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báo cáo hóa học:" Research Article Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài:Research Article Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry | Hindawi Publishing Corporation EURASIP Journal on Image and Video Processing Volume 2009 Article ID 248581 16 pages doi 10.1155 2009 248581 Research Article Triangular Wavelets An Isotropic Image Representation with Hexagonal Symmetry Kensuke Fujinoki and Oleg V. Vasilyev Department of Mechanical Engineering University of Colorado 427 UCB Boulder CO 80309 USA Correspondence should be addressed to Kensuke Fujinoki kensuke.fujinoki@gmail.com Received 19 May 2009 Accepted 14 September 2009 Recommended by James Fowler This paper introduces triangular wavelets which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. The resulting three oriented high-pass filters are symmetrically arranged on the lattice while low-pass filters have hexagonal symmetry thereby allowing an isotropic image processing in the sense that three detail components are distributed uniformly. Applying the triangular filter to images we explore applications that truly benefit from the triangular wavelets in comparison with the conventional tensor product transforms. Copyright 2009 K. Fujinoki and O. V. Vasilyev. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Image processing is one of the most demanded areas of signal processing applications where the wavelet transform has been offered significant performance advantages 1 . In most cases the wavelet transform is carried out in the tensor product form that is by applying a one-dimensional transform repeatedly in the horizontal and vertical directions. This gives the simple two-dimensional extension of wavelet transforms and yields the lower-resolution images consisting of the