Relative Magnitude of Gaussian Curvature from Shading Images Using Neural Network Yuji Iwahori 1 , Shinji Fukui 2 , Chie Fujitani 1 , Yoshinori Adachi 1 , and Robert J. Woodham 3 1 Chubu University, Matsumoto-cho 1200, Kasugai 487-8501, Japan iwahori@cs.chubu.ac.jp WWW home page: http://www.cvl.cs.chubu.ac.jp 2 Aichi University of Education, Hirosawa, Igaya-cho, Kariya 448-8542, Japan sfukui@auecc.aichi-edu.ac.jp WWW home page: http://www.aichi-edu.ac.jp 3 University of British Columbia, Vancouver, B.C. Canada V6T 1Z4 woodham@cs.ubc.ca WWW home page: http://www.cs.ubc.ca Abstract. A new approach is proposed to recover the relative mag- nitude of Gaussian curvature from three shading images using neural network. Under the assumption that the test object has the same re- flectance 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 neigh- bouring 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. 1 Introduction Surface gradient and curvature are the essential information for the shape repre- sentation. Especially, the surface curvature is the invariant and effective feature for the viewing direction, and curvature feature can be used to many applications such as the shape recovery, shape modeling, segmentation, the object recognition and pose determination in the field of computer vision. Based on the physics based vision approach, Woodham [1] developed a method to get surface curvature using the values of the surface gradients. Using the LUT (Look Up Table), the method obtains the local surface gradients by the empirical photometric stereo using a calibration sphere. Iwahori has pursued neural network implementations of photometric stereo. In [2] [3], neural network implementation with the PCA (principal component analysis) was proposed.