Differential-geometry-based surface normal vector calculation method using a time-of-flight camera.

Abstract

A surface normal vector of an object is often needed to detect an orientation of the object. A simple calculation method of the surface normal vector by means of a time-of-flight (ToF) camera is thus proposed here, using a coordinate transformation of three-dimensional irregular points acquired by the ToF camera to regular grid representation. Each point of the regular grid representation has a depth (distance from the camera) defined on the regular grid. The surface normal vector on the regular grid can be derived based on differential geometry with partial derivatives of the depth, and can then be in the form of the discretized Fourier transformation to which the fast Fourier transformation algorithm is applicable. The method of the surface normal vector calculation is thus theoretically derived. Validation of the method is also experimentally performed.