1.基本原理

? ? 邊緣檢測一般是利用微分等方法，通過對灰度躍變的分析尋找圖像上區域邊緣的技術。今天的豬腳是梯度算子和Roberts算子。

? ? 1.梯度算子是怎么來的？

? ? 答：圖像是一個二維集合，在(x, y)處的偏導數（也就是此點的最大變化率）可以寫成下圖這樣，其梯度大小本為，但由于計算量大，所以簡化成

? ? ??

? ? 2.Roberts算子是怎么來的？

? ? 答：對角線方向的梯度，其定義見下圖，這個就是Roberts算子，其梯度大小本為，但由于計算量大，所以簡化成

? ?3.Sobel算子是怎么來的？（此圖參考自https://blog.csdn.net/songzitea/article/details/17528089）

? ? 答：

?

2.代碼實現（代碼是我以前自學圖像處理時寫的，代碼很粗糙沒做任何優化，但很好理解）

/*梯度法邊緣檢測 比例scale對差分結果進行縮放*/ QImage* MainWindow:: SideGrandiant(QImage* image,double scale) {QImage* newImage = new QImage(image->width(),image->height(),QImage::Format_ARGB32);QColor color0;QColor color1;QColor color2;int r = 0;int g = 0;int b = 0;int rgb = 0;int r1 = 0;int g1 = 0;int b1 = 0;int rgb1 = 0;int a = 0;for( int y = 0; y < image->height() - 1; y++){for(int x = 0; x < image->width() - 1; x++){color0 = QColor ( image->pixel(x,y));color1 = QColor ( image->pixel(x + 1,y));color2 = QColor ( image->pixel(x,y + 1));r = abs(color0.red() - color1.red());g = abs(color0.green() - color1.green());b = abs(color0.blue() - color1.blue());rgb = r + g + b;r1 = abs(color0.red() - color2.red());g1= abs(color0.green() - color2.green());b1 = abs(color0.blue() - color2.blue());rgb1 = r1 + g1 + b1;a = rgb + rgb1;a = a * scale;a = a>255?255:a;newImage->setPixel(x,y,qRgb(a,a,a));}}return newImage; }/*Roberts法邊緣檢測 比例scale對差分結果進行縮放*/ QImage* MainWindow:: SideRobertsdiant(QImage* image,double scale) {QImage* newImage = new QImage(image->width(),image->height(),QImage::Format_ARGB32);QColor color0;QColor color1;QColor color2;QColor color3;int r = 0;int g = 0;int b = 0;int rgb = 0;int r1 = 0;int g1 = 0;int b1 = 0;int rgb1 = 0;int a = 0;for( int y = 0; y < image->height() - 1; y++){for(int x = 0; x < image->width() - 1; x++){color0 = QColor ( image->pixel(x,y));color1 = QColor ( image->pixel(x + 1,y));color2 = QColor ( image->pixel(x,y + 1));color3 = QColor ( image->pixel(x + 1,y + 1));r = abs(color0.red() - color3.red());g = abs(color0.green() - color3.green());b = abs(color0.blue() - color3.blue());rgb = r + g + b;r1 = abs(color1.red() - color2.red());g1= abs(color1.green() - color2.green());b1 = abs(color1.blue() - color2.blue());rgb1 = r1 + g1 + b1;a = rgb + rgb1;a = a * scale;a = a>255?255:a;newImage->setPixel(x,y,qRgb(a,a,a));}}return newImage; }/*sobel法邊緣檢測 比例scale對差分結果進行縮放,type表示使用那種公式 取值0或則1*/ QImage* MainWindow:: SideSobeldiant(QImage* image,double scale,int type) {QImage* newImage = new QImage(image->width(),image->height(),QImage::Format_ARGB32);QColor color0;QColor color1;QColor color2;QColor color3;QColor color4;QColor color5;QColor color6;QColor color7;QColor color8;int r = 0;int g = 0;int b = 0;int rgb = 0;int r1 = 0;int g1 = 0;int b1 = 0;int rgb1 = 0;int a = 0;for( int y = 1; y < image->height() - 1; y++){for(int x = 1; x < image->width() - 1; x++){color0 = QColor ( image->pixel(x,y));color1= QColor ( image->pixel(x-1,y-1));color2 = QColor ( image->pixel(x,y-1));color3 = QColor ( image->pixel(x+1,y));color4 = QColor ( image->pixel(x-1,y));color5 = QColor ( image->pixel(x+1,y));color6 = QColor ( image->pixel(x-1,y+1));color7= QColor ( image->pixel(x,y+1));color8 = QColor ( image->pixel(x+1,y+1));r = abs(color1.red() + color2.red() * 2 + color3.red() - color6.red() - color7.red() * 2 - color8.red());g = abs(color1.green() + color2.green() * 2 + color3.green() - color6.green() - color7.green() * 2 - color8.green());b = abs(color1.blue() + color2.blue() * 2 + color3.blue() - color6.blue() - color7.blue() * 2 - color8.blue());rgb = r + g + b;r1 = abs(color1.red() + color4.red() * 2 + color6.red() - color3.red() - color5.red() * 2 - color8.red());g1= abs(color1.green() + color4.green() * 2 + color6.green() - color3.green() - color5.green() * 2 - color8.green());b1 = abs(color1.blue() + color4.blue() * 2 + color6.blue() - color3.blue() - color5.blue() * 2 - color8.blue());rgb1 = r1 + g1 + b1;if(type == 0){if (rgb > rgb1)a = rgb;elsea = rgb1;}else if(type == 1){a = (rgb + rgb1)/2;}a = a * scale;a = a>255?255:a;newImage->setPixel(x,y,qRgb(a,a,a));}}return newImage; }

3.參考資料：

? ? 數字圖像處理——技術詳解與Visual C++實踐（左飛等著），寫代碼與寫博客的時間相差兩年，至于還參考其他的資料不，我已經忘記了，如若需要，我可以補上去

總結

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