A Unified Shape-From-Shading Approach for 3D Surface Reconstruction Using Fast Eikonal Solvers

Abstract

Object shape reconstruction from images has been an active topic in computer vision. Shape-from-shading (SFS) is an important approach for inferring 3D surface from a single shading image. In this paper, we present a unified SFS approach for surfaces of various reflectance properties using fast eikonal solvers. The whole approach consists of three main components: a unified SFS model, a unified eikonal-type partial differential image irradiance (PDII) equation, and fast eikonal solvers for the PDII equation. The first component is designed to address different reflectance properties including diffuse, specular, and hybrid reflections in the imaging process of the camera. The second component is meant to derive the PDII equation under an orthographic camera projection and a single distant point light source whose direction is the same as the camera. Finally, the last component is targeted at solving the resultant PDII equation by using fast eikonal solvers. It comprises two Godunov-based schemes with fast sweeping method that can handle the eikonal-type PDII equation. Experiments on several synthetic and real images demonstrate that each type of the surfaces can be effectively reconstructed with more accurate results and less CPU running time.

Single-Pixel Near-Infrared 3D Image Reconstruction in Outdoor Conditions

“…The NIR-SPI system architecture is divided into two stages: the first one controls the elements used to generate images by applying the already explained single-pixel imaging principle: an InGaAs photodetector (diode FGA015 @ 1550 nm), accompanied by an array of 8 × 8 NIR LEDs. Nevertheless, the spatial resolution of the objects in the scene is achieved by applying the Shape-From-Shading (SFS) [ 25 ] method and the unified reflectance model [ 26 ], additionally applying mesh enhancement algorithms, is still very much away from the aimed goal of below 10 mm at a distance of 3 m. Thus, four control spots were incorporated into the system illumination array, consisting of NIR lasers with controlled variable light intensity emulating an illumination sinusoidal signal modulated in time and four additional InGaAs photodiode pairs to measure the distance to the objects in the depicted scene with much higher precision, using the indirect Time-of-Flight (iTOF) ranging method (see Figure 3 a). The second stage of the system is responsible for processing the captured signals by the photodiode module through the use of an analog-to-digital converter (ADC), which is controlled by a Graphics Processing Unit (GPU) (see Figure 3 b).…”

A linearization-based hybrid approach for 3D reconstruction of objects in a single image

“…SFS has inspired many researchers because of the abundance of its parameters such as the reflectivity coefficient (e.g., Barron and Malik, 2011), surface reflection (e.g., Wang et al, 2020), constraints in minimization approaches (e.g., Frankot and Chellappa, 1988), solutions to partial differential equations (e.g., Quéau et al, 2017), the illumination position (e.g., Zheng and Chellappa, 1991), projection (e.g., Breuß and Yarahmadi, 2020), and ambiguity (e.g., Abada and Aouat, 2015).…”

3D Reconstruction of Non-Lambertian Surfaces by Perspective Shape-From-Shading With Fast Viscosity Solution

“…In the current study, based on our previous work [24][25][26][27], we propose a new fast perspective SFS approach for non-Lambertian surface reconstruction. The Oren-Nayar reflectance model is also adopted to approximate the surface reflectance property.…”