影像處理之Canny邊緣檢測，影像處理canny邊緣

影像處理之Canny邊緣檢測，影像處理canny邊緣

影像處理之Canny 邊緣檢測

一：曆史

Canny邊緣檢測演算法是1986年有John F. Canny開發出來一種基於映像梯度計算的邊緣

檢測演算法，同時Canny本人對計算映像邊緣提取學科的發展也是做出了很多的貢獻。盡

管至今已經許多年過去，但是該演算法仍然是映像邊緣檢測方法經典演算法之一。

二：Canny邊緣檢測演算法

經典的Canny邊緣檢測演算法通常都是從高斯模糊開始，到基於雙閾值實現邊緣串連結束

。但是在實際工程應用中，考慮到輸入映像都是彩色映像，最終邊緣串連之後的映像要

二值化輸出顯示，所以完整的Canny邊緣檢測演算法實現步驟如下：

1.      彩色映像轉換為灰階映像

2.      對映像進行高斯模糊

3.      計算映像梯度，根據梯度計算映像邊緣幅值與角度

4.      非最大訊號壓制處理（邊緣細化）

5.      雙閾值邊緣串連處理

6.      二值化映像輸出結果

三：各步詳解與代碼實現

1.      彩色映像轉灰階映像

根據彩色映像RGB轉灰階公式：gray  =  R * 0.299 + G * 0.587 + B * 0.114

將彩色映像中每個RGB像素轉為灰階值的代碼如下：

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

2.      對映像進行高斯模糊

映像高斯模糊時，首先要根據輸入參數確定高斯方差與視窗大小，這裡我設定預設方

差值視窗大小為16x16，根據這兩個參數產生高斯卷積核運算元的代碼如下：

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);}}

擷取了高斯卷積運算元之後，我們就可以對映像高斯卷積模糊，關於高斯映像模糊更詳

細的解釋可以參見這裡：http://blog.csdn.net/jia20003/article/details/7234741實現

映像高斯卷積模糊的代碼如下：

// 高斯模糊 -灰階映像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.      計算映像X方向與Y方向梯度，根據梯度計算映像邊緣幅值與角度大小

高斯模糊的目的主要為了整體降低映像雜訊，目的是為了更準確計算映像梯度及邊緣

幅值。計算映像梯度可以選擇運算元有Robot運算元、Sobel運算元、Prewitt運算元等。關於

映像梯度計算更多的解釋可以看這裡：

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

這裡採用更加簡單明了的2x2的運算元，其數學表達如下：

// 計算梯度-gradient, X放與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;// 計算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;// 計算振幅與角度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 ~ 180magnitudes[index] += 90;}}

在擷取了映像每個像素的邊緣幅值與角度之後

4.      非最大訊號壓制

訊號壓制本來是數字訊號處理中經常用的，這裡的非最大訊號壓制主要目的是實現邊

緣細化，通過該步處理邊緣像素進一步減少。非最大訊號壓制主要思想是假設3x3的

像素地區，中心像素P(x,y) 根據上一步中計算得到邊緣角度值angle，可以將角度分

為四個離散值0、45、90、135分類依據如下：

其中黃色地區取值範圍為0~22.5 與157.5～180

綠色地區取值範圍為22.5 ~ 67.5

藍色地區取值範圍為67.5~112.5

紅色地區取值範圍為112.5~157.5

分別表示上述四個離散角度的取值範圍。得到角度之後，比較中心像素角度上相鄰

兩個像素，如果中心像素小於其中任意一個，則捨棄該邊緣像素點，否則保留。一

個簡單的例子如下：

// 非最大訊號壓制演算法 3x3Arrays.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.      雙閾值邊緣串連

非最大訊號壓制以後，輸出的幅值如果直接顯示結果可能會少量的非邊緣像素被包

含到結果中，所以要通過選取閾值進行取捨，傳統的基於一個閾值的方法如果選擇

的閾值較小起不到過濾非邊緣的作用，如果選擇的閾值過大容易丟失真正的映像邊

緣，Canny提出基於雙閾值(Fuzzy threshold)方法很好的實現了邊緣選取，在實際

應用中雙閾值還有邊緣串連的作用。雙閾值選擇與邊緣串連方法通過假設兩個閾值

其中一個為高閾值TH另外一個為低閾值TL則有

a.      對於任意邊緣像素低於TL的則丟棄

b.      對於任意邊緣像素高於TH的則保留

c.      對於任意邊緣像素值在TL與TH之間的，如果能通過邊緣串連到一個像素大於

TH而且邊緣所有像素大於最小閾值TL的則保留，否則丟棄。代碼實現如下：

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++;}}

基於遞迴的邊緣尋找方法edgeLink的代碼如下：

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.      結果二值化顯示 - 不說啦，直接點，自己看吧，太簡單啦

// 二值化顯示for(int i=0; i<inPixels.length; i++){int gray = clamp((int)data[i]);outPixels[i] = gray > 0 ? -1 : 0xff000000;     }

最終運行結果：

四：完整的Canny演算法原始碼

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, heightprivate 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;}@Overridepublic BufferedImage filter(BufferedImage src, BufferedImage dest) {width = src.getWidth();height = src.getHeight();if (dest == null)dest = createCompatibleDestImage(src, null);// 映像灰階化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;}}// 計算高斯卷積核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 -灰階映像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;}}// 計算梯度-gradient, X放與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;// 計算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;// 計算振幅與角度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 ~ 180magnitudes[index] += 90;}}// 非最大訊號壓制演算法 3x3Arrays.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;}}}}// 尋找最大與最小值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);// 通常比值為 TL : TH = 1 : 3， 根據兩個閾值完成二值化邊緣串連// 邊緣串連-link edgesArrays.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++;}}// 二值化顯示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;}}

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