Error-Bounds on Curvature Estimation

Abstract

Abstract. Estimation of a digital curve's curvature at any given point is needed for many tasks in computer vision, be it differential invariants or curvature scale space. However, curvature estimation is known to be very susceptible to noise on the contour. We shall show how noise on the contour affects the relative accuracy of the curvature computation. One interesting result is that, contrary to intuition, the accurate calculation of the curvature for low-curvature regions is in fact impossible for common image-sizes, while reasonable results may under favourable conditions be obtained for higher-curvature regions.

PaCeQuant: A Tool for High-Throughput Quantification of Pavement Cell Shape Characteristics

“…Likewise, the quantification of contour-based features (group B) and PC-specific features (group D) relies on analyzing curvatures and concavities of the region boundary and thus is sensitive to small variations in shape contours (e.g. Utcke, 2003).…”

A Unified Curvature Definition for Regular, Polygonal, and Digital Planar Curves

“…According to their experiments, they validate and reinforce the conclusion of Kovalevsky (2001) that in digitized images, the estimated curvature is barely possible with a low error rate, even in high resolution images. Utcke analyzed the error-bounds of curvature (Utcke 2003); one interesting result he pointed out is that, contrary to our intuition, the accurate calculation of the curvature for low-curvature regions is in fact impossible for common image-sizes, while reasonable results under favorable conditions may be obtained for higher-curvature regions.…”

Denoising an Image by Denoising Its Curvature Image

“…The reason is that small errors require very long curves. Utcke [25] points out that the smaller the curvature, the larger the error in estimating it. Ciomaga, Monasse, and Morel [11] propose a method for increasing the accuracy in estimating a curvature image by decomposing the image in its level lines and computing the curvature at each of these curves with subpixel accuracy.…”