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Stroke-Based Surface Reconstruction

Published online by Cambridge University Press:  28 May 2015

Jooyoung Hahn ,
Jie Qiu ,
Eiji Sugisaki ,
Lei Jia ,
Xue-Cheng Tai  and
Hock Soon Seah
Jooyoung Hahn*
Affiliation:
Institute of Mathematics and Scientific Computing, University of Graz, Austria
Jie Qiu*
Affiliation:
School of Computer Engineering, Nanyang Technological University, Singapore
Eiji Sugisaki*
Affiliation:
N-Design Inc., Japan
Lei Jia*
Affiliation:
School of Computer Engineering, Nanyang Technological University, Singapore
Xue-Cheng Tai*
Affiliation:
Mathematics Institute, University of Bergen, Norway
Hock Soon Seah*
Affiliation:
School of Computer Engineering, Nanyang Technological University, Singapore
*
Corresponding author.Email address:JooyoungHahn@gmail.com
Corresponding author.Email address:JQiu@ntu.edu.sg
Corresponding author.Email address:eiji@ndesign.co.jp
Corresponding author.Email address:JIALEI@ntu.edu.sg
Corresponding author.Email address:tai@math.uib.no
Corresponding author.Email address:A@HSSEAH@ntu.edu.sg
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Abstract

In this paper, we present a surface reconstruction via 2D strokes and a vector field on the strokes based on a two-step method. In the first step, from sparse strokes drawn by artists and a given vector field on the strokes, we propose a nonlinear vector interpolation combining total variation (TV) and H1 regularization with a curl-free constraint for obtaining a dense vector field. In the second step, a height map is obtained by integrating the dense vector field in the first step. Jump discontinuities in surface and discontinuities of surface gradients can be well reconstructed without any surface distortion. We also provide a fast and efficient algorithm for solving the proposed functionals. Since vectors on the strokes are interpreted as a projection of surface gradients onto the plane, different types of strokes are easily devised to generate geometrically crucial structures such as ridge, valley, jump, bump, and dip on the surface. The stroke types help users to create a surface which they intuitively imagine from 2D strokes. We compare our results with conventional methods via many examples.

Keywords

65K1065D1865D17Surface reconstruction from a sparse vector fieldaugmented Lagrangian methodtwo-step methodcurl-free constrainttotal variation regularizationpreservation of discontinuities in surface normal vectors
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 297 - 324
Copyright
Copyright © Global Science Press Limited 2013

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