Systematic solution of primitive rotation recovery problems of known 3‐D structure from a single view

This paper considers the case where the geometrical model for a 3‐D object is given, and discusses the solution of the problem to cover the rotation of the object from a single (monocular) view image. The rigid body is represented by a set of vectors and the joint is represented by a unit vector corresponding to the rotational axis. For each rigid object, the connecting joint is included. The inner product between unit vectors as well as the scalar triple product are assumed as known. Using such a model, not only the rigid body which has widely been discussed, but also the object composed of rigid bodies and joints with the rotational degree of freedom can be handled by the same framework. In the previous paper, it was shown that such a problem to determine the rotational posture of the object can be represented by a graph, and the solvability of the problem is discussed. The basic problem represented by the tree structure is formulated. This paper defines anew the concept of connection index, and classifies the tree‐structured basic problems. For the basic problem with the connection index being 0 and 1, an algorithm is proposed which can estimate the rotations of the rigid subobject. The algorithms have the common structure for each connection index, and can be easily be constructed by defining the geometrical inference inherent to each basic problem. The usefulness of the algorithm is demonstrated through the individual experiments.