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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… (More)

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… (More)

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 irradi-ance equation has been derived as an explicit partial differential equation (PDE) under the assumptions of orthographic camera projection and distant point light source. The… (More)

This paper develops a new statistical model that can be used to recover the 3D face shape from a single image taken under arbitrary lighting conditions. The proposed statistical model combines shape and image intensity information. The latter is represented by a spherical harmonics (SH) space. Given a training data set of aligned height maps of faces and… (More)

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… (More)

This paper presents a new symmetric shape from shading (SFS) algorithm where the self-ratio image irradiance equation proposed by Zhao and Chellappa [1] 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… (More)

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… (More)

Population density of Lymnaea natalensis and L. columella and their natural infection with Fasciola gigantica were followed in two water bodies in Abu Rawash area, Giza Governorate over two years. L. natalensis snails were more abundant during December-February, while L. columella snails had high density during autumn. According to the snail size, we found… (More)

This paper is concerned with error estimates for the numerical solution of linear ordinary differential equations by global or piecewise polynomial collocation which are based on consideration of the differential operator involved and related matrices and on the residual. It is shown that a significant advantage may be obtained by considering the form of… (More)

Many different shape from shading (SFS) algorithms have emerged during the last three decades. Recently, we proposed [1] a unified framework that is capable of solving the SFS problem under various settings of imaging conditions representing the image irradiance equation of each setting as an explicit Partial Differential Equation (PDE). However, the result… (More)