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图像处理之Canny边缘检测

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标签:图像处理   canny 边缘提取 边缘检测   

图像处理之Canny 边缘检测

一:历史

Canny边缘检测算法是1986年有John F. Canny开发出来一种基于图像梯度计算的边缘

检测算法,同时Canny本人对计算图像边缘提取学科的发展也是做出了很多的贡献。尽

管至今已经许多年过去,但是该算法仍然是图像边缘检测方法经典算法之一。

二:Canny边缘检测算法

经典的Canny边缘检测算法通常都是从高斯模糊开始,到基于双阈值实现边缘连接结束

。但是在实际工程应用中,考虑到输入图像都是彩色图像,最终边缘连接之后的图像要

二值化输出显示,所以完整的Canny边缘检测算法实现步骤如下:

1.      彩色图像转换为灰度图像

2.      对图像进行高斯模糊

3.      计算图像梯度,根据梯度计算图像边缘幅值与角度

4.      非最大信号压制处理(边缘细化)

5.      双阈值边缘连接处理

6.      二值化图像输出结果

三:各步详解与代码实现

1.      彩色图像转灰度图像

根据彩色图像RGB转灰度公式:gray  =  R * 0.299 + G * 0.587 + B * 0.114

将彩色图像中每个RGB像素转为灰度值的代码如下:

int gray = (int) (0.299 * tr + 0.587 * tg + 0.114 * tb);

2.      对图像进行高斯模糊

图像高斯模糊时,首先要根据输入参数确定高斯方差与窗口大小,这里我设置默认方

差值窗口大小为16x16,根据这两个参数生成高斯卷积核算子的代码如下:

		float kernel[][] = new float[gaussianKernelWidth][gaussianKernelWidth];
		for(int x=0; x<gaussianKernelWidth; x++)
		{
			for(int y=0; y<gaussianKernelWidth; y++)
			{
				kernel[x][y] = gaussian(x, y, gaussianKernelRadius);
			}
		}

获取了高斯卷积算子之后,我们就可以对图像高斯卷积模糊,关于高斯图像模糊更详

细的解释可以参见这里:http://blog.csdn.net/jia20003/article/details/7234741实现

图像高斯卷积模糊的代码如下:

// 高斯模糊 -灰度图像
int krr = (int)gaussianKernelRadius;
for (int row = 0; row < height; row++) {
	for (int col = 0; col < width; col++) {
		index = row * width + col;
		double weightSum = 0.0;
		double redSum = 0;
		for(int subRow=-krr; subRow<=krr; subRow++)
		{
			int nrow = row + subRow;
			if(nrow >= height || nrow < 0)
			{
				nrow = 0;
			}
			for(int subCol=-krr; subCol<=krr; subCol++)
			{
				int ncol = col + subCol;
				if(ncol >= width || ncol <=0)
				{
					ncol = 0;
				}
				int index2 = nrow * width + ncol;
				int tr1 = (inPixels[index2] >> 16) & 0xff;
				redSum += tr1*kernel[subRow+krr][subCol+krr];
				weightSum += kernel[subRow+krr][subCol+krr];
			}
		}
		int gray = (int)(redSum / weightSum);
		outPixels[index] = gray;
	}
}

3.      计算图像X方向与Y方向梯度,根据梯度计算图像边缘幅值与角度大小

高斯模糊的目的主要为了整体降低图像噪声,目的是为了更准确计算图像梯度及边缘

幅值。计算图像梯度可以选择算子有Robot算子、Sobel算子、Prewitt算子等。关于

图像梯度计算更多的解释可以看这里:

http://blog.csdn.net/jia20003/article/details/7664777。

这里采用更加简单明了的2x2的算子,其数学表达如下:

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// 计算梯度-gradient, X放与Y方向
data = new float[width * height];
magnitudes = new float[width * height];
for (int row = 0; row < height; row++) {
	for (int col = 0; col < width; col++) {
		index = row * width + col;
		// 计算X方向梯度
		float xg = (getPixel(outPixels, width, height, col, row+1) - 
				getPixel(outPixels, width, height, col, row) + 
				getPixel(outPixels, width, height, col+1, row+1) -
				getPixel(outPixels, width, height, col+1, row))/2.0f;
		float yg = (getPixel(outPixels, width, height, col, row)-
				getPixel(outPixels, width, height, col+1, row) +
				getPixel(outPixels, width, height, col, row+1) -
				getPixel(outPixels, width, height, col+1, row+1))/2.0f;
		// 计算振幅与角度
		data[index] = hypot(xg, yg);
		if(xg == 0)
		{
			if(yg > 0)
			{
				magnitudes[index]=90;						
			}
			if(yg < 0)
			{
				magnitudes[index]=-90;
			}
		}
		else if(yg == 0)
		{
			magnitudes[index]=0;
		}
		else
		{
			magnitudes[index] = (float)((Math.atan(yg/xg) * 180)/Math.PI);					
		}
		// make it 0 ~ 180
		magnitudes[index] += 90;
	}
}

在获取了图像每个像素的边缘幅值与角度之后

4.      非最大信号压制

信号压制本来是数字信号处理中经常用的,这里的非最大信号压制主要目的是实现边

缘细化,通过该步处理边缘像素进一步减少。非最大信号压制主要思想是假设3x3的

像素区域,中心像素P(x,y) 根据上一步中计算得到边缘角度值angle,可以将角度分

为四个离散值0、45、90、135分类依据如下:

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其中黄色区域取值范围为0~22.5 与157.5~180

绿色区域取值范围为22.5 ~ 67.5

蓝色区域取值范围为67.5~112.5

红色区域取值范围为112.5~157.5

分别表示上述四个离散角度的取值范围。得到角度之后,比较中心像素角度上相邻

两个像素,如果中心像素小于其中任意一个,则舍弃该边缘像素点,否则保留。一

个简单的例子如下:

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// 非最大信号压制算法 3x3
Arrays.fill(magnitudes, 0);
for (int row = 0; row < height; row++) {
	for (int col = 0; col < width; col++) {
		index = row * width + col;
		float angle = magnitudes[index];
		float m0 = data[index];
		magnitudes[index] = m0;
		if(angle >=0 && angle < 22.5) // angle 0
		{
			float m1 = getPixel(data, width, height, col-1, row);
			float m2 = getPixel(data, width, height, col+1, row);
			if(m0 < m1 || m0 < m2)
			{
				magnitudes[index] = 0;
			}
		}
		else if(angle >= 22.5 && angle < 67.5) // angle +45
		{
			float m1 = getPixel(data, width, height, col+1, row-1);
			float m2 = getPixel(data, width, height, col-1, row+1);
			if(m0 < m1 || m0 < m2)
			{
				magnitudes[index] = 0;
			}
		}
		else if(angle >= 67.5 && angle < 112.5) // angle 90
		{
			float m1 = getPixel(data, width, height, col, row+1);
			float m2 = getPixel(data, width, height, col, row-1);
			if(m0 < m1 || m0 < m2)
			{
				magnitudes[index] = 0;
			}
		}
		else if(angle >=112.5 && angle < 157.5) // angle 135 / -45
		{
			float m1 = getPixel(data, width, height, col-1, row-1);
			float m2 = getPixel(data, width, height, col+1, row+1);
			if(m0 < m1 || m0 < m2)
			{
				magnitudes[index] = 0;
			}
		}
		else if(angle >=157.5) // angle 0
		{
			float m1 = getPixel(data, width, height, col, row+1);
			float m2 = getPixel(data, width, height, col, row-1);
			if(m0 < m1 || m0 < m2)
			{
				magnitudes[index] = 0;
			}
		}
	}
}

1.      双阈值边缘连接

非最大信号压制以后,输出的幅值如果直接显示结果可能会少量的非边缘像素被包

含到结果中,所以要通过选取阈值进行取舍,传统的基于一个阈值的方法如果选择

的阈值较小起不到过滤非边缘的作用,如果选择的阈值过大容易丢失真正的图像边

缘,Canny提出基于双阈值(Fuzzy threshold)方法很好的实现了边缘选取,在实际

应用中双阈值还有边缘连接的作用。双阈值选择与边缘连接方法通过假设两个阈值

其中一个为高阈值TH另外一个为低阈值TL则有

a.      对于任意边缘像素低于TL的则丢弃

b.      对于任意边缘像素高于TH的则保留

c.      对于任意边缘像素值在TL与TH之间的,如果能通过边缘连接到一个像素大于

TH而且边缘所有像素大于最小阈值TL的则保留,否则丢弃。代码实现如下:

Arrays.fill(data, 0);
int offset = 0;
for (int row = 0; row < height; row++) {
	for (int col = 0; col < width; col++) {
		if(magnitudes[offset] >= highThreshold && data[offset] == 0)
		{
			edgeLink(col, row, offset, lowThreshold);
		}
		offset++;
	}
}
基于递归的边缘寻找方法edgeLink的代码如下:

private void edgeLink(int x1, int y1, int index, float threshold) {
	int x0 = (x1 == 0) ? x1 : x1 - 1;
	int x2 = (x1 == width - 1) ? x1 : x1 + 1;
	int y0 = y1 == 0 ? y1 : y1 - 1;
	int y2 = y1 == height -1 ? y1 : y1 + 1;
	
	data[index] = magnitudes[index];
	for (int x = x0; x <= x2; x++) {
		for (int y = y0; y <= y2; y++) {
			int i2 = x + y * width;
			if ((y != y1 || x != x1)
				&& data[i2] == 0 
				&& magnitudes[i2] >= threshold) {
				edgeLink(x, y, i2, threshold);
				return;
			}
		}
	}
}

6.      结果二值化显示 - 不说啦,直接点,自己看吧,太简单啦

// 二值化显示
for(int i=0; i<inPixels.length; i++)
{
	int gray = clamp((int)data[i]);
	outPixels[i] = gray > 0 ? -1 : 0xff000000;     
}
最终运行结果:

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四:完整的Canny算法源代码

package com.gloomyfish.filter.study;

import java.awt.image.BufferedImage;
import java.util.Arrays;

public class CannyEdgeFilter extends AbstractBufferedImageOp {
	private float gaussianKernelRadius = 2f;
	private int gaussianKernelWidth = 16;
	private float lowThreshold;
	private float highThreshold;
	// image width, height
	private int width;
	private int height;
	private float[] data;
	private float[] magnitudes;

	public CannyEdgeFilter() {
		lowThreshold = 2.5f;
		highThreshold = 7.5f;
		gaussianKernelRadius = 2f;
		gaussianKernelWidth = 16;
	}

	public float getGaussianKernelRadius() {
		return gaussianKernelRadius;
	}

	public void setGaussianKernelRadius(float gaussianKernelRadius) {
		this.gaussianKernelRadius = gaussianKernelRadius;
	}

	public int getGaussianKernelWidth() {
		return gaussianKernelWidth;
	}

	public void setGaussianKernelWidth(int gaussianKernelWidth) {
		this.gaussianKernelWidth = gaussianKernelWidth;
	}

	public float getLowThreshold() {
		return lowThreshold;
	}

	public void setLowThreshold(float lowThreshold) {
		this.lowThreshold = lowThreshold;
	}

	public float getHighThreshold() {
		return highThreshold;
	}

	public void setHighThreshold(float highThreshold) {
		this.highThreshold = highThreshold;
	}

	@Override
	public BufferedImage filter(BufferedImage src, BufferedImage dest) {
		width = src.getWidth();
		height = src.getHeight();
		if (dest == null)
			dest = createCompatibleDestImage(src, null);
		// 图像灰度化
		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 ta = 0, tr = 0, tg = 0, tb = 0;
			for (int col = 0; col < width; col++) {
				index = row * width + col;
				ta = (inPixels[index] >> 24) & 0xff;
				tr = (inPixels[index] >> 16) & 0xff;
				tg = (inPixels[index] >> 8) & 0xff;
				tb = inPixels[index] & 0xff;
				int gray = (int) (0.299 * tr + 0.587 * tg + 0.114 * tb);
				inPixels[index] = (ta << 24) | (gray << 16) | (gray << 8)
						| gray;
			}
		}
		
		// 计算高斯卷积核
		float kernel[][] = new float[gaussianKernelWidth][gaussianKernelWidth];
		for(int x=0; x<gaussianKernelWidth; x++)
		{
			for(int y=0; y<gaussianKernelWidth; y++)
			{
				kernel[x][y] = gaussian(x, y, gaussianKernelRadius);
			}
		}
		// 高斯模糊 -灰度图像
		int krr = (int)gaussianKernelRadius;
		for (int row = 0; row < height; row++) {
			for (int col = 0; col < width; col++) {
				index = row * width + col;
				double weightSum = 0.0;
				double redSum = 0;
				for(int subRow=-krr; subRow<=krr; subRow++)
				{
					int nrow = row + subRow;
					if(nrow >= height || nrow < 0)
					{
						nrow = 0;
					}
					for(int subCol=-krr; subCol<=krr; subCol++)
					{
						int ncol = col + subCol;
						if(ncol >= width || ncol <=0)
						{
							ncol = 0;
						}
						int index2 = nrow * width + ncol;
						int tr1 = (inPixels[index2] >> 16) & 0xff;
						redSum += tr1*kernel[subRow+krr][subCol+krr];
						weightSum += kernel[subRow+krr][subCol+krr];
					}
				}
				int gray = (int)(redSum / weightSum);
				outPixels[index] = gray;
			}
		}
		
		// 计算梯度-gradient, X放与Y方向
		data = new float[width * height];
		magnitudes = new float[width * height];
		for (int row = 0; row < height; row++) {
			for (int col = 0; col < width; col++) {
				index = row * width + col;
				// 计算X方向梯度
				float xg = (getPixel(outPixels, width, height, col, row+1) - 
						getPixel(outPixels, width, height, col, row) + 
						getPixel(outPixels, width, height, col+1, row+1) -
						getPixel(outPixels, width, height, col+1, row))/2.0f;
				float yg = (getPixel(outPixels, width, height, col, row)-
						getPixel(outPixels, width, height, col+1, row) +
						getPixel(outPixels, width, height, col, row+1) -
						getPixel(outPixels, width, height, col+1, row+1))/2.0f;
				// 计算振幅与角度
				data[index] = hypot(xg, yg);
				if(xg == 0)
				{
					if(yg > 0)
					{
						magnitudes[index]=90;						
					}
					if(yg < 0)
					{
						magnitudes[index]=-90;
					}
				}
				else if(yg == 0)
				{
					magnitudes[index]=0;
				}
				else
				{
					magnitudes[index] = (float)((Math.atan(yg/xg) * 180)/Math.PI);					
				}
				// make it 0 ~ 180
				magnitudes[index] += 90;
			}
		}
		
		// 非最大信号压制算法 3x3
		Arrays.fill(magnitudes, 0);
		for (int row = 0; row < height; row++) {
			for (int col = 0; col < width; col++) {
				index = row * width + col;
				float angle = magnitudes[index];
				float m0 = data[index];
				magnitudes[index] = m0;
				if(angle >=0 && angle < 22.5) // angle 0
				{
					float m1 = getPixel(data, width, height, col-1, row);
					float m2 = getPixel(data, width, height, col+1, row);
					if(m0 < m1 || m0 < m2)
					{
						magnitudes[index] = 0;
					}
				}
				else if(angle >= 22.5 && angle < 67.5) // angle +45
				{
					float m1 = getPixel(data, width, height, col+1, row-1);
					float m2 = getPixel(data, width, height, col-1, row+1);
					if(m0 < m1 || m0 < m2)
					{
						magnitudes[index] = 0;
					}
				}
				else if(angle >= 67.5 && angle < 112.5) // angle 90
				{
					float m1 = getPixel(data, width, height, col, row+1);
					float m2 = getPixel(data, width, height, col, row-1);
					if(m0 < m1 || m0 < m2)
					{
						magnitudes[index] = 0;
					}
				}
				else if(angle >=112.5 && angle < 157.5) // angle 135 / -45
				{
					float m1 = getPixel(data, width, height, col-1, row-1);
					float m2 = getPixel(data, width, height, col+1, row+1);
					if(m0 < m1 || m0 < m2)
					{
						magnitudes[index] = 0;
					}
				}
				else if(angle >=157.5) // angle 0
				{
					float m1 = getPixel(data, width, height, col, row+1);
					float m2 = getPixel(data, width, height, col, row-1);
					if(m0 < m1 || m0 < m2)
					{
						magnitudes[index] = 0;
					}
				}
			}
		}
		// 寻找最大与最小值
		float min = 255;
		float max = 0;
		for(int i=0; i<magnitudes.length; i++)
		{
			if(magnitudes[i] == 0) continue;
			min = Math.min(min, magnitudes[i]);
			max = Math.max(max, magnitudes[i]);
		}
		System.out.println("Image Max Gradient = " + max + " Mix Gradient = " + min);

		// 通常比值为 TL : TH = 1 : 3, 根据两个阈值完成二值化边缘连接
		// 边缘连接-link edges
		Arrays.fill(data, 0);
		int offset = 0;
		for (int row = 0; row < height; row++) {
			for (int col = 0; col < width; col++) {
				if(magnitudes[offset] >= highThreshold && data[offset] == 0)
				{
					edgeLink(col, row, offset, lowThreshold);
				}
				offset++;
			}
		}
		
		// 二值化显示
		for(int i=0; i<inPixels.length; i++)
		{
			int gray = clamp((int)data[i]);
			outPixels[i] = gray > 0 ? -1 : 0xff000000;     
		}
		setRGB(dest, 0, 0, width, height, outPixels );
		return dest;
	}
	
	public int clamp(int value) {
		return value > 255 ? 255 :
			(value < 0 ? 0 : value);
	}
	
	private void edgeLink(int x1, int y1, int index, float threshold) {
		int x0 = (x1 == 0) ? x1 : x1 - 1;
		int x2 = (x1 == width - 1) ? x1 : x1 + 1;
		int y0 = y1 == 0 ? y1 : y1 - 1;
		int y2 = y1 == height -1 ? y1 : y1 + 1;
		
		data[index] = magnitudes[index];
		for (int x = x0; x <= x2; x++) {
			for (int y = y0; y <= y2; y++) {
				int i2 = x + y * width;
				if ((y != y1 || x != x1)
					&& data[i2] == 0 
					&& magnitudes[i2] >= threshold) {
					edgeLink(x, y, i2, threshold);
					return;
				}
			}
		}
	}
	
	private float getPixel(float[] input, int width, int height, int col,
			int row) {
		if(col < 0 || col >= width)
			col = 0;
		if(row < 0 || row >= height)
			row = 0;
		int index = row * width + col;
		return input[index];
	}
	
	private float hypot(float x, float y) {
		return (float) Math.hypot(x, y);
	}
	
	private int getPixel(int[] inPixels, int width, int height, int col,
			int row) {
		if(col < 0 || col >= width)
			col = 0;
		if(row < 0 || row >= height)
			row = 0;
		int index = row * width + col;
		return inPixels[index];
	}
	
	private float gaussian(float x, float y, float sigma) {
		float xDistance = x*x;
		float yDistance = y*y;
		float sigma22 = 2*sigma*sigma;
		float sigma22PI = (float)Math.PI * sigma22;
		return (float)Math.exp(-(xDistance + yDistance)/sigma22)/sigma22PI;
	}

}
转载请务必注明出自本博客-gloomyfish

图像处理之Canny边缘检测

标签:图像处理   canny 边缘提取 边缘检测   

原文地址:http://blog.csdn.net/jia20003/article/details/41173767

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