-%Implementation the NCut metric calculation
+%Calculation of the NCut metric
 %   Usage nCutValue = calculateNcut (anAffinityMat , clusterIdx), where:
 %       Inputs
-%       - anAffinityMat is a rectagular, symmetrical affinity matrix
+%       - anAffinityMat is a rectangular, symmetrical affinity matrix
 %           representation of an image
 %       - clusterIdx is a vector storing the cluster Id of each node
 %       Output
@@ -11,15 +11,17 @@ function nCutValue = calculateNcut (anAffinityMat , clusterIdx)
     % Gets the unique cluster IDs
     clusterIds = unique(clusterIdx);
     if size(clusterIds, 1) ~= 2
-        error('Too many different clusters! Number of clusters should be two');
+        error('Too many different clusters! Number of clusters must be two');
     end
 
+    % Finds the indices of the samples of each cluster
     clusterOneIndices = (clusterIdx == clusterIds(1));
     clusterTwoIndices = (clusterIdx == clusterIds(2));
 
+    % Calculates the N-Cut metric
     nCutValue = 2 - ...
-        (sum(sum(anAffinityMat(clusterOneIndices, clusterOneIndices'))) / ...
+        (sum(sum(anAffinityMat(clusterOneIndices, clusterOneIndices))) / ...
         sum(sum(anAffinityMat(clusterOneIndices, :))) + ...
-        sum(sum(anAffinityMat(clusterTwoIndices, clusterTwoIndices'))) / ...
+        sum(sum(anAffinityMat(clusterTwoIndices, clusterTwoIndices))) / ...
         sum(sum(anAffinityMat(clusterTwoIndices, :))));
 end

Assignment_2/demo1.m

@@ -1,3 +1,4 @@
+%% Initialization
 clear
 clear all
 
@@ -6,20 +7,27 @@ rng(1);
 
 load('dip_hw_2.mat');
 
+%% Executes experiments for the affinity matrix
+% Clustering into two clusters
 clusters = mySpectralClustering(d1a, 2);
+
+% Presents results
 clusters = clusters ./ 2;
-%clusters = reshape(clusters, 4, []);
 figure();
-imshow(clusters);
+imshow(clusters');
 
+% Clustering into three clusters
 clusters = mySpectralClustering(d1a, 3);
+
+% Presents results
 clusters = clusters ./ 3;
-%clusters = reshape(clusters, 4, []);
 figure();
-imshow(clusters);
+imshow(clusters');
 
+% Clustering into four clusters
 clusters = mySpectralClustering(d1a, 4);
+
+% Presents results
 clusters = clusters ./ 4;
-%clusters = reshape(clusters, 4, []);
 figure();
-imshow(clusters);
+imshow(clusters');

Assignment_2/demo2.m

@@ -1,3 +1,4 @@
+%% Initialization
 clear
 clear all
 
@@ -14,19 +15,28 @@ graph2 = Image2Graph(d2b);
 figure();
 imshow(d2a);
 
+% Clustering into two clusters
 clusters = mySpectralClustering(graph1, 2);
+
+% Presents results
 clusters = clusters ./ 2;
 clusters = reshape(clusters, size(d2a, 1), []);
 figure();
 imshow(clusters);
 
+% Clustering into three clusters
 clusters = mySpectralClustering(graph1, 3);
+
+% Presents results
 clusters = clusters ./ 3;
 clusters = reshape(clusters, size(d2a, 1), []);
 figure();
 imshow(clusters);
 
+% Clustering into four clusters
 clusters = mySpectralClustering(graph1, 4);
+
+% Presents results
 clusters = clusters ./ 4;
 clusters = reshape(clusters, size(d2a, 1), []);
 figure();
@@ -36,26 +46,35 @@ imshow(clusters);
 figure();
 imshow(d2b);
 
+% Clustering into two clusters
 clusters = mySpectralClustering(graph2, 2);
+
+% Presents results
 figure();
 imshow(meanClustersColorRGB(d2b, reshape(clusters, size(d2b, 1), [])));
-% clusters = clusters ./ 2;
+clusters = clusters ./ 2;
-% clusters = reshape(clusters, size(d2a, 1), []);
+clusters = reshape(clusters, size(d2a, 1), []);
-% figure();
+figure();
-% imshow(clusters);
+imshow(clusters);
 
+% Clustering into three clusters
 clusters = mySpectralClustering(graph2, 3);
+
+% Presents results
 figure();
 imshow(meanClustersColorRGB(d2b, reshape(clusters, size(d2b, 1), [])));
-% clusters = clusters ./ 3;
+clusters = clusters ./ 3;
-% clusters = reshape(clusters, size(d2a, 1), []);
+clusters = reshape(clusters, size(d2a, 1), []);
-% figure();
+figure();
-% imshow(clusters);
+imshow(clusters);
 
+% Clustering into four clusters
 clusters = mySpectralClustering(graph2, 4);
+
+% Presents results
 figure();
 imshow(meanClustersColorRGB(d2b, reshape(clusters, size(d2b, 1), [])));
-% clusters = clusters ./ 4;
+clusters = clusters ./ 4;
-% clusters = reshape(clusters, size(d2a, 1), []);
+clusters = reshape(clusters, size(d2a, 1), []);
-% figure();
+figure();
-% imshow(clusters);
+imshow(clusters);

Assignment_2/demo3a.m

@@ -1,3 +1,4 @@
+%% Initialization
 clear
 clear all
 
@@ -14,19 +15,28 @@ graph2 = Image2Graph(d2b);
 figure();
 imshow(d2a);
 
+% Clustering into two clusters
 clusters = myNCuts(graph1, 2);
+
+% Presents results
 clusters = clusters ./ 2;
 clusters = reshape(clusters, size(d2a, 1), []);
 figure();
 imshow(clusters);
 
+% Clustering into three clusters
 clusters = myNCuts(graph1, 3);
+
+% Presents results
 clusters = clusters ./ 3;
 clusters = reshape(clusters, size(d2a, 1), []);
 figure();
 imshow(clusters);
 
+% Clustering into four clusters
 clusters = myNCuts(graph1, 4);
+
+% Presents results
 clusters = clusters ./ 4;
 clusters = reshape(clusters, size(d2a, 1), []);
 figure();
@@ -36,26 +46,35 @@ imshow(clusters);
 figure();
 imshow(d2b);
 
+% Clustering into two clusters
 clusters = myNCuts(graph2, 2);
+
+% Presents results
 figure();
 imshow(meanClustersColorRGB(d2b, reshape(clusters, size(d2b, 1), [])));
-% clusters = clusters ./ 2;
+clusters = clusters ./ 2;
-% clusters = reshape(clusters, size(d2a, 1), []);
+clusters = reshape(clusters, size(d2a, 1), []);
-% figure();
+figure();
-% imshow(clusters);
+imshow(clusters);
 
+% Clustering into three clusters
 clusters = myNCuts(graph2, 3);
+
+% Presents results
 figure();
 imshow(meanClustersColorRGB(d2b, reshape(clusters, size(d2b, 1), [])));
-% clusters = clusters ./ 3;
+clusters = clusters ./ 3;
-% clusters = reshape(clusters, size(d2a, 1), []);
+clusters = reshape(clusters, size(d2a, 1), []);
-% figure();
+figure();
-% imshow(clusters);
+imshow(clusters);
 
+% Clustering into four clusters
 clusters = myNCuts(graph2, 4);
+
+% Presents results
 figure();
 imshow(meanClustersColorRGB(d2b, reshape(clusters, size(d2b, 1), [])));
-% clusters = clusters ./ 4;
+clusters = clusters ./ 4;
-% clusters = reshape(clusters, size(d2a, 1), []);
+clusters = reshape(clusters, size(d2a, 1), []);
-% figure();
+figure();
-% imshow(clusters);
+imshow(clusters);

Assignment_2/demo3b.m

@@ -1,3 +1,4 @@
+%% Initialization
 clear
 clear all
 
@@ -17,6 +18,7 @@ imshow(d2a);
 clusters = myNCuts(graph1, 2);
 NCut1 = calculateNcut(graph1, clusters);
 
+% Presents results
 clusters = clusters - 1;
 clusters = reshape(clusters, size(d2a, 1), []);
 figure();
@@ -29,6 +31,7 @@ imshow(d2b);
 clusters = myNCuts(graph2, 2);
 NCut2 = calculateNcut(graph2, clusters);
 
+% Presents results
 figure();
 imshow(meanClustersColorRGB(d2b, reshape(clusters, size(d2b, 1), [])));
 

Assignment_2/demo3c.m

@@ -1,3 +1,4 @@
+%% Initialization
 clear
 clear all
 
@@ -15,19 +16,52 @@ figure();
 imshow(d2a);
 
 clusters = recursiveNCuts(graph1);
-clusters = clusters ./ 2;
+
+% Presents results
 clusters = reshape(clusters, size(d2a, 1), []);
+clustersR = clusters;
+clustersG = clusters;
+clustersB = clusters;
+
+for cluster = 1:size(unique(clusters), 1)
+    clustersR(clusters == cluster) = rand;
+    clustersG(clusters == cluster) = rand;
+    clustersB(clusters == cluster) = rand;
+end
+clusters(:, :, 1) = clustersR;
+clusters(:, :, 2) = clustersG;
+clusters(:, :, 3) = clustersB;
+
 figure();
 imshow(clusters);
 
+clearvars clustersR clustersG clustersB cluster
+
 %% Executes recursive experiments for the second image
 figure();
 imshow(d2b);
 
 clusters = recursiveNCuts(graph2);
+
+% Presents results
+clusters = reshape(clusters, size(d2b, 1), []);
 figure();
-imshow(meanClustersColorRGB(d2b, reshape(clusters, size(d2b, 1), [])));
+imshow(meanClustersColorRGB(d2b, clusters));
-% clusters = clusters ./ 2;
+
-% clusters = reshape(clusters, size(d2a, 1), []);
+clustersR = clusters;
-% figure();
+clustersG = clusters;
-% imshow(clusters);
+clustersB = clusters;
+
+for cluster = 1:size(unique(clusters), 1)
+    clustersR(clusters == cluster) = rand;
+    clustersG(clusters == cluster) = rand;
+    clustersB(clusters == cluster) = rand;
+end
+clusters(:, :, 1) = clustersR;
+clusters(:, :, 2) = clustersG;
+clusters(:, :, 3) = clustersB;
+
+figure();
+imshow(clusters);
+
+clearvars clustersR clustersG clustersB cluster

Assignment_2/meanClustersColorRGB.m

@@ -1,28 +1,37 @@
-function segIm = meanClustersColorRGB(image, clusters)
+function coloredIm = meanClustersColorRGB(image, clusters)
-%MEANCLUSTERSCOLOR Summary of this function goes here
+%meanClustersColorRGB assigns the mean color of each cluster to the cluster
-%   Detailed explanation goes here
+%   Usage coloredIm = meanClustersColorRGB (image, clusters), where:
+%       Inputs
+%       - image is the original image
+%       - clusters is a matrix of the same dimensions as the image that
+%           holds the cluster ID of each pixel
+%       Output
+%       - coloredIm is the image produced by assigning the mean color of
+%           each cluster to the cluster's pixels
 
+    % Initializes helper variables
     redChannel = image(:, :, 1);
     greenChannel = image(:, :, 2);
     blueChannel = image(:, :, 3);
 
-    segImR = clusters;
+    coloredImR = clusters;
-    segImG = clusters;
+    coloredImG = clusters;
-    segImB = clusters;
+    coloredImB = clusters;
 
+    % Assigns the mean color to each cluster
     for cluster = 1:max(max(clusters))
         meanR = mean(redChannel(clusters == cluster));
         meanG = mean(greenChannel(clusters == cluster));
         meanB = mean(blueChannel(clusters == cluster));
 
-        segImR(clusters == cluster) = meanR;
+        coloredImR(clusters == cluster) = meanR;
-        segImG(clusters == cluster) = meanG;
+        coloredImG(clusters == cluster) = meanG;
-        segImB(clusters == cluster) = meanB;
+        coloredImB(clusters == cluster) = meanB;
     end
 
-    segIm = zeros(size(image, 1), size(image, 2), 3);
+    coloredIm = zeros(size(image, 1), size(image, 2), 3);
-    segIm(:, :, 1) = segImR;
+    coloredIm(:, :, 1) = coloredImR;
-    segIm(:, :, 2) = segImG;
+    coloredIm(:, :, 2) = coloredImG;
-    segIm(:, :, 3) = segImB;
+    coloredIm(:, :, 3) = coloredImB;
 end
 

Assignment_2/myNCuts.m

@@ -2,18 +2,25 @@ function clusterIdx = myNCuts (anAffinityMat, k)
 %Implementation of the N-cuts algorithm
 %   Usage clusterIdx = myNCuts (anAffinityMat, k), where:
 %       Inputs
-%       - anAffinityMat is a rectagular, symmetrical affinity matrix
+%       - anAffinityMat is a rectangular, symmetrical affinity matrix
 %           representation of an image
 %       - k is the desired number of clusters
 %       Output
 %       - clusterIdx is a vector storing the cluster Id of each node
 
+    % Makes sure preconditions are met
     if ~issymmetric(anAffinityMat)
         error('The affinity matrix provided is not symmetric.');
     end
+    if k < 2
+        error('The number of clusters must be greater than two.');
+    end
 
+    % Calculates the eigenvectors
     D = diag(sum(anAffinityMat, 2));
-    L = D - anAffinityMat;
+    [eigenvectorsMatrix, ~] = eigs(double(D - anAffinityMat), double(D), ...
-    [eigenvectorsMatrix, ~] = eigs(double(L), double(D), k, 'sm');
+        k, 'sm');
+    
+    % Does the clustering using K-Means
     clusterIdx = kmeans(eigenvectorsMatrix, k);
 end

Assignment_2/mySpectralClustering.m

@@ -2,17 +2,24 @@ function clusterIdx = mySpectralClustering (anAffinityMat, k)
 %Implementation of spectral clustering
 %   Usage clusterIdx = mySpectralClustering (anAffinityMat, k), where:
 %       Inputs
-%       - anAffinityMat is a rectagular, symmetrical affinity matrix
+%       - anAffinityMat is a rectangular, symmetrical affinity matrix
 %           representation of an image
 %       - k is the desired number of clusters
 %       Output
 %       - clusterIdx is a vector storing the cluster Id of each node
 
+    % Makes sure preconditions are met
     if ~issymmetric(anAffinityMat)
         error('The affinity matrix provided is not symmetric.');
     end
+    if k < 2
+        error('The number of clusters must be greater than two.');
+    end
+
+    % Calculates the eigenvectors
+    [eigenvectorsMatrix, ~] = eigs(double( ...
+        diag(sum(anAffinityMat, 2)) - anAffinityMat), k, 'sm');
     
-    L = diag(sum(anAffinityMat, 2)) - anAffinityMat;
+    % Does the clustering using K-Means
-    [eigenvectorsMatrix, ~] = eigs(double(L), k, 'sm');
     clusterIdx = kmeans(eigenvectorsMatrix, k);
 end

Assignment_2/recursiveNCuts.m

@@ -1,26 +1,43 @@
-function clusters = recursiveNCuts(graph)
+function clusterIdx = recursiveNCuts(anAffinityMat)
-%RECURSIVENCUTS Summary of this function goes here
+%Implementation of the recursive N-cuts algorithm
-%   Detailed explanation goes here
+%   Usage clusters = recursiveNCuts (anAffinityMat), where:
+%       Inputs
+%       - anAffinityMat is a rectangular, symmetrical affinity matrix
+%           representation of an image
+%       Output
+%       - clusterIdx is a vector storing the cluster Id of each node
 
-    clusters = myNCuts(graph, 2);
+    % Makes sure preconditions are met
+    if ~issymmetric(anAffinityMat)
+        error('The affinity matrix provided is not symmetric.');
+    end
+
+    % Executes clustering using N-Cuts algorithm
+    clusterIdx = myNCuts(anAffinityMat, 2);
     
-    if (nnz(clusters == 1) < 5 || nnz(clusters == 2) < 5)
+    % Checks stop conditions
+    if (nnz(clusterIdx == 1) < 5 || nnz(clusterIdx == 2) < 5)
         return;
     end
-    
+    NCut = calculateNcut(anAffinityMat, clusterIdx);
-    NCut = calculateNcut(graph, clusters);
     if (NCut > 0.85)
         return;
     end
     
-    clusterOneIndices = (clusters == 1);
+    % Finds indices of each cluster
-    clusterTwoIndices = (clusters == 2);
+    clusterOneIndices = (clusterIdx == 1);
+    clusterTwoIndices = (clusterIdx == 2);
     
-    firstSubClusters = recursiveNCuts(graph(clusterOneIndices, clusterOneIndices'));
+    % Recursively calls itself for each part of the matrix
-    secondSubClusters = recursiveNCuts(graph(clusterTwoIndices, clusterTwoIndices'));
+    firstSubClusters = recursiveNCuts(anAffinityMat(clusterOneIndices, ...
+        clusterOneIndices));
+    secondSubClusters = recursiveNCuts(anAffinityMat(clusterTwoIndices, ...
+        clusterTwoIndices));
     
+    % Makes sure the IDs of the clusters of each half are unique
     secondSubClusters = secondSubClusters + size(unique(firstSubClusters), 1);
     
-    clusters(clusterOneIndices) = firstSubClusters;
+    % Re-merges the sub-cluster arrays
-    clusters(clusterTwoIndices) = secondSubClusters;
+    clusterIdx(clusterOneIndices) = firstSubClusters;
+    clusterIdx(clusterTwoIndices) = secondSubClusters;
 end