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.
Highlights
Shape-From-shading (SFS), initiated by Horn [1,2], is a classical method for determining the shape of a 3D surface from a one intensity image
A partial differential Image Irradiance Equation (IIR) with this model is set up under a single distant point light source and an orthographic camera projection whose direction coincides with the light source
Equation (5) can only be established under the assumptions that are a single distant point light source and an orthographic camera projection whose direction coincides with the light source or a nearby point light source attached to the projection center of the camera performing a perspective projection
Summary
Shape-From-shading (SFS), initiated by Horn [1,2], is a classical method for determining the shape of a 3D surface from a one intensity image. He described the SFS problem by the so-called. The second step is that of building a numerical scheme to acquire a solution of the IIR, which is the 3D shape of the known intensity image. Since the pioneering work of Horn, the majority of the SFS works focuses on how to build a numerical scheme with the simple Lambertian model; many SFS algorithms have been reported (one can see the extensive list of the references in the three surveys [3,4,5]). According to Zhang et al [4], Durou et al [5], and Tozza and Falcone [6], these algorithms are roughly divided into two categories: PDE-based approaches and optimization
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