Boundary conditions for Shape from Shading

The Shape From Shading is one of a computer vision field. It studies the 3D reconstruction of an object from a single grayscale image. The difficulty of this field can be expressed in the local ambiguity (convex / concave). J.Shi and Q.Zhu have proposed a method (Global View) to solve the local ambiguity. This method based on the graph theory and the relationship between the singular points. In this work we will show that the use of singular points is not sufficient and requires further information on the object to resolve this ambiguity.

A Machine learning approach for Shape From Shading

The aim of Shape From Shading (SFS) problem is to reconstruct the relief of an object from a single gray level image. In this paper we present a new method to solve the problem of SFS using Machine learning method. Our approach belongs to Local resolution category. The orientation of each part of the object is represented by the perpendicular vector to the surface (Normal Vector), this vector is defined by two angles SLANT and TILT, such as the TILT is the angle between the normal vector and Z-axis, and the SLANT is the angle between the the X-axis and the projection of the normal to the plane. The TILT can be determined from the gray level, the unknown is the SLANT. To calculate the normal of each part of the surface (pixel) a supervised Machine learning method has been proposed. This method divided into three steps: the first step is the preparation of the training data from 3D mathematical functions and synthetic objects. The second step is the creation of database of examples from 3D objects (off-line process). The third step is the application of test images (on-line process). The idea is to find for each pixel of the test image the most similar element in the examples database using a similarity value.