Configuration Estimate of Trihedral Vertex from a Single View

In a previous paper, we introduced “perspective angle transform” (PAT) to analyze the relationship between an angle seen under the condition of “central projection” and an actual angle. The present paper discusses mainly (based on the previous paper) the connotative interpretation of trihedral vertices by using information on an image. This is a problem in reconstructing a three‐dimensional (3‐D) configuration of the trihedral vertex from a central projection image in which all the angles are known. An algorithm to express this problem is introduced so that the problem can be analyzed. An algebraic solution based on the perspective angle transform is given for a case where at least two of the three angles in a trihedral vertex are right angles (i.e., a two‐‐orthogonal vertex or a three‐orthogonal vertex). The number of solutions and the possibility of their interpretations are also analyzed. A one‐dimensional search algorithm (or the examination method for the hypothesis of a normal image) based on the interpretation of the two‐orthogonal vertex is introduced for interpretation of a trihedral vertex. The number of solutions is examined statistically by using a computer simulation. This paper will be useful for analyzing scenes and robot‐vision, whichever images employ central or parallel projection.