This paper describes a new method to determine the 3-D position coordinates of a Lambertian surface from four shaded images acquired with an actively controlled, nearby moving point light source. The method treats both the case when the initial position of the light source is known and the case when it is unknown.

This paper proposes a new approach to recover the sign of local surface curvature of object from three shading images using neural network. The RBF (Radial Basis Function) neural network is used to learn the mapping of three image irradiances to the position on a sphere. Then, the learned neural network maps the image irradiances at the neighbor pixels of the test object taken from three illuminating directions of light sources onto the sphere images taken under the same illuminating condition. Using the property that basic six kinds of surface curvature has the different relative locations of the local five points mapped on the sphere, not only the Gaussian curvature but also the kind of curvature is directly recovered locally from the relation of the locations on the mapped points on the sphere without knowing the values of surface gradient for each point. Further, two step neural networks which combines the forward mapping and its inverse mapping one can be used to get the local confidence estimate for the obtained results. The entire approach is non-parametric, empirical in that no explicit assumptions are made about light source directions or surface reflectance. Results are demonstrated by the experiments for real images.

This paper proposes a new method to recover the sign of local Gaussian curvature from multiple (more than three) shading images. The information required to recover the sign of Gaussian curvature is obtained by applying Principal Components Analysis (PCA) to the normalized irradiance measurements. The sign of the Gaussian curvature is recovered based on the relative orientation of measurements obtained on a local five point test pattern to those in the 2-D subspace called the eigen plane. Using multiple shading images gives a more accurate and robust result and minimizes the effect of shadows by allowing a larger area of the visible surface to be analyzed compared to methods using only three shading images. Furthermore, it allows the method to be applied to specular surfaces. Since PCA removes linear correlation among images, the method can produce results of high quality even when the light source directions are not widely dispersed.

An implementation of photometric stereo is described in which all directions of illumination are close to and rotationally symmetric about the viewing direction. THis has practical value but gives rise to a problem that is numerically ill-conditioned. Ill-conditioning is overcome in two ways. First, many more than the theoretical minimum number of images are acquired. Second, principal components analysis (PCA) is used as a linear preprocessing technique to determine a reduced dimensionality subspace to use as input. The approach is empirical. The ability of a radial basis function (RBF) neural network to do non-parametric functional approximation is exploited. One network maps image irradiance to surface normal. A second network maps surface normal to image irradiance. The two networks are trained using samples from a calibration sphere. Comparison between the actual input and the inversely predicted input is used as a confidence estimate. Results on real data are demonstrated.

This paper proposes a new method to determine the shape of a surface by learning the mapping between three image irradiances observed under illumination from three lighting directions and the corresponding surface gradient. The method uses Phong reflectance function to describe specular reflectance. Lambertian reflectance is included as a special case. A neural network is constructed to estimate the values of reflectance parameters and the object surface gradient distribution under the assumption that the values of reflectance parameters are not known in advance. The method reconstructs the surface gradient distribution after determining the values of reflectance parameters of a test object using two step neural network which consists of one to extract two gradient parameters from three image irradiances and its inverse one. The effectiveness of this proposed neural network is confirmed by computer simulations and by experiment with a real object.