Fuzzy C-Means聚合算法在图像分割(segmentation)和图像视觉处理中常常被用到聚合算法之
一本文是完全基于JAVA语言实现Fuzzy C-Means聚合算法，并可以运用到图像处理中实现简
单的对象提取。
一：数学原理
在解释数学原理之前，请先看看这个链接算是热身吧
http://home.deib.polimi.it/matteucc/Clustering/tutorial_html/cmeans.html。
看不懂没关系。我的解释足够详细，小学毕业都可以学会，本人就是小学毕业。
Fuzzy C-means算法主要是比较RGB空间的每个像素值与Cluster中的每个中心点值，最终给
每个像素指派一个值(0~1之间)说明该像素更接近于哪里Cluster的中心点，模糊规则是该像
素对所有cluster的值之和为1。简单的举例：假设图像中有三个聚类cluster1，cluster2，cluster3，
像素A对三个聚类的值分别为a1, a2, a3, 根据模糊规则a1 + a2 + a3 = 1。更进一步，如果a1
最大，则该像素比较接近于Cluster1。计算总的对象值J：
二：算法流程
初始输入参数:
a. 指定的聚类个数numberOfClusters,
b. 指定的最大循环次数maxIteration
c. 指定的最小终止循环差值deltaValue
大致流程如下：
1. 初始化所有像素点值与随机选取每个Cluster的中心点，初始化每个像素点P[i]对应
Cluster的模糊值p[i][k]并计算cluster index。
2. 计算对象值J
3. 计算每个Cluster的颜色值，产生新的图像像素
4. 计算每个像素的对应每个cluster的模糊值，更新每个像素的Cluster Index
5. 再次计算对象值J，并与第二步的对象值相减，如果差值小于deltaValue或者达到最大
循环数，停止计算输出结果图像，否则继续2 ～ 4
三：关键代码解析
欧几里德距离计算方法如下：
private double calculateEuclideanDistance(ClusterPoint p, ClusterCentroid c) { // int pa = (p.getPixelColor() >> 24) & 0xff; int pr = (p.getPixelColor() >> 16) & 0xff; int pg = (p.getPixelColor() >> 8) & 0xff; int pb = p.getPixelColor() & 0xff; // int ca = (c.getPixelColor() >> 24) & 0xff; int cr = (c.getPixelColor() >> 16) & 0xff; int cg = (c.getPixelColor() >> 8) & 0xff; int cb = c.getPixelColor() & 0xff; return Math.sqrt(Math.pow((pr - cr), 2.0) + Math.pow((pg - cg), 2.0) + Math.pow((pb - cb), 2.0)); }计算每个像素与每个Cluster的Fuzzy数值的代码如下：
public void stepFuzzy() { for (int c = 0; c < this.clusters.size(); c++) { for (int h = 0; h < this.points.size(); h++) { double top; top = calculateEuclideanDistance(this.points.get(h), this.clusters.get(c)); if (top < 1.0) top = Eps; // sumTerms is the sum of distances from this data point to all clusters. double sumTerms = 0.0; for (int ck = 0; ck < this.clusters.size(); ck++) { sumTerms += top / calculateEuclideanDistance(this.points.get(h), this.clusters.get(ck)); } // Then the membership value can be calculated as... fuzzyForPixels[h][c] = (double)(1.0 / Math.pow(sumTerms, (2 / (this.fuzzy - 1)))); } }; this.recalculateClusterMembershipValues(); }计算并更新每个像素的Cluster index的代码如下：
private void recalculateClusterMembershipValues() { for (int i = 0; i < this.points.size(); i++) { double max = 0.0; double min = 0.0; double sum = 0.0; double newmax = 0; ClusterPoint p = this.points.get(i); //Normalize the entries for (int j = 0; j < this.clusters.size(); j++) { max = fuzzyForPixels[i][j] > max ? fuzzyForPixels[i][j] : max; min = fuzzyForPixels[i][j] < min ? fuzzyForPixels[i][j] : min; } //Sets the values to the normalized values between 0 and 1 for (int j = 0; j < this.clusters.size(); j++) { fuzzyForPixels[i][j] = (fuzzyForPixels[i][j] - min) / (max - min); sum += fuzzyForPixels[i][j]; } //Makes it so that the sum of all values is 1 for (int j = 0; j < this.clusters.size(); j++) { fuzzyForPixels[i][j] = fuzzyForPixels[i][j] / sum; if (Double.isNaN(fuzzyForPixels[i][j])) { fuzzyForPixels[i][j] = 0.0; } newmax = fuzzyForPixels[i][j] > newmax ? fuzzyForPixels[i][j] : newmax; } // ClusterIndex is used to store the strongest membership value to a cluster, used for defuzzification p.setClusterIndex(newmax); }; }四：运行效果
五：算法源代码
FuzzyCMeansProcessor - 算法类
package com.gloomyfish.segmentation.fuzzycmeans; import java.awt.image.BufferedImage; import java.util.ArrayList; import java.util.List; import java.util.Random; import com.gloomyfish.filter.study.AbstractBufferedImageOp; public class FuzzyCMeansProcessor extends AbstractBufferedImageOp { private List<ClusterPoint> points; private List<ClusterCentroid> clusters; private BufferedImage originalImage; private BufferedImage processedImage; private double Eps = Math.pow(10, -5); private double[][] fuzzyForPixels; // Gets or sets objective function private double numObj; public void setObj(double j) { this.numObj = j; } public double getObj() { return this.numObj; } private float fuzzy; // default is 2 private int numCluster; // number of clusters in image public BufferedImage getResultImage() { return this.processedImage; } public FuzzyCMeansProcessor(/*List<ClusterPoint> points, List<ClusterCentroid> clusters, */float fuzzy, BufferedImage myImage, int numCluster) { points = new ArrayList<ClusterPoint>(); int width = myImage.getWidth(); int height = myImage.getHeight(); int index = 0; int[] inPixels = new int[width*height]; myImage.getRGB( 0, 0, width, height, inPixels, 0, width ); for (int row = 0; row < myImage.getHeight(); ++row) { for (int col = 0; col < myImage.getWidth(); ++col) { index = row * width + col; int color = inPixels[index]; points.add(new ClusterPoint(row, col, color)); } } clusters = new ArrayList<ClusterCentroid>(); //Create random points to use a the cluster centroids Random random = new Random(); for (int i = 0; i < numCluster; i++) { int randomNumber1 = random.nextInt(width); int randomNumber2 = random.nextInt(height); index = randomNumber2 * width + randomNumber1; clusters.add(new ClusterCentroid(randomNumber1, randomNumber2, inPixels[index])); } this.originalImage = myImage; this.fuzzy = fuzzy; this.numCluster = numCluster; double diff; // Iterate through all points to create initial U matrix fuzzyForPixels = new double[this.points.size()][this.clusters.size()]; for (int i = 0; i < this.points.size(); i++) { ClusterPoint p = points.get(i); double sum = 0.0; for (int j = 0; j < this.clusters.size(); j++) { ClusterCentroid c = this.clusters.get(j); diff = Math.sqrt(Math.pow(calculateEuclideanDistance(p, c), 2.0)); fuzzyForPixels[i][j] = (diff == 0) ? Eps : diff; sum += fuzzyForPixels[i][j]; } } // re-calculate the membership value for one point of all clusters, and make suer it's sum of value is 1 recalculateClusterMembershipValues(); } public void calculateClusterCentroids() { for (int j = 0; j < this.clusters.size(); j++) { ClusterCentroid clusterCentroid = this.clusters.get(j); double l = 0.0; clusterCentroid.setRedSum(0); clusterCentroid.setBlueSum(0); clusterCentroid.setGreenSum(0); clusterCentroid.setMemberShipSum(0); double redSum = 0; double greenSum = 0; double blueSum = 0; double memebershipSum = 0; double pixelCount = 1; for (int i = 0; i < this.points.size(); i++) { ClusterPoint p = this.points.get(i); l = Math.pow(fuzzyForPixels[i][j], this.fuzzy); int ta = (p.getPixelColor() >> 24) & 0xff; int tr = (p.getPixelColor() >> 16) & 0xff; int tg = (p.getPixelColor() >> 8) & 0xff; int tb = p.getPixelColor() & 0xff; redSum += l * tr; greenSum += l * tg; blueSum += l * tb; memebershipSum += l; if (fuzzyForPixels[i][j] == p.getClusterIndex()) { pixelCount += 1; } } int clusterColor = (255 << 24) | ((int)(redSum / memebershipSum) << 16) | ((int)(greenSum / memebershipSum) << 8) | (int)(blueSum / memebershipSum); clusterCentroid.setPixelColor(clusterColor); } //update the original image // Bitmap tempImage = new Bitmap(myImageWidth, myImageHeight, PixelFormat.Format32bppRgb); BufferedImage tempImage = createCompatibleDestImage( originalImage, null ); int width = tempImage.getWidth(); int height = tempImage.getHeight(); int index = 0; int[] outPixels = new int[width*height]; for (int j = 0; j < this.points.size(); j++) { for (int i = 0; i < this.clusters.size(); i++) { ClusterPoint p = this.points.get(j); if (fuzzyForPixels[j][i] == p.getClusterIndex()) { int row = (int)p.getX(); // row int col = (int)p.getY(); // column index = row * width + col; outPixels[index] = this.clusters.get(i).getPixelColor(); } } } // fill the pixel data setRGB( tempImage, 0, 0, width, height, outPixels ); processedImage = tempImage; } /// <summary> /// Perform one step of the algorithm /// </summary> public void stepFuzzy() { for (int c = 0; c < this.clusters.size(); c++) { for (int h = 0; h < this.points.size(); h++) { double top; top = calculateEuclideanDistance(this.points.get(h), this.clusters.get(c)); if (top < 1.0) top = Eps; // sumTerms is the sum of distances from this data point to all clusters. double sumTerms = 0.0; for (int ck = 0; ck < this.clusters.size(); ck++) { sumTerms += top / calculateEuclideanDistance(this.points.get(h), this.clusters.get(ck)); } // Then the membership value can be calculated as... fuzzyForPixels[h][c] = (double)(1.0 / Math.pow(sumTerms, (2 / (this.fuzzy - 1)))); } }; this.recalculateClusterMembershipValues(); } public double calculateObjectiveFunction() { double Jk = 0.0; for (int i = 0; i < this.points.size();i++) { for (int j = 0; j < this.clusters.size(); j++) { Jk += Math.pow(fuzzyForPixels[i][j], this.fuzzy) * Math.pow(this.calculateEuclideanDistance(points.get(i), clusters.get(j)), 2); } } return Jk; } private void recalculateClusterMembershipValues() { for (int i = 0; i < this.points.size(); i++) { double max = 0.0; double min = 0.0; double sum = 0.0; double newmax = 0; ClusterPoint p = this.points.get(i); //Normalize the entries for (int j = 0; j < this.clusters.size(); j++) { max = fuzzyForPixels[i][j] > max ? fuzzyForPixels[i][j] : max; min = fuzzyForPixels[i][j] < min ? fuzzyForPixels[i][j] : min; } //Sets the values to the normalized values between 0 and 1 for (int j = 0; j < this.clusters.size(); j++) { fuzzyForPixels[i][j] = (fuzzyForPixels[i][j] - min) / (max - min); sum += fuzzyForPixels[i][j]; } //Makes it so that the sum of all values is 1 for (int j = 0; j < this.clusters.size(); j++) { fuzzyForPixels[i][j] = fuzzyForPixels[i][j] / sum; if (Double.isNaN(fuzzyForPixels[i][j])) { fuzzyForPixels[i][j] = 0.0; } newmax = fuzzyForPixels[i][j] > newmax ? fuzzyForPixels[i][j] : newmax; } // ClusterIndex is used to store the strongest membership value to a cluster, used for defuzzification p.setClusterIndex(newmax); }; } private double calculateEuclideanDistance(ClusterPoint p, ClusterCentroid c) { // int pa = (p.getPixelColor() >> 24) & 0xff; int pr = (p.getPixelColor() >> 16) & 0xff; int pg = (p.getPixelColor() >> 8) & 0xff; int pb = p.getPixelColor() & 0xff; // int ca = (c.getPixelColor() >> 24) & 0xff; int cr = (c.getPixelColor() >> 16) & 0xff; int cg = (c.getPixelColor() >> 8) & 0xff; int cb = c.getPixelColor() & 0xff; return Math.sqrt(Math.pow((pr - cr), 2.0) + Math.pow((pg - cg), 2.0) + Math.pow((pb - cb), 2.0)); } @Override public BufferedImage filter(BufferedImage src, BufferedImage dest) { return processedImage; } }
package com.gloomyfish.segmentation.fuzzycmeans; public class ClusterPoint { private double x; private double y; private int pixelColor; private int originalPixelColor; private double clusterIndex; public ClusterPoint(double x, double y, int col) { this.x = x; this.y = y; this.pixelColor = col; this.originalPixelColor = col; this.clusterIndex = -1; } public double getX() { return x; } public void setX(double x) { this.x = x; } public double getY() { return y; } public void setY(double y) { this.y = y; } public int getPixelColor() { return pixelColor; } public void setPixelColor(int pixelColor) { this.pixelColor = pixelColor; } public int getOriginalPixelColor() { return originalPixelColor; } public void setOriginalPixelColor(int originalPixelColor) { this.originalPixelColor = originalPixelColor; } public double getClusterIndex() { return clusterIndex; } public void setClusterIndex(double clusterIndex) { this.clusterIndex = clusterIndex; } }
package com.gloomyfish.segmentation.fuzzycmeans; public class ClusterCentroid { private double x; private double y; private int pixelColor; private double redSum; private double greenSum; private double blueSum; private double memberShipSum; private int originalPixelColor; public ClusterCentroid(double x, double y, int color) { this.x = x; this.y = y; this.originalPixelColor = color; this.pixelColor = color; } public double getX() { return x; } public void setX(double x) { this.x = x; } public double getY() { return y; } public void setY(double y) { this.y = y; } public int getPixelColor() { return pixelColor; } public void setPixelColor(int pixelColor) { this.pixelColor = pixelColor; } public double getRedSum() { return redSum; } public void setRedSum(double redSum) { this.redSum = redSum; } public double getGreenSum() { return greenSum; } public void setGreenSum(double greenSum) { this.greenSum = greenSum; } public double getBlueSum() { return blueSum; } public void setBlueSum(double blueSum) { this.blueSum = blueSum; } public double getMemberShipSum() { return memberShipSum; } public void setMemberShipSum(double memberShipSum) { this.memberShipSum = memberShipSum; } public int getOriginalPixelColor() { return originalPixelColor; } public void setOriginalPixelColor(int originalPixelColor) { this.originalPixelColor = originalPixelColor; } }算法调用：
int numClusters = 2; // (int)numericUpDown2.Value; int maxIterations = 20; //(int)numericUpDown3.Value; double accuracy = 0.00001; // (double)numericUpDown4.Value; FuzzyCMeansProcessor alg = new FuzzyCMeansProcessor(numClusters, sourceImage, numClusters); int k = 0; do { k++; alg.setObj(alg.calculateObjectiveFunction()); alg.calculateClusterCentroids(); alg.stepFuzzy(); double Jnew = alg.calculateObjectiveFunction(); System.out.println("Run method accuracy of delta value = " + Math.abs(alg.getObj() - Jnew)); if (Math.abs(alg.getObj() - Jnew) < accuracy) break; } while (maxIterations > k); resultImage = alg.getResultImage(); this.repaint(); }六：Fuzzy C-means不足之处
需要提供额外的参数，不能自动识别Cluster，运行时间比较长。
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