PHLST with adaptive tiling and its application toantarctic remote sensing image approximation

Zhihua Zhang; Naoki Saito

doi:10.3934/ipi.2014.8.321

Article Contents

2014, Volume 8, Issue 1: 321-337. Doi: 10.3934/ipi.2014.8.321

This issue Previous Article A local information based variational model for selective image segmentation Next Article

PHLST with adaptive tiling and its application to antarctic remote sensing image approximation

Zhihua Zhang^1, and
Naoki Saito^2,

1.
College of Global Change and Earth System Science, Beijing Normal University, Beijing, 100875
2.
Department of Mathematics, University of California, Davis, California, 95616

Received: June 30, 2011

Revised: February 29, 2012

Published: January 2014

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Abstract

We propose an efficient nonlinear approximation scheme using the Polyharmonic Local Sine Transform (PHLST) of Saito and Remy combined with an algorithm to tile a given image automatically and adaptively according to its local smoothness and singularities. To measure such local smoothness, we introduce the so-called local Besov indices of an image, which is based on the pointwise modulus of smoothness of the image. Such an adaptive tiling of an image is important for image approximation using PHLST because PHLST stores the corner and boundary information of each tile and consequently it is wasteful to divide a smooth region of a given image into a set of smaller tiles. We demonstrate the superiority of the proposed algorithm using Antarctic remote sensing images over the PHLST using the uniform tiling. Analysis of such images including their efficient approximation and compression has gained its importance due to the global climate change.

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Mathematics Subject Classification: Primary: 42C40, 65D18; Secondary: 68W25.

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