Affine-permutation invariance of 2-D shapes

Affine-permutation Symmetry: Invariance and Shape Space

Studying similarity of objects by looking at their shapes arises naturally in many applications. However, under different viewpoints one and the same object appears to have different shapes. In addition, the correspondence between their feature points are unknown to the viewer. In this paper, we introduce the concept of intrinsic shape of an object that is invariant to affine-permutation shape ...

Ph.D. Prospectus Affine-Permutation Shape Invariance: Distance and Geometry

Divergence Analysis of Discrete 2-d Shapes

In this paper we introduce a second order differential operator in order to partition discrete objects into meaningful parts. One of these parts contains all points of the object’s medial axis which is a widely used shape descriptor. Since aliasing is a fundamental problem for methods based on the boundary of discrete objects we use a bilateral filter to reduce the artefacts significantly. As a...

On permutation-invariance of limit theorems

By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d. sequences. This observation not only explains the remarkable properties of lacunary trigonometric series, but also provides a powerful tool in many areas of analysis, such the theory of orthogonal series and Banach space theory. In contrast to i.i.d. sequenc...

Nonexistence of Permutation Binomials of Certain Shapes

Suppose xm+axn is a permutation polynomial over Fp, where p > 5 is prime and m > n > 0 and a ∈ Fp. We prove that gcd(m−n, p−1) / ∈ {2, 4}. In the special case that either (p− 1)/2 or (p− 1)/4 is prime, this was conjectured in a recent paper by Masuda, Panario and Wang.