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Algorithms 2018, 11(5), 75; https://doi.org/10.3390/a11050075

A New Oren–Nayar Shape-from-Shading Approach for 3D Reconstruction Using High-Order Godunov-Based Scheme

1
School of Optoelectronic Engineering, Xi’an Technological University, Xi’an 710021, China
2
Shaanxi Province Key Laboratory of Optoelectronic Measurement and Instrument Technology, Xi’an Technological University, Xi’an 710021, China
*
Author to whom correspondence should be addressed.
Received: 17 April 2018 / Revised: 13 May 2018 / Accepted: 16 May 2018 / Published: 18 May 2018
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Abstract

3D shape reconstruction from images has been an important topic in the field of robot vision. Shape-From-Shading (SFS) is a classical method for determining the shape of a 3D surface from a one intensity image. The Lambertian reflectance is a fundamental assumption in conventional SFS approaches. Unfortunately, when applied to characterize the reflection attribute of the diffuse reflection, the Lambertian model is tested to be inexact. In this paper, we present a new SFS approach for 3D reconstruction of diffuse surfaces whose reflection attribute is approximated by the Oren–Nayar reflection model. The partial differential Image Irradiance Equation (IIR) is set up with this model under a single distant point light source and an orthographic camera projection whose direction coincides with the light source. Then, the IIR is converted into an eikonal equation by solving a quadratic equation that includes the 3D surface shape. The viscosity solution of the resulting eikonal equation is approximated by using the high-order Godunov-based scheme that is accelerated by means of an alternating sweeping strategy. We conduct the experiments on synthetic and real-world images, and the experimental results illustrate the effectiveness of the presented approach. View Full-Text
Keywords: 3D reconstruction; shape-from-shading; Oren–Nayar reflection model; eikonal equation; Godunov-based scheme; alternating sweeping strategy 3D reconstruction; shape-from-shading; Oren–Nayar reflection model; eikonal equation; Godunov-based scheme; alternating sweeping strategy
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Wang, G.; Chu, Y. A New Oren–Nayar Shape-from-Shading Approach for 3D Reconstruction Using High-Order Godunov-Based Scheme. Algorithms 2018, 11, 75.

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