# Deformable Surface 3D Reconstruction from a Single Image by Linear Programming

• Ma, Wenjuan (Department of Digital Media Technology,Zhejiang Sci-Tech University) ;
• Sun, Shusen (Department of Digital Media Technology,Zhejiang Sci-Tech University)
• Accepted : 2017.02.07
• Published : 2017.06.30

#### Abstract

We present a method for 3D shape reconstruction of inextensible deformable surfaces from a single image. The key of our approach is to represent the surface as a 3D triangulated mesh and formulate the reconstruction problem as a sequence of Linear Programming (LP) problems. The LP problem consists of data constraints which are 3D-to-2D keypoint correspondences and shape constraints which are designed to retain original lengths of mesh edges. We use a closed-form method to generate an initial structure, then refine this structure by solving the LP problem iteratively. Compared with previous methods, ours neither involves smoothness constraints nor temporal consistency, which enables us to recover shapes of surfaces with various deformations from a single image. The robustness and accuracy of our approach are evaluated quantitatively on synthetic data and qualitatively on real data.

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