Curvilinear structure detections

最新推荐文章于 2022-03-25 20:53:24 发布

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原文链接：https://yq.aliyun.com/articles/399295

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#sketch

本文介绍了一种基于结构的检测器——曲率检测器(PCBR)的工作原理。不同于传统使用边缘检测的方法，该检测器利用曲直线结构(即脊状结构)来生成图像的结构草图，提供比梯度幅度图像更清晰的线条与边缘响应。

此部分参考处

As a structure-based detector, PCBR does not use edges, instead, it uses curvilinear structures, also called ridges. Curvilinear structures detection generates a single response for both lines and edges, producing a clearer structural sketch of an image than is usually provided by the gradient magnitude image. The Steger's algorithm ^[2] is modified to get the curvilinear images. As only the first step of this algorithm is used which is to calculate the principal curvature images, the principal curvature is adopted as the name of this detector. To get the principal curvature, the Hessian matrix is calculated:

$H(\mathbf{x}) = \begin{bmatrix} L_{xx}(\mathbf{x}) & L_{xy}(\mathbf{x})\\ L_{xy}(\mathbf{x}) & L_{yy}(\mathbf{x})\\ \end{bmatrix}$

where $L_{aa}(\mathbf{x})$ is second partial derivative of the image evaluated at point x in the $a$ direction and $L_{ab}(\mathbf{x})$ is the mixed partial second derivative of the image evaluated at point x in the $a$ and $b$ directions. The maximum and minimum eigenvalues of this matrix form two images which correspond to white lines on black background and black lines on white background.