Akihiro SUGIMOTO
Object Recognition by Combining Paraperspective Images
Abstract:This paper provides a study on object recognition under paraperspective projection. Discussed is the problem of determining whether or not a given image was obtained from a 3-D object to be recognized. First it is clarified that paraperspective projection is the first-order approximation of perspective projection. Then it is shown that, if we represent an object as a set of its feature points, any paraperspective image can be expressed as a linear combination of three appropriate paraperspective images. We show that any paraperspective image of an object enjoys this property even if it undergoes not only a rigid transformation but also an affine transformation. Particularly in the case of a rigid transformation, the coefficients of the combination have to satisfy two conditions: orthogonality and norm equality. A simple algorithm to solve the above problem based on these properties is presented: a linear, single-shot algorithm. Some experimental results with artificial images are also given; it is found that the algorithm correctly solves the problem for perspective projection as well as for paraperspective projection. Our investigation shows that there exists a simple linear algorithm for recognizing a 3-D object. Namely, we only have to store three images and, whenever a new image is given, we simply determine whether it can be expressed as a combination of the three images.
Key Words: paraperspective projection, linear combination, representation of transformations, 3-D object recognition.