Segmentation-based wavelet transform for still-image compression

Gerard Mozelle; Abdellatif Seghier; Francoise J. Preteux

doi:10.1117/12.253445

8 October 1996 Segmentation-based wavelet transform for still-image compression

Gerard Mozelle, Abdellatif Seghier, Francoise J. Preteux

Proceedings Volume 2823, Statistical and Stochastic Methods for Image Processing; (1996) https://doi.org/10.1117/12.253445
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

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 (V_j^Omega)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 V_j^(Omega ) + 1 onto the space (V_j^(Omega )) perpendicular. Finally the mathematical results provide a simple and fast algorithm adapted to polygonal regions.

Citation Download Citation

Gerard Mozelle, Abdellatif Seghier, and Francoise J. Preteux "Segmentation-based wavelet transform for still-image compression", Proc. SPIE 2823, Statistical and Stochastic Methods for Image Processing, (8 October 1996); https://doi.org/10.1117/12.253445

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KEYWORDS

Wavelets

Image segmentation

Image compression

Heart

Algorithm development

Wavelet transforms

Projection systems

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