图像处理之计算二值连通区域的质心

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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