Accurate 3-D modeling of the human teeth helps patients avoid the discomfort of the mold process, and improves the data accuracy for oral surgeons, orthodontists and dental care personnel. Since the surface of the human tooth is almost textureless, Shape from Shading (SFS) has been successfully adopted in solving this problem. This paper evaluates 3-D tooth reconstruction using three SFS models. Based on quantitative error analysis and curvature analysis using Robust Point Matching (RPM) and visualization results, the assumption of a perspective camera projection and an Oren-Nayar reflectance model has been proved to be the most ideal for extracting crown information from an image of a human tooth. Three reconstructed teeth have been shown to demonstrate the performance of this model.

This paper presents a new symmetric shape from shading (SFS) algorithm where the self-ratio image irradiance equation proposed by Zhao and Chellappa is formulated as a partial differential equation (PDE) with a Dirichlet boundary condition. This PDE is solved using the Lax-Friedrichs sweeping method. The potential of the proposed symmetric SFS algorithm is demonstrated by several experiments on synthetic and real data. As an application, the proposed algorithm is used for 3-D face reconstruction.

Most of the shape from shading (SFS) algorithms have been developed under the simplifying assumptions of a Lambertian surface, an orthographic projection, and a distant light source. Due to the difficulty of the SFS problem, only a small number of algorithms have been proposed for surfaces with non-Lambertian reflectance, and among those, only very few algorithms are applicable for surfaces with specular and diffuse reflectance. In this paper we propose a unified framework that is capable of solving the SFS problem under various settings of imaging conditions i.e., Lambertian or non-Lambertian, orthographic or perspective projection, and distant or nearby light source. The proposed algorithm represents the image irradiance equation of each setting as an explicit Partial Differential Equation (PDF). In our implementation we use the Lax-Friedrichs sweeping method to solve this PDF. To demonstrate the efficiency of the proposed algorithm, several comparisons with the state of the art of the SFS literature are given.

This paper presents a new method for recovering the shape of hybrid surfaces that have both diffuse reflection and specular reflection using shape from shading (SFS). The image irradiance equation has been derived as an explicit partial differential equation (PDE) under the assumptions of orthographic camera projection and distant point light source. The reflectance model of Ward has been used to express the hybrid reflection as a linear combination from the diffuse and specular components. The resulting PDE is solved using the Lax-Friedrichs sweeping method. The proposed algorithm is evaluated by using both synthetic data and real images and the experimental results show the efficiency of the approach.

Lambert’s model for diffuse reflection is a main assumption in most of shape from shading (SFS) literature. Even with this simplified model, the SFS is still a difficult problem. Nevertheless, Lambert’s model has been proven to be an inaccurate approximation of the diffuse component of the surface reflectance. In this paper, we propose a new solution of the SFS problem based on a more comprehensive diffuse reflectance model: the Oren and Nayar model. In this work, we slightly modify this more realistic model in order to take into account the attenuation of the illumination due to distance. Using the modified non-Lambertian reflectance, we design a new explicit Partial Differential Equation (PDE) and then solve it using Lax-Friedrichs Sweeping method. Our experiments on synthetic data show that the proposed modeling gives a unique solution without any information about the height at the singular points of the surface. Additional results for real data are presented to show the efficiency of the proposed method . To the best of our knowledge, this is the first non-Lambertian SFS formulation that eliminates the concave/convex ambiguity which is a well known problem in SFS.

This paper presents a statistical learning-based solution to the camera calibration problem in which the support vector machines (SVM) are used for the estimation of the projection matrix elements. The projection matrix is obtained explicitly by using a dot product kernel in the formulation of the SVM algorithm. The mean field theory is used to approximate an efficient learning procedure for the SVM algorithm. In order to assess the robustness of the proposed approach against noise, the experiments using synthetic data are carried out at different noise levels. The proposed approach is evaluated also with real 3D reconstruction experiments. The experimental results illustrate that the proposed calibration approach is efficient and more robust against noise than other known approaches for camera calibration.