A 3-d surface reconstruction approach based on postnonlinear ICA model

Photometric stereo technique deals with the reconstruction of three-dimensional (3-D) shape of an object by using several images of the same surface taken from the same viewpoint but under illuminations from different directions. In this paper, we propose a new photometric stereo scheme based on a new reflectance model and the postnonlinear (PNL) independent components analysis (ICA) method. The proposed nonlinear reflectance model consists of diffuse components and specular components for modeling the surface reflectance of a stereo object in an image. Unlike the previous approaches, these two components are not separated and processed individually in the proposed model. An unsupervised learning adaptation algorithm is developed to estimate the reflectance model based on image intensities. In this algorithm, the PNL ICA method is used to obtain the surface normal on each point of an image. Then, the 3-D surface model is reconstructed based on the estimated surface normal on each point of image by using the enforcing integrability method. Two experiments are performed to assess the performance of the proposed approach. We test our algorithm on synthetically generated images for the reconstruction of surface of objects and on a number of real images captured from the Yale Face Database B. These testing images contain variability due to illumination and varying albedo in each point of surface of human faces. All the experimental results are compared to those of the existing photometric stereo approaches tested on the same images. The results clearly indicate the superiority of the proposed nonlinear reflectance model over the conventional Lambertian model and the other linear hybrid reflectance model.