Extraction of curved lines from images

A method to extract curvilinear structures and their widths from digital images is presented. The approach is based on differential geometric properties of the image function. For each pixel, the second order Taylor polynomial is computed by convolving the image with the derivatives of a Gaussian smoothing kernel. Line points are required to have a vanishing gradient and a high curvature in the direction perpendicular to the line. The resulting filter generates a single response for each line. The line position can be determined with sub-pixel accuracy and the algorithm scales to lines of arbitrary width. A procedure to determine the width of the lines is described. It is based on locating the corresponding edge points of each line point in the direction perpendicular to the line with sub-pixel accuracy