Local Curvature from Gradients of the Orientation Tensor Field
Klas Nordberg, Hans E. Knutsson, Gösta H. Granlund · 1995
This paper presents an algorithm for estimation of local curvature from gradients of a tensor field that represents local orientation. The algorithm is based on an operator representation of the orientation tensor, which means that change of local orientation corresponds to a rotation of the eigenvectors of the tensor. The resulting curvature descriptor is a vector that points in the direction of the image in which the local orientation rotates anti-clockwise and the norm of the vector is the inverse of the radius of curvature. Two coefficients are defined that relate the change of local orientation with either curves or radial patterns. 1 Introduction Two-dimensional curvature can be defined in different ways. For example, curvature can be defined as the rate of change of the tangent angle with respect to the curve length. An other way is to first estimate local orientation, resulting in a field of orientation descriptors, and then consider its variation with respect to the image coo...