A general method for overlap control in image warping

Abstract A new general solution for the construction of one-to-one image warping functions is presented. The algorithm takes a set of user specified translations and constructs a set of one-to-one warps by interpolation and scaling. These are concatenated to produce a single one-to-one warping function, which prevents overlap in the resultant warped image.

[1]  Sung Yong Shin,et al.  Scattered Data Interpolation with Multilevel B-Splines , 1997, IEEE Trans. Vis. Comput. Graph..

[2]  J. Meinguet Multivariate interpolation at arbitrary points made simple , 1979 .

[3]  Demetri Terzopoulos,et al.  Multilevel computational processes for visual surface reconstruction , 1983, Comput. Vis. Graph. Image Process..

[4]  Heinrich Müller,et al.  Image warping with scattered data interpolation , 1995, IEEE Computer Graphics and Applications.

[5]  W. Schempp,et al.  Multivariate Approximation Theory IV , 1989 .

[6]  Sung Yong Shin,et al.  Image morphing using deformable surfaces , 1994, Proceedings of Computer Animation '94.

[7]  Richard Franke,et al.  Smooth interpolation of large sets of scattered data , 1980 .

[8]  Kikuo Fujimura,et al.  Foldover-Free Image Warping , 1998, Graph. Model. Image Process..

[9]  Fujio Yamaguchi,et al.  Computer-Aided Geometric Design , 2002, Springer Japan.

[10]  Robert E. Barnhill,et al.  Representation and Approximation of Surfaces , 1977 .

[11]  Sung Yong Shin,et al.  Image metamorphosis using snakes and free-form deformations , 1995, SIGGRAPH.

[12]  C. Chui,et al.  Approximation Theory II , 1976 .

[13]  Helmuth Späth,et al.  Two-dimensional spline interpolation algorithms , 1993 .

[14]  Jean Duchon,et al.  Splines minimizing rotation-invariant semi-norms in Sobolev spaces , 1976, Constructive Theory of Functions of Several Variables.

[15]  D. Shepard A two-dimensional interpolation function for irregularly-spaced data , 1968, ACM National Conference.

[16]  Demetri Terzopoulos,et al.  The Computation of Visible-Surface Representations , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  George Wolberg,et al.  Digital image warping , 1990 .

[18]  L. Schumaker Fitting surfaces to scattered data , 1976 .

[19]  C. Olech Locally one-to-one mappings and a classical theorem on schlicht functions , 1963 .

[20]  Lance Williams,et al.  Animating images with drawings , 1994, SIGGRAPH.