Summary: Gaussian curvature encodes important information about object shape. This paper presents a technique to classify a local surface into several classes from multiple images acquired under different conditions of illumination. Previous approaches require a separate calibration sphere as a reference object, while the proposed approach requires no calibration object like a sphere. Instead, a target object is rotated with some fixed angles in both the vertical and the horizontal directions and the target object itself generates a virtual sphere. In our recent work, only the geometrical calculation is employed to generate a virtual sphere, however this geometrical calculation causes the error between actual marker position and estimated position based on the assumption of the orthographic projection. To generate the virtual sphere with higher accuracy, we adopt a neural network approximation, which is introduced to achieve high accuracy of the virtual sphere image. Experiments with real data are demonstrated.