In this paper, we conduct a series of experiments to evaluate the translation invariant property of a set of discrete wavelet features in a face graph. Using local-area power spectrum estimation based on discrete wavelet transform, we compute a feature vector that possesses both efficient space-frequency structure and translation invariant properties.

We propose a statistical model for natural language that begins by considering language as a monoid, then representing it in complex matrices with a compatible translation invariant probability measure. We interpret the probability measure as arising via the Born rule from a translation invariant matrix product state.

In this paper, we propose image restoration algorithms based on adaptive wavelet–domain statistical models. We present a method to estimate the model parameters from the observations, and solve the restoration problem in orthonormal and translation-invariant wavelet domains. Substantial improvements over previous wavelet–based restoration methods are obtained. The use of a translation-invariant...

A translation surface is a compact surface with a geometric structure. Translation surfaces arise in complex analysis, the classification of surface diffeomorphisms and the study of polygonal billiards. This structure can be defined via complex analytic methods (where it is called an abelian differential). It can also be described as a pair of measured foliations but for our purposes the follow...

We discuss restrictions of two-dimensional translation-invariant Gibbs measures to a one-dimensional layer. We prove that there exists a translation invariant a.s. absolutely convergent potential making these restrictions into weakly Gibbsian measures. We discuss the existence of the thermodynamic functions for this potential and the variational principle for the weakly Gibbsian measures.

The properties of the Radon transform are used to derive the transformation invariant to translation, rotation and scaling. The invariant transformation involves translation compensation, angle representation and 1-D Fourier transform. The new object recognition method is studied experimentally in two domains, mammogram labels recognition and face recognition. For mammogram labels, the recognit...

We discuss restrictions of two-dimensional translation-invariant Gibbs measures to a one-dimensional layer. We prove that there exists a translation invariant a.s. absolutely convergent potential making these restrictions into weakly Gibbsian measures. We discuss the existence of the thermodynamic functions for this potential and the variational principle for the weakly Gibbsian measures.

We obtain asymptotic expressions for the Green kernels of certain non-translation invariant transition matrices using methods of semiclassical and microlocal analysis. Combined with a result by Bach and Møller this yields asymptotic formulas for the truncated two-point correlation functions of certain non-translation invariant lattice models of real-valued spins.

We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the source, while the focal surface is translation invariant. This is done by constructing explicitly the focal set of the reflected line congruence (2-paramete...

Place recognition is a key module in robotic navigation. The existing line of studies mostly focuses on visual place to recognize previously visited places solely based their appearance. In this article, we address structural by recognizing appearance, namely from range sensors. Extending our previous work rotation invariant spatial descriptor, the proposed descriptor completes generic robust b...