Hierarchical subsampling giving fractal regions

Recursive image subsampling which yields support areas approaching fractals is described and analyzed using iterated function systems. The subsampling scheme is suitable in, e.g., hierarchical image processing and image coding schemes. For hexagonally sampled images a hierarchical subsampling structure is given which yields hexagon-like regions with fractal borders.

[1]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[2]  William J. Gilbert The Division Algorithm in Complex Bases , 1996, Canadian Mathematical Bulletin.

[3]  A. Watson,et al.  A hexagonal orthogonal-oriented pyramid as a model of image representation in visual cortex , 1989, IEEE Transactions on Biomedical Engineering.

[4]  William A. Pearlman,et al.  Image Coding on a Hexagonal Pyramid with Noise Spectrum Shaping , 1989, Other Conferences.

[5]  F. Michel Dekking,et al.  Replicating Superfigures and Endomorphisms of Free Groups , 1982, J. Comb. Theory, Ser. A.

[6]  F. Glazer,et al.  Scene Matching by Hierarchical Correlation , 1983 .

[7]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[8]  William J. Gilbert,et al.  Geometry of Radix Representations , 1981 .

[9]  Eero P. Simoncelli,et al.  Non-separable extensions of quadrature mirror filters to multiple dimensions , 1990, Proc. IEEE.

[10]  P. Burt Tree and pyramid structures for coding hexagonally sampled binary images , 1980 .

[11]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[12]  Edward H. Adelson,et al.  Orthogonal Pyramid Transforms For Image Coding. , 1987, Other Conferences.

[13]  H. J. Song,et al.  FRACTILES DERIVED FROM GENERALIZED DIGIT SYSTEMS , 1996 .

[14]  Roger T. Stevens Understanding Self-Similar Fractals: A Graphical Guide to the Curves of Nature , 1995 .

[15]  Jean-Pierre Crettez,et al.  A model for cell receptive fields in the visual striate cortex , 1982, Comput. Graph. Image Process..

[16]  G. Gelbrich,et al.  Fractal escher salamanders and other animals , 1998 .

[17]  William J. Gilbert,et al.  Fractal geometry derived from complex bases , 1982 .

[18]  Karlheinz Gröchenig,et al.  Multiresolution analysis, Haar bases, and self-similar tilings of Rn , 1992, IEEE Trans. Inf. Theory.

[19]  Christoph Bandt,et al.  Self-similar sets. V. Integer matrices and fractal tilings of ⁿ , 1991 .

[20]  S. L. Tanimoto,et al.  A hexagonal pyramid data structure for image processing , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  A B Watson,et al.  Efficiency of a model human image code. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[22]  Jorge Nuno Silva,et al.  Mathematical Games , 1959, Nature.

[23]  A B Watson,et al.  Perceptual-components architecture for digital video. , 1990, Journal of the Optical Society of America. A, Optics and image science.

[24]  Götz Gelbrich,et al.  Self‐affine Lattice Reptiles with Two Pieces in IRn , 1996 .

[25]  H. V. Koch Une méthode géométrique élémentaire pour l’étude de certaines questions de la théorie des courbes planes , 1906 .