On shape classifications and invariants

Shape Matching Based on Invariants

Flux Invariants for Shape

We consider the average outward flux through a Jordan curve of the gradient vector field of the Euclidean distance function to the boundary of a 2D shape. Using an alternate form of the divergence theorem, we show that in the limit as the area of the region enclosed by such a curve shrinks to zero, this measure has very different behaviours at medial points than at non-medial ones, providing a ...

Shape Reconstruction with A Priori Knowledge Based on Integral Invariants

We investigate the applicability of integral invariants as geometrical shape descriptors in the context of ill-posed inverse problems. We propose the use of a Tikhonov functional, where the penalty term is based on the difference of integral invariants. As a case example, we consider the problem of inverting the Radon transform of an object with only limited angular data available. We approxima...

On Classifications of Random Polynomials

 Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+...

Improved moment invariants for shape discrimination

Moment invariants have been frequently used as features for shape recognition. They are computed based on the information provided by both the shape boundary and its interior region. Although several fast algorithms for computing traditional moment invariants have been proposed, none has ever shown the theoretical results of moment invariants computed based on the shape boundary only. This pape...