Coordinate rotation invariance of image characteristics for 3d shape and motion recovery
Kenichi Kanatani · Systems and Computers in Japan · 1988
Abstract In order to determine the shape and the motion of the object from its projection, it suffices to derive and solve the equation relating the parameters specifying the shape and the motion of the object with the features measured on the image. The equation is usually nonlinear, and is difficult to solve in the analytic way. This paper notes that there is no inherent coordinate system on the image, and any two coordinate systems are equivalent. By combining the features of the image, coordinate‐rotation‐invariant parameters (invariances) are derived. By this scheme, the geometrical meaning of the image characteristics is made clear, and the analytic solution is obtained in a natural way. The idea is demonstrated for the cases of the optical flow analysis and the surface recovery by texture, as examples.