A Fast Progressive Image Sampling Using Lifting Scheme And Non-Uniform B-Splines

This paper proposes lifting scheme based a new fast algorithm for progressive image acquisition that enables an approximation of whole image at each step. The detail coefficients of second generation wavelets have been used to find the most significant samples. An image, which is considered here as the functions of non-uniform B-splines over the Delaunay triangulation, is developed by using recursively obtained scattered data set of significant pixels. The efficiency of the present method is shown and the visual qualities of the multiresolution images are compared with those obtained by other methods.

[1]  Michael Unser,et al.  Variational image reconstruction from arbitrarily spaced samples: a fast multiresolution spline solution , 2005, IEEE Transactions on Image Processing.

[2]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[3]  Thomas Strohmer,et al.  Computationally attractive reconstruction of bandlimited images from irregular samples , 1997, IEEE Trans. Image Process..

[4]  Akram Aldroubi,et al.  Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces , 2001, SIAM Rev..

[5]  Wim Sweldens,et al.  The lifting scheme: a construction of second generation wavelets , 1998 .

[6]  Kevin Amaratunga,et al.  Wavelet triangulated irregular networks , 2003, Int. J. Geogr. Inf. Sci..

[7]  Yehoshua Y. Zeevi,et al.  The farthest point strategy for progressive image sampling , 1997, IEEE Trans. Image Process..

[8]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

[9]  W. Sweldens.  The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[10]  Albert Cohen,et al.  Compact representation of images by edge adapted multiscale transforms , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[11]  Yonina C. Eldar,et al.  Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples , 2000, IEEE Trans. Signal Process..

[12]  Minh N. Do,et al.  Ieee Transactions on Image Processing the Contourlet Transform: an Efficient Directional Multiresolution Image Representation , 2022 .

[13]  Samuel Rippa,et al.  Minimal roughness property of the Delaunay triangulation , 1990, Comput. Aided Geom. Des..

[14]  Carlos Vázquez,et al.  Reconstruction of nonuniformly sampled images in spline spaces , 2005, IEEE Transactions on Image Processing.