Local all-pass geometric deformations

Christopher Gilliam, Thierry Blu

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

This paper deals with the estimation of a deformation that describes the geometric transformation between two images. To solve this problem, we propose a novel framework that relies upon the brightness consistency hypothesis-a pixel's intensity is maintained throughout the transformation. Instead of assuming small distortion and linearizing the problem (e.g. via Taylor Series expansion), we propose to interpret the brightness hypothesis as an all-pass filtering relation between the two images. The key advantages of this new interpretation are that no restrictions are placed on the amplitude of the deformation or on the spatial variations of the images. Moreover, by converting the all-pass filtering to a linear forward-backward filtering relation, our solution to the estimation problem equates to solving a linear system of equations, which leads to a highly efficient implementation. Using this framework, we develop a fast algorithm that relates one image to another, on a local level, using an all-pass filter and then extracts the deformation from the filter-hence the name "Local All-Pass" (LAP) algorithm. The effectiveness of this algorithm is demonstrated on a variety of synthetic and real deformations that are found in applications, such as image registration and motion estimation. In particular, when compared with a selection of image registration algorithms, the LAP obtains very accurate results for significantly reduced computation time and is very robust to noise corruption.

Original languageEnglish
Pages (from-to)1010-1025
Number of pages16
JournalIEEE Transactions on Image Processing
Volume27
Issue number2
DOIs
Publication statusPublished - Feb 2018

Bibliographical note

Funding Information:
Manuscript received December 22, 2016; revised June 11, 2017 and September 6, 2017; accepted October 5, 2017. Date of publication October 23, 2017; date of current version December 4, 2017. This work was supported in part by Huawei and in part by The Hong Kong Research Grants Council under Grant CUHK14200114. This paper was presented in part at the IEEE International Conference on Acoustics, Speech and Signal Processing, Brisbane, Queensland, Australia, and the IEEE International Conference on Image Processing, Quebec City, ON, Canada, 2015. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Weisheng Dong. (Corresponding author: Christopher Gilliam.) C. Gilliam is with the School of Engineering, RMIT University, Melbourne, VIC 3000, Australia (e-mail: dr.christopher.gilliam@ieee.org).

Funding Information:
This work was supported in part by Huawei and in part by The Hong Kong Research Grants Council under Grant CUHK14200114. This paper was presented in part at the IEEE International Conference on Acoustics, Speech and Signal Processing, Brisbane, Queensland, Australia, and the IEEE International Conference on Image Processing, Quebec City, ON, Canada, 2015. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Weisheng Dong.

Publisher Copyright:
© 2017 IEEE.

Keywords

  • All-pass filters
  • Geometric deformations
  • Image registration
  • Motion estimation
  • Spline and piecewise polynomial interpolation

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design

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