On an efficient sparse representation of objects of general shape via continuous extension and wavelet approximation (with Z. Zhang), International Journal of Wavelets, Multiresolution, and Information Processing, vol.8, no.2, pp.253-269, 2010.


In this paper, we discuss the continuous extension and wavelet approximation of the detected object on a general domain of R2. We first extend continuously the image to a square T and such that it vanishes on boundary ∂T. On T \ Ω, the extension has a simple and clear representation which is determined by the equation of the boundary ∂T. We expand the extension into wavelet series on R2. Since the extension tool is polynomials, by the moment theorem, we know that the sequence of wavelet coefficients obtained by us is sparse. Therefore, we can approximate and analyze the internal information of the object very well even if we only store a few wavelet coefficients.

Keywords: object-oriented image analysis, continuous extension, wavelet approximation

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