A Local Curvature Operator

TLDR: In this article, a 2D local operator is described for computing the local curvature of intensity isocontours in a digital image, which directly estimates the average local curvatures of the isointensity contours, and does not require the explicit detection of edges.

Abstract: A 2-D local operator is described for computing the local curvature of intensity isocontours in a digital image. The operator directly estimates the average local curvature of the isointensity contours, and does not require the explicit detection of edges. In a manner similar to the Hueckel operator, a series of 2D basis functions defined over a circular local neighborhood extract a set of coefficients from the image at each point of investigation. These coefficients describe an approximation to a circular arc assumed to pass through the neighborhood center, and the curvature is taken as the inverse of the estimated arc radius. The optimal set of basis functions for approximating this particular target pattern is shown to be the Fourier series. Discretization of the continuous basis functions can create anisotropy problems for the local operator; however, these problems can be overcome either by using a set of correction functions, or by choosing a discrete function which closely approximates the circular neighborhood. The method is validated using known geometric shapes and is shown to be accurate in estimating both curvature and the orientation of the isocontours. When applied to a test image the curvature operator provides regional curvature measurements compatible with visible edges in the image.