We examine the dimension of the invariant measure for some singular circle homeomorphisms for a variety of rotation numbers, through both the thermodynamic formalism and numerical computation. The maps we consider include those induced by the action of the standard map on an invariant curve at the critical parameter value beyond which the curve is destroyed. Our results indicate that the dimens...

We introduce a method for estimation of rotation invariant local shape descriptors for 3D models. This method follows a successful idea commonly used to obtain rotation invariant descriptors in 2D images, and improves it by tackling the difficulty of the 3 degrees of freedom that exists in 3D models. Our method is simple, yet it achieves high levels of invariance after rotation transformations,...

In this paper we present a novel approach to match two images in presenting large scale and rotation changes. The proposed approach is based on scale invariant region description. Scale invariant region is detected by a two-step process and represented by a new descriptor. The descriptor is a two-dimensional gray-level histogram. Different descriptors can be directly compared. In addition, our ...

Invariant object recognition is maybe the most basic and fundamental property of our visual system. It is the basis of many other cognitive tasks, like motor actions and social interactions. Hence, the theoretical understanding and modeling of invariant object recognition is one of the central problems in computational neuroscience. Indeed, object recognition consists of two different tasks: cl...

A second-order architecture is presented here for translation, rotation and scale invariant processing of 2-D images mapped to n input units. This new architecture has a complexity of O( n) weights as opposed to the O( n3 ) weights usually required for a third-order, rotation invariant architecture. The reduction in complexity is due to the use of discrete frequency information. Simulations sho...

Non-local means is a recently proposed denoising technique that better preserves image structures than other methods. However, the computational cost of non-local means is prohibitive, especially for large 3D images. Modifications have previously been proposed to reduce the cost, which result in image artefacts. This paper proposes a compact rotation invariant descriptor. Testing demonstrates i...

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences enc...

We consider pointwise, box, and Hausdorff dimensions of invariant measures for circle diffeomorphisms. We discuss the cases of rational, Diophantine, and Liouville rotation numbers. Our main result is that for any Liouville number τ there exists a C∞ circle diffeomorphism with rotation number τ such that the pointwise and box dimensions of its unique invariant measure do not exist. Moreover, th...

A rotation-invariant texture recognition system is presented. A steerable orientedpyramid is used to extract representative features for the input textures. The steerability of the filter set allows a ship to an invariant representation via a DFT-encoding step. Supervised classijkation follows. State-of-the-art recognition results are presented on a 30 texture database with a comparison across ...

Since Moser’s seminal work it is well known that the invariant curves of smooth nearly integrable twist maps of the cylinder with Diophantine rotation number are preserved under perturbation. In this paper we show that, in the analytic class, the result extends to Bryuno rotation numbers. First, we will show that the series expansion for the invariant curves in powers of the perturbation parame...