A class of bases in L2 for the sparse representations of integral operators
SIAM Journal on Mathematical Analysis
Digital image coding using Legendre transform
Circuits, Systems, and Signal Processing
Fractal functions and wavelet expansions based on several scaling functions
Journal of Approximation Theory
A study of orthonormal multi-wavelets
Applied Numerical Mathematics - Special issue on selected keynote papers presented at 14th IMACS World Congress, Atlanta, NJ, July 1994
Multiscale Fourier descriptors for defect image retrieval
Pattern Recognition Letters
Matching 2d shapes using u descriptors
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
IEEE Transactions on Signal Processing
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This paper constructs a class of fourband piecewise polynomials multiwavelets (abbreviated as QVLets), whose scaling functions and wavelet functions have explicit expressions, and its wavelets consist of continuous and discontinuous functions. Unlike Fourier trigonometric, Walsh system and V system, there is no Gibbs phenomenon at breakpoints or endpoints and "singular" phenomenon, and its approximation error is very small also, if we apply partial sum of QVLets series to represent planar curves or surfaces. Afterwards, we use QVLets coefficients to analyze image shape, and obtain a class of shape descriptors, i.e., QV descriptors, which are a class of invariants based on translation, scale and rotation. Finally, we confirm with experiments that approximation error of QVLets is less than that of Fourier, Walsh and V system; the experimental result also indicates that the difference between images can be illustrated by QV distance, and QV descriptors are a class of feature invariants.