Average error based adaptive regularization control for the gradient constancy variational stereo model

Izhar Ali Amur; Khuda Bux Amur; Muzafar Bashir Arain; Mohsin Ali Amur; K.N Memon

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Average error based adaptive regularization control for the gradient constancy variational stereo model

Author(s)

Izhar Ali Amur Department of General Faculty, Shaheed Benazir Bhutto University, Shaheed Benazir Abad, Nawabshah, Pakistan

Khuda Bux Amur Department Mathematics and Statistics,QUEST Nawabshah, SBA, Pakistan

Muzafar Bashir Arain Department Mathematics and Statistics,QUEST Nawabshah, SBA, Pakistan

Mohsin Ali Amur Department of General Faculty, Shaheed Benazir Bhutto University, Shaheed Benazir Abad, Nawabshah, Pakistan

K.N Memon Department Mathematics and Statistics,QUEST Nawabshah, SBA, Pakistan

Abstract

The study of the stereo vision problems is most crucial and challenging task in image processing and computer vision. The Stereo Vision problems address the investigation of the correspondence between the two images of same scene (stereo pairs) captured from two diferent views. Generally, these problems are inverse and ill posed. To deal with such problems the energy-based regularization techniques are considered as an efficient and most successful approaches. The adaptive finite element method is used here as discretization method for the partial diferential equation obtained from the optimization of the designed energy functional. Such type of the regularization generally depends on the smoothness parameters, and their suitable choice. The choice of the smoothing parameter in an adaptive way and specifically their choice as a scalar function over the whole computational domain is an interesting idea. In this work, a variational model based on the gradient constancy assumption is proposed, moreover a post optimization method (mesh refinement strategy) is designed which is based on a priori estimate called average absolute disparity error estimate. The post optimization is based on an adaptive intelligent algorithm which is efficient in identifying the less regular regions of the computed disparity image and reduces the value of the parameter to refine the grid. Consequently, the smoothness appears in the solution which is the main goal.

Publication Details

Page(s) 156-169

DOI DOI not available

Published Journal: VFAST Transactions on Mathematics, Volume: 11, Issue: 1, Year: 2023

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Keywords

Image Processing, Finite Element Method, priori estimate, Subject Classification, Adaptive regularization, Applies Mathematics, Computational Science, Stereo Depth

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