图像处理之计算二值连通区域的质心
一：几何距(Geometric Moments)知识与质心寻找原理
1. Image Moments是图像处理中非常有用的算法，可以用来计算区域图像
的质心，方向等几何特性，同时Mpq的高阶具有旋转不变性，可以用来
实现图像比较分类，正是因为Moments有这些特性，很多手绘油画效果
也会基于该算法来模拟实现。它的数学表达为：
它的低阶M00，M01, M10可以用来计算质心，中心化以后M11,M02,M20
可以用来计算区域的方向/角度
2. 什么是质心就是通过该点，区域达到一种质量上的平衡状态，可能物理学上讲的比较多，简单点的
说就是规则几何物体的中心，不规则的可以通过挂绳子的方法来寻找。
二：算法流程
1. 输入图像转换为二值图像
2. 通过连通组件标记算法找到所有的连通区域，并分别标记
3. 对每个连通区域运用计算几何距算法得到质心
4. 用不同颜色绘制连通区域与质心，输出处理后图像
三：算法效果
左边为原图， 右边蓝色为连通组件标记算法处理以后结果，白色点为质心
四：关键代码解析
1. 计算几何距算法代码
doublem00 = moments(pixels, width, height, 0, 0);
doublexCr = moments(pixels, width, height, 1, 0) / m00;// row
doubleyCr = moments(pixels, width, height, 0, 1) / m00;// column
return new double[]{xCr, yCr};
2. 连通组件标记算法代码参见这里:
http://blog.csdn.net/jia20003/article/details/7628371
五：程序源代码
package com.gloomyfish.image.moments; import java.awt.image.BufferedImage; import com.gloomyfish.filter.study.AbstractBufferedImageOp; import com.gloomyfish.rice.analysis.FastConnectedComponentLabelAlg; // Geometric Moments Computing // low-order moments - calculate the center point // second-order moments - get angle size // projection - public class GeometricMomentsFilter extends AbstractBufferedImageOp { @Override public BufferedImage filter(BufferedImage src, BufferedImage dest) { int width = src.getWidth(); int height = src.getHeight(); if ( dest == null ) dest = createCompatibleDestImage( src, null ); // first step - make it as binary image output pixel int[] inPixels = new int[width*height]; int[] outPixels = new int[width*height]; getRGB( src, 0, 0, width, height, inPixels ); int index = 0; for(int row=0; row<height; row++) { int tr = 0; for(int col=0; col<width; col++) { index = row * width + col; tr = (inPixels[index] >> 16) & 0xff; if(tr > 127) { outPixels[index] = 1; } else { outPixels[index] = 0; } } } // second step, connected component labeling algorithm FastConnectedComponentLabelAlg ccLabelAlg = new FastConnectedComponentLabelAlg(); ccLabelAlg.setBgColor(0); int[] labels = ccLabelAlg.doLabel(outPixels, width, height); int max = 0; for(int i=0; i<labels.length; i++) { if(max < labels[i]) { System.out.println("Label Index = " + labels[i]); max = labels[i]; } } // third step, calculate center point of each region area(connected component) int[] input = new int[labels.length]; GeometricMomentsAlg momentsAlg = new GeometricMomentsAlg(); momentsAlg.setBACKGROUND(0); double[][] labelCenterPos = new double[max][2]; for(int i=1; i<=max; i++) { for(int p=0; p<input.length; p++) { if(labels[p] == i) { input[p] = labels[p]; } else { input[p] = 0; } } labelCenterPos[i-1] = momentsAlg.getGeometricCenterCoordinate(input, width, height); } // render the each connected component center position for(int row=0; row<height; row++) { for(int col=0; col<width; col++) { index = row * width + col; if(labels[index] == 0) { outPixels[index] = (255 << 24) | (0 << 16) | (0 << 8) | 0; // make it as black for background } else { outPixels[index] = (255 << 24) | (0 << 16) | (0 << 8) | 100; // make it as blue for each region area } } } // make it as white color for each center position for(int i=0; i<max; i++) { int crow = (int)labelCenterPos[i][0]; int ccol = (int)labelCenterPos[i][1]; index = crow * width + ccol; outPixels[index] = (255 << 24) | (255 << 16) | (255 << 8) | 255; } setRGB( dest, 0, 0, width, height, outPixels ); return dest; } }
Moment算法代码：
package com.gloomyfish.image.moments; public class GeometricMomentsAlg { private int BACKGROUND = 0; // background color private int labelIndex = 1; public GeometricMomentsAlg() { System.out.println("Geometric Moments Algorithm Initialziation..."); } public int getLabelIndex() { return labelIndex; } public void setLabelIndex(int labelIndex) { this.labelIndex = labelIndex; } public int getBACKGROUND() { return BACKGROUND; } public void setBACKGROUND(int bACKGROUND) { BACKGROUND = bACKGROUND; } public double[] getGeometricCenterCoordinate(int[] pixels, int width, int height) { double m00 = moments(pixels, width, height, 0, 0); double xCr = moments(pixels, width, height, 1, 0) / m00; // row double yCr = moments(pixels, width, height, 0, 1) / m00; // column return new double[]{xCr, yCr}; } public double moments(int[] pixels, int width, int height, int p, int q) { double mpq = 0.0; int index = 0; for(int row=0; row<height; row++) { for(int col=0; col<width; col++) { index = row * width + col; if(pixels[index] == BACKGROUND) continue; mpq += Math.pow(row, p) * Math.pow(col, q); } } return mpq; } public double centralMoments(int[] pixel, int width, int height, int p, int q) { double m00 = moments(pixel, width, height, 0, 0); double xCr = moments(pixel, width, height, 1, 0) / m00; double yCr = moments(pixel, width, height, 0, 1) / m00; double cMpq = 0.0; int index = 0; for(int row=0; row<height; row++) { for(int col=0; col<width; col++) { index = row * width + col; if(pixel[index] == BACKGROUND) continue; cMpq += Math.pow(row - xCr, p) * Math.pow(col - yCr, q); } } return cMpq; } public double normalCentralMoments(int[] pixel, int width, int height, int p, int q) { double m00 = moments(pixel, width, height, 0, 0); double normal = Math.pow(m00, ((double)(p+q+2))/2.0d); return centralMoments(pixel, width, height, p, q)/normal; } }
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