Abstract
In this paper, we address 3D reconstruction of surfaces deforming isometrically. Given that an isometric surface is represented by means of a triangular mesh and that feature/point correspondences on an image are available, the goal is to estimate the 3D positions of the mesh vertices. To perform such monocular reconstruction, a common practice is to adopt linear deformation model. We also integrate this model into a least-squares optimization. However, this model is obtained through a learning process requiring an adequate data set of possible mesh deformations. Providing this prior data is the primary goal of this work and therefore a novel reconstruction technique is proposed for a mesh overlaid across a typical isometric surface. This technique consists in the use of a range camera accompanied by a conventional camera and implements the path from the depth of the feature points to the 3D positions of the vertices through convex programming. The idea is to use the high-resolution images from the RGB camera in combination with the low-resolution depth map to enhance mesh deformation estimation. With this approach, multiple deformations of the mesh are recovered with the possibility that the resulting deformation model is simply extended to any other isometric surfaces for monocular reconstruction. Experimental results show that the proposed approach is robust to noise and generates accurate reconstructions.
Highlights
The reconstruction of objects from a single image is under-constrained, meaning that the recovery of 3D shape is an inherently ambiguous problem
We introduce an algorithm that falls within a particular class of methods which follow the same basic principle, namely, mesh representation along with linear deformation model [17, 18, 24, 28]
4 Reconstruction using a D-RGB camera setup In order to build an adequate data set of mesh deformations for learning the deformation model, we propose a reconstruction approach for a typical surface based on a D-RGB camera setup
Summary
The reconstruction of objects from a single image is under-constrained, meaning that the recovery of 3D shape is an inherently ambiguous problem. Assuming that a triangular mesh is used to represent an isometric surface and that a set of feature/point correspondences on an image of the surface have been provided, the objective is to determine the 3D positions of the mesh vertices To carry out this monocular reconstruction, we formulate a non-linear least-squares optimization that integrates the linear deformation model, deformation-based constraints which we call isometric constraints, and the projection equations in order to solve for 3D positions of the mesh vertices. This technique aims to estimate a regular 3D mesh overlaid across a generic isometric surface and is used to recover several different deformations of the mesh in a way that makes it possible to extend the computed deformation model to other isometric surfaces for monocular reconstruction In developing this approach, we use a conventional RGB camera aided by a range camera. Applying the approach just described to a variety of mesh deformations leads to the required data, thereby computing the deformation model
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