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Proceedings Paper

Segmentation-based wavelet transform for still-image compression
Author(s): Gerard Mozelle; Abdellatif Seghier; Francoise J. Preteux
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Paper Abstract

In order to address simultaneously the two functionalities, content-based scalability required by MPEG-4, we introduce a segmentation-based wavelet transform (SBWT). SBWT takes into account both the mathematical properties of multiresolution analysis and the flexibility of region-based approaches for image compression. The associated methodology has two stages: 1) image segmentation into convex and polygonal regions; 2) 2D-wavelet transform of the signal corresponding to each region. In this paper, we have mathematically studied a method for constructing a multiresolution analysis (VjOmega)j (epsilon) N adapted to a polygonal region which provides an adaptive region-based filtering. The explicit construction of scaling functions, pre-wavelets and orthonormal wavelets bases defined on a polygon is carried out by using scaling functions is established by using the theory of Toeplitz operators. The corresponding expression can be interpreted as a location property which allow defining interior and boundary scaling functions. Concerning orthonormal wavelets and pre-wavelets, a similar expansion is obtained by taking advantage of the properties of the orthogonal projector P(V(j(Omega )) perpendicular from the space Vj(Omega ) + 1 onto the space (Vj(Omega )) perpendicular. Finally the mathematical results provide a simple and fast algorithm adapted to polygonal regions.

Paper Details

Date Published: 8 October 1996
PDF: 16 pages
Proc. SPIE 2823, Statistical and Stochastic Methods for Image Processing, (8 October 1996); doi: 10.1117/12.253445
Show Author Affiliations
Gerard Mozelle, Institut National des Telecommunications (France)
Abdellatif Seghier, Univ. de Paris-Sud (France)
Francoise J. Preteux, Institut National des Telecommunications (France)

Published in SPIE Proceedings Vol. 2823:
Statistical and Stochastic Methods for Image Processing
Edward R. Dougherty; Francoise J. Preteux; Jennifer L. Davidson, Editor(s)

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