Corners Always Scatter

Strictly Convex Corners Scatter

We prove the absence of non-scattering energies for potentials in the plane having a corner of angle smaller than π. This extends the earlier result of Bl̊asten, Päivärinta and Sylvester who considered rectangular corners. In three dimensions, we prove a similar result for any potential with a circular conic corner whose opening angle is outside a countable subset of (0, π).

Finding Corners

Many important image cues such as 'T'-,'X'and 'L'junctions have a local two-dimensional structure. Conventional edge detectors are designed for one-dimensional 'events'. Even the best edge operators can not reliably detect these two-dimensional features. This contribution proposes a solution to the two-dimensional problem. In this paper, I address the following: • 'L'-junction detection. Previo...

Cutting Corners

Parallelogram Polyominoes and Corners

(Received) We give an equation satissed by the generating function for parallelogram polyominoes according to the area, the width and the number of left path corners. Next, we give an explicit formula for the generating function of these polyominoes according to the area, the width and the number of right and left paths corners.

Smoothing images creates corners

The isophote curvature times the gradient magnitude to some power has been studied in the literature as a measure of cornerness in images. Stability in terms of sampling noise has been proposed by selecting corners at high scale and locating them at fine scale. We will examine the problem of tracking extrema of these measures in the Linear Scale-Space using catastrophe theory. This enables us t...