Technology of recognizing a 3‐dimensional object and finding its direction from a 2‐dimensional image is important in practical applications such as classification of industrial products. A typical conventional method for this purpose uses the 3‐dimensional structure of the object such as its edges and surface shapes. However, extraction of a 3‐dimensional structure with a high accuracy, notably that of an arbitrary shaped object, is difficult.

This paper proposes a method of recognizing a 3‐dimensional object by using a 2‐dimensional collation. A 2‐dimensional collation which requires no 3‐dimensional feature has never seriously been examined, because it has been considered that the amounts of computation and a memory for learning the 2‐dimensional image data (which are very complex due to the variations of viewing and lighting angles) are not acceptable. The proposed method can learn a 3‐dimensional object as a set of 2‐dimensional images by using a new parametric eigenspace approach with a small memory capacity. The proposed method can easily learn a 3‐dimensional object from its 2‐dimensional image, and can recognize the object and estimate its pose. This paper includes experimental comparisons between the proposed method and other 2‐dimensional collation methods.