Paper Info
Title
Planar Shape Interpolation Based On Teichmüller Mapping.
Abstract
Shape interpolation is a classical problem in computer graphics and has been widely investigated in the past two decades. Ideal shape interpolation should be natural and smooth which have good properties such as affine and conformal reproduction, bounded distortion, no fold-overs, etc. In this paper, we present a new approach for planar shape interpolation based on Teichmüller maps - a special type of maps in the class of quasi-conformal maps. The algorithm consists of two steps. In the first step, a Teichmüller map is computed from the source shape to the target shape, and then the Beltrami coefficient is interpolated such that the conformal distortion is linear with respect to the time variable. In the second step, the intermediate shape is reconstructed by solving the Beltrami equation locally over each triangle and then stitching the mapped triangles by conformal transformations. The new approach preserves all the good properties mentioned above and produces more natural and more uniform intermediate shapes than the start-of-the-art methods. Especially, the conformal distortion changes linearly with respect to the time variable. Experiment results show that our method can produce appealing results regardless of interpolating between the same or different objects.
Year
DOI
Venue
2016
10.1111/cgf.13002
Comput. Graph. Forum
Field
DocType
Volume
Affine transformation,Computer vision,Image stitching,Interpolation,Beltrami equation,Conformal map,Artificial intelligence,Distortion,Image scaling,Mathematics,Bounded function
Journal
35
Issue
ISSN
Citations 
7
0167-7055
0
PageRank 
References 
Authors
0.34
26
2
Name
Order
Citations
PageRank
Xianshun Nian100.34
Falai Chen240332.47