## 1 Introduction
They proposed a linear program for realizing the approach to solve the disambiguation problem for SFS. As for the modeling process of the surface reflection, few are reported in the SFS literature. Generally, the Lambertian reflectance is a fundamental assumption in conventional SFS approaches for approximating the reflection attribute of the diffuse reflection. Unfortunately, the Lambertian model has been tested to be inexact, especially for rough diffuse surfaces [PERSON] and [PERSON] [PERSON] and [PERSON] (2000). [PERSON] and [PERSON] (2000) adopted the Deformable Models and Oren-Nayar Deformable Models and Oren-Nayar (2000) model to construct an approach for non-Lambertian SFS and estimating the light direction. [PERSON] and [PERSON] [PERSON] and [PERSON] (2000) also reported a non-Lambertian SFS with the Oren-Nayar model and presented two solutions: the analytic solution and the lookup table. [PERSON] and [PERSON] [PERSON] and [PERSON] (2000) gave several non-Lambertian SFS models and solved the partial differential IIR using the Lax-Friedrichs sweeping scheme [PERSON] (2000). [PERSON] and [PERSON] and [PERSON] and [PERSON] (2000) proposed a unified formulation for several non-Lambertian SFS models, solved by a semi-Lagrangian approximation scheme and proved a convergence result. In these non-Lambertian SFS approaches, the distant point light source and the orthographic camera projection are adopted. Because of their simplicity, our current study is based on these models. Of course, recent research focuses on the more realistic imaging model, including a nearby point light source and perspective camera projection. [PERSON] and [PERSON] [PERSON] and [PERSON] (2000) used the model proposed by [PERSON] and [PERSON] [PERSON] and [PERSON] (2000), where the point light source is ideally attached to the camera's projection center, and a light attenuation term \(1/r^{2}\) (\(r\) defines the distance between the position of the light source and the 3D surface point) has been considered in order to eliminate the ambiguity regarding convex and concave that makes the non-Lambertian SFS problem ill-posed. Moreover, [PERSON] et al. [PERSON] et al. (2019) extended the work of [PERSON] et al. [PERSON] et al. (2019): they used spherical surface parameterization to Oren-Nayar reflection model and thus could resolve an arbitrary position of the point light source. Nevertheless, the solving process needs transform the fast-marching method described in Cartesian coordinates [PERSON] and [PERSON] (1992) into spherical coordinates. In this paper, we present a new Oren-Nayar SFS approach for 3D reconstruction of diffuse surfaces by extending our work Oren-Nayar reflection model is also applied to approximate the reflection attribute of the diffuse reflection. Then, a partial differential 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. Although several works [PERSON] and [PERSON] (2000); [PERSON] and [PERSON] (2000); [PERSON] and [PERSON] (2000) have been reported in this situation,our main contribution is that we convert the IIR into a standard eikonal PDE by solving a quadratic equation which includes the 3D surface shape, after which we try to obtain the viscosity solution of the resulting eikonal equation by using the high-order Godunov-based scheme.