图像的常规边缘检测(梯度算子、Roberts算子和Sobel算子)之c++实现（qt+不调包）

1.基本原理

    边缘检测一般是利用微分等方法&＃xff0c;通过对灰度跃变的分析寻找图像上区域边缘的技术。今天的猪脚是梯度算子和Roberts算子。

    1.梯度算子是怎么来的&＃xff1f;

    答&＃xff1a;图像是一个二维集合&＃xff0c;在(x, y)处的偏导数&＃xff08;也就是此点的最大变化率&＃xff09;可以写成下图这样&＃xff0c;其梯度大小本为&＃xff0c;但由于计算量大&＃xff0c;所以简化成

    2.Roberts算子是怎么来的&＃xff1f;

    答&＃xff1a;对角线方向的梯度&＃xff0c;其定义见下图&＃xff0c;这个就是Roberts算子&＃xff0c;其梯度大小本为&＃xff0c;但由于计算量大&＃xff0c;所以简化成

   3.Sobel算子是怎么来的&＃xff1f;&＃xff08;此图参考自https://blog.csdn.net/songzitea/article/details/17528089&＃xff09;

    答&＃xff1a;

2.代码实现&＃xff08;代码是我以前自学图像处理时写的&＃xff0c;代码很粗糙没做任何优化&＃xff0c;但很好理解&＃xff09;

/*梯度法边缘检测 比例scale对差分结果进行缩放*/
QImage* MainWindow:: SideGrandiant(QImage* image,double scale)
{QImage* newImage &＃61; new QImage(image->width(),image->height(),QImage::Format_ARGB32);QColor color0;QColor color1;QColor color2;int r &＃61; 0;int g &＃61; 0;int b &＃61; 0;int rgb &＃61; 0;int r1 &＃61; 0;int g1 &＃61; 0;int b1 &＃61; 0;int rgb1 &＃61; 0;int a &＃61; 0;for( int y &＃61; 0; y height() - 1; y&＃43;&＃43;){for(int x &＃61; 0; x width() - 1; x&＃43;&＃43;){color0 &＃61; QColor ( image->pixel(x,y));color1 &＃61; QColor ( image->pixel(x &＃43; 1,y));color2 &＃61; QColor ( image->pixel(x,y &＃43; 1));r &＃61; abs(color0.red() - color1.red());g &＃61; abs(color0.green() - color1.green());b &＃61; abs(color0.blue() - color1.blue());rgb &＃61; r &＃43; g &＃43; b;r1 &＃61; abs(color0.red() - color2.red());g1&＃61; abs(color0.green() - color2.green());b1 &＃61; abs(color0.blue() - color2.blue());rgb1 &＃61; r1 &＃43; g1 &＃43; b1;a &＃61; rgb &＃43; rgb1;a &＃61; a * scale;a &＃61; a>255?255:a;newImage->setPixel(x,y,qRgb(a,a,a));}}return newImage;
}/*Roberts法边缘检测 比例scale对差分结果进行缩放*/
QImage* MainWindow:: SideRobertsdiant(QImage* image,double scale)
{QImage* newImage &＃61; new QImage(image->width(),image->height(),QImage::Format_ARGB32);QColor color0;QColor color1;QColor color2;QColor color3;int r &＃61; 0;int g &＃61; 0;int b &＃61; 0;int rgb &＃61; 0;int r1 &＃61; 0;int g1 &＃61; 0;int b1 &＃61; 0;int rgb1 &＃61; 0;int a &＃61; 0;for( int y &＃61; 0; y height() - 1; y&＃43;&＃43;){for(int x &＃61; 0; x width() - 1; x&＃43;&＃43;){color0 &＃61; QColor ( image->pixel(x,y));color1 &＃61; QColor ( image->pixel(x &＃43; 1,y));color2 &＃61; QColor ( image->pixel(x,y &＃43; 1));color3 &＃61; QColor ( image->pixel(x &＃43; 1,y &＃43; 1));r &＃61; abs(color0.red() - color3.red());g &＃61; abs(color0.green() - color3.green());b &＃61; abs(color0.blue() - color3.blue());rgb &＃61; r &＃43; g &＃43; b;r1 &＃61; abs(color1.red() - color2.red());g1&＃61; abs(color1.green() - color2.green());b1 &＃61; abs(color1.blue() - color2.blue());rgb1 &＃61; r1 &＃43; g1 &＃43; b1;a &＃61; rgb &＃43; rgb1;a &＃61; a * scale;a &＃61; a>255?255:a;newImage->setPixel(x,y,qRgb(a,a,a));}}return newImage;
}/*sobel法边缘检测 比例scale对差分结果进行缩放,type表示使用那种公式 取值0或则1*/
QImage* MainWindow:: SideSobeldiant(QImage* image,double scale,int type)
{QImage* newImage &＃61; 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 &＃61; 0;int g &＃61; 0;int b &＃61; 0;int rgb &＃61; 0;int r1 &＃61; 0;int g1 &＃61; 0;int b1 &＃61; 0;int rgb1 &＃61; 0;int a &＃61; 0;for( int y &＃61; 1; y height() - 1; y&＃43;&＃43;){for(int x &＃61; 1; x width() - 1; x&＃43;&＃43;){color0 &＃61; QColor ( image->pixel(x,y));color1&＃61; QColor ( image->pixel(x-1,y-1));color2 &＃61; QColor ( image->pixel(x,y-1));color3 &＃61; QColor ( image->pixel(x&＃43;1,y));color4 &＃61; QColor ( image->pixel(x-1,y));color5 &＃61; QColor ( image->pixel(x&＃43;1,y));color6 &＃61; QColor ( image->pixel(x-1,y&＃43;1));color7&＃61; QColor ( image->pixel(x,y&＃43;1));color8 &＃61; QColor ( image->pixel(x&＃43;1,y&＃43;1));r &＃61; abs(color1.red() &＃43; color2.red() * 2 &＃43; color3.red() - color6.red() - color7.red() * 2 - color8.red());g &＃61; abs(color1.green() &＃43; color2.green() * 2 &＃43; color3.green() - color6.green() - color7.green() * 2 - color8.green());b &＃61; abs(color1.blue() &＃43; color2.blue() * 2 &＃43; color3.blue() - color6.blue() - color7.blue() * 2 - color8.blue());rgb &＃61; r &＃43; g &＃43; b;r1 &＃61; abs(color1.red() &＃43; color4.red() * 2 &＃43; color6.red() - color3.red() - color5.red() * 2 - color8.red());g1&＃61; abs(color1.green() &＃43; color4.green() * 2 &＃43; color6.green() - color3.green() - color5.green() * 2 - color8.green());b1 &＃61; abs(color1.blue() &＃43; color4.blue() * 2 &＃43; color6.blue() - color3.blue() - color5.blue() * 2 - color8.blue());rgb1 &＃61; r1 &＃43; g1 &＃43; b1;if(type &＃61;&＃61; 0){if (rgb > rgb1)a &＃61; rgb;elsea &＃61; rgb1;}else if(type &＃61;&＃61; 1){a &＃61; (rgb &＃43; rgb1)/2;}a &＃61; a * scale;a &＃61; a>255?255:a;newImage->setPixel(x,y,qRgb(a,a,a));}}return newImage;
}

3.参考资料&＃xff1a;

    数字图像处理——技术详解与Visual C&＃43;&＃43;实践&＃xff08;左飞等著&＃xff09;&＃xff0c;写代码与写博客的时间相差两年&＃xff0c;至于还参考其他的资料不&＃xff0c;我已经忘记了&＃xff0c;如若需要&＃xff0c;我可以补上去