Object recognition by combining paraperspective images

摘要

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 and the object undergoes a rigid transformation or an affine transformation, any paraperspective image can be expressed as a linear combination of several appropriate paraperspective images: we need at least three images for rigid transformations; whereas we need at least two images for affine transformations. 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 synthetic images and real images are also given.