Ensemble samplers with affine invariance

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 ...

The Affine Scale Invariance of Minimization Algorithms

Let f(x) be a general objective function and let f'x) = h + mf(Ax + d). An analytic estimation of the minimum of one would resemble an analytic estimation of the other in all nontrivial respects. However, the use of a minimization algorithm on either might or might not lead to apparently unrelated sequences of calculations. This paper is devoted to providing a general theory for the affine scal...

Coplanar circles, quasi-affine invariance and calibration

We define the lines associated with two coplanar circles, and give the distributions of any two coplanar circles and their associated lines. Further we prove that the distribution of two coplanar circles with no real intersection and their associated lines is a quasi-affine invariance. Then the results are applied to calibrating a camera. The calibration method has the advantages: (1) it is bas...

Steganography with Imperfect Samplers

The goal of steganography is to pass secret messages by disguising them as innocent-looking covertexts. Real world stegosystems are often broken because they make invalid assumptions about the system’s ability to sample covertexts. We examine whether it is possible to weaken this assumption. By modeling the covertext distribution as a stateful Markov process, we create a sliding scale between r...

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