8 October 1996 Segmentation-based wavelet transform for still-image compression
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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.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Gerard Mozelle, Abdellatif Seghier, Francoise J. Preteux, "Segmentation-based wavelet transform for still-image compression", Proc. SPIE 2823, Statistical and Stochastic Methods for Image Processing, (8 October 1996); doi: 10.1117/12.253445; https://doi.org/10.1117/12.253445
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