Relative Magnitude of Gaussian Curvature from Shading Images Using Neural Network

Abstract

A new approach is proposed to recover the relative magnitude of Gaussian curvature from three shading images using neural network. Under the assumption that the test object has the same reflectance property as the calibration sphere of known shape, RBF neural network learns the mapping of three observed image intensities to the corresponding coordinates of (x,y). Three image intensities at the neighbouring points around any point are input to the neural network and the corresponding coordinates (x,y) are mapped onto a sphere. The previous approaches recovered the sign of Gaussian curvature from mapped points onto a sphere, further, this approach proposes a method to recover the relative magnitude of Gaussian curvature at any point by calulating the surrounding area consisting of four mapped points onto a sphere. Results are demonstrated by the experiments for the real object.