TY - JOUR
T1 - Use of two-dimensional deformable mesh structures for video coding, Part I - The synthesis problem
T2 - Mesh-based function approximation and mapping
AU - Wang, Yao
AU - Lee, Ouseb
N1 - Funding Information:
Manuscript received December 15, 1994; revised November 5, 1995. This paper was recommended by Associate Editor W. Li. This paper is based upon work supported by the National Science Foundation under Grant No. MIP-9211481 and by the New York State Center for Advanced Technology in Telecommunications at Polytechnic University, Brooklyn, NY. Y. Wang is with Department of Electrical Engineering, Polytechnic University, Brooklyn, NY 11201 USA. 0. Lee was with Polytechnic University, Brooklyn, NY 11201 USA. He is now with the Department of Information and Telecommunications, Hanshin University, Osan, Kyung Gi Province, Korea. Publisher Item Identifier S 1051-8215(96)07103-0.
PY - 1996
Y1 - 1996
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0030405980&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0030405980&partnerID=8YFLogxK
U2 - 10.1109/76.544735
DO - 10.1109/76.544735
M3 - Article
AN - SCOPUS:0030405980
SN - 1051-8215
VL - 6
SP - 636
EP - 646
JO - IEEE Transactions on Circuits and Systems for Video Technology
JF - IEEE Transactions on Circuits and Systems for Video Technology
IS - 6
ER -