Merge pull request #233 from rudrajit1729/master

Added Hierarchical Clustering and Median Filtering

Author: master-fury

Image_Processing/src/Filters/src/median_filter/Median_Filter.c

@@ -0,0 +1,187 @@
+#include<stdio.h>
+#include<string.h>
+#include<math.h>
+#include<time.h>
+#define W_MAX 1
+#define ROW 512
+#define COL 512
+#define T1 15
+#define T2 25
+
+double P[50]; double img[700][700]; double orig[512][512];
+
+// Utility Function - Creates input image matrix
+double getImg(char *s){
+	FILE *fp;
+	int i, j, r, c; double d, MSE = 0, dim = ROW * COL;
+	fp = fopen(s, "r");
+	// Create Matrix
+	for(i = W_MAX; i < ROW+W_MAX; i++){
+		for(j = W_MAX; j < COL+W_MAX; j++){
+			fscanf(fp, "%lf ", &d);
+			img[i][j] = d;
+			MSE += pow((orig[i-W_MAX][j-W_MAX] - img[i][j]), 2);
+			// Padding
+			if (i == W_MAX){
+				for(r = i-1; r >= i-W_MAX; r--) img[r][j] = img[i][j];
+			}
+			if(i == W_MAX + ROW - 1){
+				for(r = i+1; r <= i+W_MAX; r++) img[r][j] = img[i][j];
+			}
+			if(j == W_MAX){
+				for(c = j-1; c >= j-W_MAX; c--) img[i][c] = img[i][j];
+			}
+			if(j == W_MAX + COL - 1){
+				for(c = j+1; c <= j+W_MAX; c++) img[i][c] = img[i][j];
+			}
+		}
+	}
+	// Corner Padding
+	// Upper Corners
+	for(i = 0; i < W_MAX; i++){
+		// Left Corner
+		for(j = 0; j < W_MAX; j++)
+			img[i][j] = img[W_MAX][W_MAX];
+		// Right Corner
+		for(j = W_MAX+ COL; j< W_MAX+COL+W_MAX;j++)
+			img[i][j] = img[W_MAX][W_MAX+COL-1];
+	}
+	// Lower Corners
+	for(i = W_MAX+ROW; i < W_MAX+ROW+W_MAX; i++){
+		// Left Corner
+		for(j = 0; j < W_MAX; j++)
+			img[i][j] = img[W_MAX+ROW-1][W_MAX];
+		// Right Corner
+		for(j = W_MAX+ COL; j< W_MAX+COL+W_MAX;j++)
+			img[i][j] = img[W_MAX+ROW-1][W_MAX+COL-1];
+	}
+
+	fclose(fp);
+	MSE /= dim;
+	return MSE;
+}
+
+// Utility Function - Saves output image
+double saveImg(char *s){
+	FILE *fp;
+	fp = fopen(s, "w");
+	// Change According to size
+	fprintf(fp, "P2 512 512 255\n");
+	int i, j; double MSE = 0, dim = ROW*COL;
+	for(i = W_MAX; i < ROW + W_MAX; i++){
+		for(j = W_MAX; j< COL + W_MAX; j++){
+			MSE += pow((orig[i-W_MAX][j-W_MAX] - img[i][j]), 2);
+			fprintf(fp, "%d ", (int)img[i][j]);
+		}
+	}
+	fclose(fp);
+	MSE /= dim;
+	return MSE;
+}
+
+// Calculates Structural Similarity Index of Images
+double getSSIM(){
+	double C1 = pow(0.01*255, 2), C2 = pow(0.03*255, 2), dim = ROW * COL;
+	double Vx = 0, Vy = 0, COV = 0, SSIM, o, e;
+	int i, j, ux = 0, uy = 0;
+	for(i = W_MAX; i < ROW + W_MAX; i++){
+		for(j = W_MAX; j< COL + W_MAX; j++){
+			ux += orig[i-W_MAX][j-W_MAX];
+			uy += img[i][j];			
+		}
+	}
+	ux /= dim; uy /= dim;
+	for(i = W_MAX; i < ROW + W_MAX; i++){
+		for(j = W_MAX; j< COL + W_MAX; j++){
+			o = orig[i-W_MAX][j-W_MAX];
+			e = img[i][j];
+			Vx += pow((o-ux),2);
+			Vy += pow((e-uy), 2);
+			COV += (o-ux)*(e-uy);
+		}
+	}
+	Vx /= dim; Vy /= dim;
+	COV /= dim;
+	SSIM = ((2*ux*uy + C1) * (2*COV + C2))/((pow(ux, 2) + pow(uy, 2) + C1) * (Vx + Vy + C2));
+	return SSIM;
+}
+
+// Utility - Returns median of first n numbers in P
+double Median(int n){
+	int i, d; double t, ans;
+	// Sort the array - Insertion sort
+	for(i = 1; i < n; i++){
+		d = i;
+		while (d > 0 && P[d] < P[d-1]){
+			t = P[d];
+			P[d] = P[d-1];
+			P[d-1] = t;
+			d--;
+		}
+	}
+	// If n odd return mid element
+	if (n&1)
+		ans = P[n/2];
+	// Else retuen
+	else
+		ans = (P[n/2 - 1] + P[n/2])/2;
+	return ans;
+}
+
+// Filter - Median Filtering
+double Filter(int r, int c){
+	int cnt = 0, i, j, w=1; double M;
+	for(i = r-w; i <= r+w; i++){
+			for(j = c-w; j <= c+w; j++){
+			P[cnt++] = img[i][j];
+		}
+	}
+	M = Median(cnt);
+	return M;
+}
+
+// Standard Median Filtering
+double SMF(char *s){
+	int i, j; double MSE;
+	for(i = W_MAX; i < ROW + W_MAX; i++){
+		for(j = W_MAX; j < COL + W_MAX; j++){
+			// if(img[i][j]==0 || img[i][j]==255)
+				img[i][j] = Filter(i, j);
+		}
+	}
+	// Metric Calculation
+	MSE = saveImg(s);
+	return MSE;
+}
+
+int main() {
+   int i, j; 
+   clock_t start, end; double CPU_TIME;
+   double MAXINT = pow(255, 2), RMSE, MSE1, MSE2, PSNR, d, IEF, SSIM;
+
+   // Get Original Image for PSNR calculation
+   FILE *fp;
+   fp = fopen("Original_Image.pgm", "r");
+   for(i = 0; i < ROW; i++){
+	   	for(j = 0; j < COL; j++){
+	   		fscanf(fp, "%lf ", &d);
+	   		orig[i][j] = d;
+	   	}
+   }
+   fclose(fp);
+
+   start = clock();
+   // Replace this with the src image name and the dest image name where the image needs to be saved
+   MSE1 = getImg("Src Image");
+   MSE2 = SMF("Dest Image");
+   end = clock();
+   CPU_TIME = ((double) (end - start)) / CLOCKS_PER_SEC;
+   // Peak Signal to Noise Ratio
+   PSNR = 10 * log10(MAXINT/MSE2);
+   // MSE1 (orig, noisy), MSE2 (orig, enhanced)
+   IEF = MSE1/MSE2;
+   RMSE = pow(MSE2, 0.5);
+   SSIM = getSSIM();
+   printf("RMSE = %.4lf\tPSNR = %.4lf\tSSIM = %lf\tIEF = %.4lf\tTIME = %.2lfs\n", RMSE, PSNR, SSIM, IEF, CPU_TIME);
+	}
+}

Image_Processing/src/Filters/src/median_filter/README.md

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+# Median Filtering on Image(SMF)
+Median Filtering is a neighborhood filtering technique used in order to remove noise from images and enhance its quality.
+
+Often during Image capturing and acquisition(specially in medical images) the image is disturbed by Salt and Pepper Noise(SPN)[Original pixel replaced by either maximum intenstiy pixel
+or minimum intensity pixel] which mainly occurs due to certain faults in sensors
+while capturing the image. Having noise in image makes it difficult for Computer Aided Detection(CAD). Nowadays, many Machine Learning and Deep Learning techniques are being applied on 
+medical images for computer aided diagnosis to reduce human error. Image Preprocessing is an important stage before the image can be fed to the model. Not restricting to that itself,
+Image Enhancement plays an important role in improving the quality of images and removing errors/noises from them.
+
+## Algorithm 
+The main idea of the median filter is to run through the signal entry by entry, replacing each entry with the median of neighboring entries. 
+The pattern of neighbors is called the "window", which slides, entry by entry, over the entire signal. For one-dimensional signals, the most obvious window is just the
+first few preceding and following entries, whereas for two-dimensional (or higher-dimensional) data the window 
+must include all entries within a given radius or ellipsoidal region (i.e. the median filter is not a separable filter).
+
+In Median filtering the edge detection becomes a bit difficult but that again is improved as we switch to fuzzy removal of noise. Median Filter is the most commonly used filter
+just for the fact that it is computationally faster than other existing techniques.
+
+## Metric Calculation
+The popular metrics for judging the quality of enhancement technique are - RMSE, PSNR, SSIM, & IEF. 
+
+These are statistical measures that judge the quality of output relying on data and mathematics. 
+
+Check on the links to have a brief idea about the concepts. In *Median_Filter.c* these concepts are applied for images where each pixel acts as a data point.
+
+1. Root Mean Squared Error(RMSE) - [Click To Know More](https://en.wikipedia.org/wiki/Root-mean-square_deviation)
+
+2. Peak Signal to Noise Ratio(PSNR) - [Click To Know More](https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio)
+
+3. Structural Similarity(SSIM) - [Click To Know More](https://en.wikipedia.org/wiki/Structural_similarity)
+
+4. Image Enhancement Factor(IEF) - [Click To Know More](https://in.mathworks.com/matlabcentral/answers/450377-how-to-calculate-enhancement-factor-for-an-image)
+
+## Results
+The SMF technique is used for removal of Salt and Pepper Noise but works well with other noises as well. SMF works well for upto 60% noise percentage. Above that it fails, new algorithms such as
+fuzzy median technique, Adaptive Weighted Mean Filtering technique and a lot more have been introduced as an add on of this algorithm and that works upto 85% noise.

Machine_Learning/src/Hierarchical Clustering/Dendogram.PNG

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+#Hierarchical Clustering
+
+#Importing the libraries
+import numpy as np
+import matplotlib.pyplot as plt
+import pandas as pd
+
+#Importing the mall dataset 
+dataset = pd.read_csv('Mall_Customers.csv')
+X = dataset.iloc[:,[3, 4]].values
+
+#Using the dendogram to find the optimal number of clusters
+import scipy.cluster.hierarchy  as sch
+dendogram = sch.dendrogram(sch.linkage(X, method = 'ward'))# ward method minimizes within cluster variance
+plt.title('Dendogram')
+plt.xlabel('Customers')
+plt.ylabel('Eucledian Distances')
+plt.show()
+
+#Fitting hierarchical clustering to the dataset
+from sklearn.cluster import AgglomerativeClustering
+hc = AgglomerativeClustering(n_clusters = 5, affinity = 'euclidean', linkage = 'ward')
+y_hc = hc.fit_predict(X)
+
+#Visualizing the clusters
+plt.scatter(X[y_hc==0, 0], X[y_hc==0, 1], s = 100, c = 'red', label = 'Careful')
+plt.scatter(X[y_hc==1, 0], X[y_hc==1, 1], s = 100, c = 'blue', label = 'Standard')
+plt.scatter(X[y_hc==2, 0], X[y_hc==2, 1], s = 100, c = 'green', label = 'Target')
+plt.scatter(X[y_hc==3, 0], X[y_hc==3, 1], s = 100, c = 'cyan', label = 'Careless')
+plt.scatter(X[y_hc==4, 0], X[y_hc==4, 1], s = 100, c = 'magenta', label = 'Sensible')
+plt.title('Cluster of Clients')
+plt.xlabel('Annual Income(k$)')
+plt.ylabel('Spending Score(1-100)')
+plt.legend()
+plt.show()
+'''Analysing the graph
+    RED - High income, low expenditure --> Careful
+    BLUE - Average income, average expenditure --> Standard
+    GREEN - High income, high expenditure --> Target
+    CYAN - Low income, high expenditure --> Careless
+    MAGENTA - Low income, low expenditure --> Sensible
+   Changing the labels from Cluster"i" to the respective tags
+'''