Recognition of planar shapes by a semi-differential invariant for moving triangles

Consider the recognition of planar contours of several moving triangles using pictures taken by camera. Our new idea is that we take pictures of not only rotated triangles but also image trajectories of circles placed properly. We apply this method to the recognition of three-dimensional tetrahedrons by showing that each angle between two face planes is measured only from the circles on face triangles in addition to recognizing face triangles. The method uses the semi-differential invariance for pseudo-perspective projection which can recognize local figures.