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
。
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 entriesfor (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 1for (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 1for (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 defuzzificationp.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 functionprivate double numObj;public void setObj(double j) {this.numObj = j;}public double getObj() {return this.numObj;}private float fuzzy; // default is 2private int numCluster; // number of clusters in imagepublic 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 centroidsRandom 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 matrixfuzzyForPixels = 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 1recalculateClusterMembershipValues();}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(); // rowint col = (int)p.getY(); // columnindex = row * width + col;outPixels[index] = this.clusters.get(i).getPixelColor();}}}// fill the pixel datasetRGB( 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 entriesfor (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 1for (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 1for (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 defuzzificationp.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));}@Overridepublic BufferedImage filter(BufferedImage src, BufferedImage dest) {return processedImage;}}ClusterPoint- 存储图像像素点对象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;}}ClusterCentroid – 存储Cluster信息对象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：
人生谁无少年时，甜苦酸辛各自知。
