EXTRACTING LINES USING DIFFERENTIAL GEOMETRY AND GAUSSIAN SMOOTHING

摘要

A new approach to the extraction of curvilinear structures from digital images is described. The approach is based on computing a second order Taylor polynomial for each pixel in the image by convolution with derivatives of a Gaussian smoothing kernel. Line points are found based on differential geometric properties of this polynomial: they are required to have a vanishing gradient and a high curvature in the direction perpendicular to the line. The line direction is obtained from the eigenvectors of the Hessian matrix. Because Gaussian masks are used to determine the polynomial the filter generates only a single response for each line. Furthermore, the line position can be determined with sub-pixel precision and the algorithm scales to lines of arbitrary width. An analysis about the scale-space behaviour of two typical line types (parabolic and bar-shaped) is given. From this analysis, requirements and useful values for the parameters of the filter can be derived. Furthermore, an algorithm that links the individual line points into lines and junctions is given. Its advantage is that it preserves the maximum number of line points while providing a topologically sound data structure of lines and junctions. The versatility of the presented algorithm is illustrated through examples on a number of different aerial images.