Use of two-dimensional deformable mesh structures for video coding, Part I - The synthesis problem: Mesh-based function approximation and mapping

Yao Wang, Ouseb Lee

Research output: Contribution to journalArticle

Abstract

This paper explores the use of a deformable mesh (also known as control grid) structure for motion analysis and synthesis in an image sequence. In Part I, we focus on the synthesis problem, i.e., how to interpolate an image function given nodal positions and values and how to predict a present image frame from a reference one given nodal displacements between the two images. For this purpose, we review the fundamental theory and numerical techniques that have been developed in the finite element method for function approximation and mapping using a mesh structure. Specifically, we focus on i) the use of shape functions for node-based function interpolation and mapping and ii) the use of regular master elements to simplify numerical calculations involved in dealing with irregular mesh structures. In addition to a general introduction that is applicable to an arbitrary mesh structure, we also present specific results for triangular and quadrilateral mesh structures, which are the most useful two-dimensional (2-D) meshes. Finally, we describe how to apply the above results for motion compensated frame prediction and interpolation. In Part II, we will present algorithms developed for the analysis problem, including scene-adaptive mesh generation and nodal displacement estimation. It is shown that the concepts of shape functions and master elements are crucial for developing computationally efficient algorithms for both the analysis and synthesis problems.

Original languageEnglish (US)
Pages (from-to)636-646
Number of pages11
JournalIEEE Transactions on Circuits and Systems for Video Technology
Volume6
Issue number6
DOIs
StatePublished - 1996

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Image coding
Interpolation
Mesh generation
Finite element method

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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title = "Use of two-dimensional deformable mesh structures for video coding, Part I - The synthesis problem: Mesh-based function approximation and mapping",
abstract = "This paper explores the use of a deformable mesh (also known as control grid) structure for motion analysis and synthesis in an image sequence. In Part I, we focus on the synthesis problem, i.e., how to interpolate an image function given nodal positions and values and how to predict a present image frame from a reference one given nodal displacements between the two images. For this purpose, we review the fundamental theory and numerical techniques that have been developed in the finite element method for function approximation and mapping using a mesh structure. Specifically, we focus on i) the use of shape functions for node-based function interpolation and mapping and ii) the use of regular master elements to simplify numerical calculations involved in dealing with irregular mesh structures. In addition to a general introduction that is applicable to an arbitrary mesh structure, we also present specific results for triangular and quadrilateral mesh structures, which are the most useful two-dimensional (2-D) meshes. Finally, we describe how to apply the above results for motion compensated frame prediction and interpolation. In Part II, we will present algorithms developed for the analysis problem, including scene-adaptive mesh generation and nodal displacement estimation. It is shown that the concepts of shape functions and master elements are crucial for developing computationally efficient algorithms for both the analysis and synthesis problems.",
author = "Yao Wang and Ouseb Lee",
year = "1996",
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