The connection between text compression and the measure of entropy of a source seems to be well known but poorly documented. We try to partially remedy this situation by showing that the topological entropy is a lower bound for the compression ratio of any compressor. We show that for factorial sources the 1978 version of the Ziv-Lempel compression algorithm achieves this lower bound.

This study deals with the effects of lossy image compression in the visual analysis of remotely sensed images. The experiments consider two factors with interaction: the type of landscape and the degree of lossy compression. Three landscapes and two areas for each landscape (with different homogeneity) have been selected. For every of the six study area, color 1:5000 orthoimages have been submi...

Topological simplification techniques and topology preserving compression approaches for 2D vector fields have been developed quite independently of each other. In this paper we propose a combination of both approaches: a vector field should be compressed in such a way that its important topological features (both critical points and separatrices) are preserved while its unimportant features ar...

For a countable amenable group Γ and an element f in the integral group ring ZΓ being invertible in the group von Neumann algebra of Γ, we show that the entropy of the shift action of Γ on the Pontryagin dual of the quotient of ZΓ by its left ideal generated by f is the logarithm of the Fuglede-Kadison determinant of f . For the proof, we establish an `-version of Rufus Bowen’s definition of to...

In this paper, we propose an adaptive fast solver for a general class of symmetric positive definite (SPD) matrices which include the well-known graph Laplacian. We achieve this by developing an adaptive operator compression scheme and a multiresolution matrix factorization algorithm which achieve nearly optimal performance on both complexity and well-posedness. To develop our adaptive operator...

The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D convex polyhedron by means of planes, containing only its faces. This allows not to consider topological aspects of the problem (connectivity information amo...

This paper details a geometric compression technique for triangulated 3D polyhedral models which significantly reduces their storage and transmission costs. The method is based on entropy and run-length encoding of vertex and triangle spanning trees. This losslessly compresses mesh connectivity to less than two bits per triangle on average. Vertex positions and properties are quantized and enco...

paulownia is one of the fast-growing species that was attended to supply industrial requirement in recent years. the application of this species is limited because of low density, so wood modification via compression and densification is an effective method. for this purpose, the paulownia boles were prepared from shastkalateh forest and cut into blocks with 60×20×20 mm dimension. the variable ...

This paper presents a new approach for the lossless compression of engineering data, represented by triangles. The method works in two steps a topology compression followed by an entropy compression. The topology compression is based on the five states; one is automatically recognized by the compressor/decompressor and the remaining is coded by four commands. This approach for topology compress...