Relative Magnitude of Gaussian Curvature Using Neural Network and Object Rotation of Two Degrees of Freedom

Wepropose a new approach to recover the relative magnitude of Gaussian curvaturefrom multiple images. Previous approaches recover the sign of Gaussian cur- vature from the spatial relationship of points mapped onto a sphere. Here, the relative magnitude of Gaussian curvature is recovered at each point. No calibration object is required. Instead, the test object itself is rotated in both the vertical and horizontal directions to estimate the position coordinates of a markerpoint. An RBF neu- ral network learns the mapping of intensities to marker� position coordinates along a virtual sphere. That is, self-calibration is performed by moving a markerpoint. The neural network represents the mapping of observed image intensitiesto coordinates on a virtual sphere. Self-calibration makes it possible then to recover the relative magnitude of Gaussian curvature at each point. Experiments on real data are demonstrated.