Stationary Stochastic Processes and Fractal Data Compression

1997 ◽  
Vol 07 (03) ◽  
pp. 551-567 ◽  
Author(s):  
Michael F. Barnsley ◽  
Anca Deliu ◽  
Ruifeng Xie
Keyword(s):  
Data Compression ◽  
Iterated Function System ◽  
Geometrical Approach ◽  
Compression Method ◽  
Compression Algorithms ◽  
Piecewise Affine ◽  
Affine Mappings ◽  
Iterated Function ◽  
Stationary Stochastic Processes ◽  
Lossless Data Compression

It is shown that the invariant measure of a stationary nonatomic stochastic process yields an iterated function system with probabilities and an associated dynamical system that provide the basis for optimal lossless data compression algorithms. The theory is illustrated for the case of finite-order Markov processes: For a zero-order process, it produces the arithmetic compression method; while for higher order processes it yields dynamical systems, constructed from piecewise affine mappings from the interval [0, 1] into itself, that may be used to store information efficiently. The theory leads to a new geometrical approach to the development of compression algorithms.

On Piecewise Affine Mappings in $R^n $

1975 ◽  
Vol 29 (4) ◽  
pp. 680-689 ◽  
Author(s):  
Werner C. Rheinboldt ◽  
James S. Vandergraft
Keyword(s):  
Piecewise Affine ◽  
Affine Mappings

On an area-preserving inverse curvature flow of convex closed plane curves

2021 ◽  
Vol 280 (8) ◽  
pp. 108931
Author(s):  
Laiyuan Gao ◽  
Shengliang Pan ◽  
Dong-Ho Tsai
Keyword(s):  
Curvature Flow ◽  
Plane Curves ◽  
Area Preserving ◽  
Closed Plane
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