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  "contentMarkdown": "# Sobel operator\n\n> 创建时间：2021/2/25 21:01\n\n  * Sobel operator\n    * 背景知识\n      * 术语\n      * 算子(operator)\n      * 差分算子\n      * 图像处理中的卷积\n    * Sobel边缘检测\n    * 代码\n    * Ref\n\n## 背景知识\n\n索贝尔算子（Sobel operator）主要用作边缘检测，在技术上，它是一离散性差分算子，用来运算图像亮度函数的灰度之近似值。在图像的任何一点使用此算子，将会产生对应的灰度矢量或是其法矢量。\n\n### 术语\n\n  * 边缘：灰度或结构等信息的突变处，边缘是一个区域的结束，也是另一个区域的开始，利用该特征可以分割图像。\n\n  * 边缘点：图像中具有坐标[x，y]，且处在强度显著变化的位置上的点。\n\n  * 边缘段：对应于边缘点坐标[x，y]及其方位 ，边缘的方位可能是梯度角。\n\n### 算子(operator)\n\n算子（英语：Operator）是将一个元素在向量空间（或模）中转换为另一个元素的映射。\n\n![Alt text](assets/1614307655559.png)\n\n摘录知乎的回答（<https://www.zhihu.com/question/24989360/answer/29702293>）：\n算子含义为操作、运算等等。算子可以理解为，把一个函数变成另一个函数的东西。\n函数是从数到数的映射。\n泛函是从函数到数的映射。\n算子是从函数到函数的映射。\n当然，有的时候这几个词可以混用，比如可以可以把数当作常函数，那么普通的函数也可以看作泛函或算子；再比如考虑从算子到算子的映射，你仍然可以叫它算子。\n\n![Alt text](assets/1614309214023.png)\n\n### 差分算子\n\n百度百科：\n差分算子是一种算子，对任一实函数f(x)，若记Δf(x)=f(x+1)-f(x)，则称Δ为向前差分算子，简称差分算子。差分是计算数学的基本概念之一，指离散函数在离散节点上的改变量。\n\n维基百科：\n差分，又名差分函数或差分运算，是数学中的一个概念。它将原函数\n映射到\n。差分运算，相应于微分运算，是微积分中重要的一个概念。\n\n### 图像处理中的卷积\n\n![Alt text](assets/1614325004782.png)\n\n所谓两个函数的卷积，本质上就是先将一个函数翻转，然后进行滑动叠加。\n在图像处理的中，卷积处理的结果，其实就是把每个像素周边的像素都考虑进来，进行加权求和。\n\n![Alt text](assets/1614325088192.png)\n\n![Alt text](assets/1614325113469.png)\n\n![Alt text](assets/1614325174627.png)\n\n![Alt text](assets/1614325147490.png)\n\n计算卷积时，就可以用 f 和 g’ 的内积：\n\n![Alt text](assets/1614325218437.png)\n\n使用卷积，实质上是使用一个矩阵，表示像素点周围各个像素点的权值，对范围内的像素值做加权求平均。\n\n## Sobel边缘检测\n\n使用Sobel算子对传进来的图像像素做卷积。\n卷积的实质是在求梯度值。\n卷积核( convolution kernels)\n\n![Alt text](assets/1614325564506.png)\n\n> 可以直观地看到，用这两个矩阵与像素及其周围的像素点求卷积之后，像素亮度在x或y轴方向上变化越大，得到的值的绝对值越大。\n\nThe kernels can be applied separately to the input image, to produce separate measurements of the gradient component in each orientation.\n\n> A very common operator for doing this is a Sobel Operator, which is an approximation to a derivative of an image.\n\nThese can then be combined together to find the absolute magnitude of the gradient at each point and the orientation of that gradient.\n\n![Alt text](assets/1614326498086.png)\n\nTypically, an approximate magnitude is computed using:\n\n![Alt text](assets/1614326508239.png)\n\nThe angle of orientation of the edge (relative to the pixel grid) giving rise to the spatial gradient is given by:\n\n![Alt text](assets/1614326609475.png)\n\n![Alt text](assets/1614326653052.png)\n\n## 代码\n\n```cpp\nstring s = String.Empty;\n\n```\n\n## Ref\n\n<https://zh.wikipedia.org/zh-cn/%E7%AE%97%E5%AD%90>\n<https://www.zhihu.com/question/24989360/answer/29702293>\n<https://baike.baidu.com/item/%E5%B7%AE%E5%88%86%E7%AE%97%E5%AD%90>\n<https://medium.datadriveninvestor.com/understanding-edge-detection-sobel-operator-2aada303b900>\n<http://homepages.inf.ed.ac.uk/rbf/HIPR2/sobel.htm>\n<http://recreationstudios.blogspot.com/search/label/Compute%20Shader>\n"
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