Direct Object Recognition Using No Higher Than Second or Third Order Statistics of the Image

Abstract

Novel algorithms for object recognition are described that directly recover the transformations relating the image to its model. Unlike methods fitting the typical conventional framework, these new methods do not require exhaustive search for each feature correspondence in order to solve for the transformation. Yet they allow simultaneous object identification and recovery of the transformation. Given hypothesized % potentially corresponding regions in the model and data (2D views) --- which are from planar surfaces of the 3D objects --- these methods allow direct compututation of the parameters of the transformation by which the data may be generated from the model. We propose two algorithms: one based on invariants derived from no higher than second and third order moments of the image, the other via a combination of the affine properties of geometrical and the differential attributes of the image. Empirical results on natural images demonstrate the effectiveness of the proposed algorithms. A sensitivity analysis of the algorithm is presented. We demonstrate in particular that the differential method is quite stable against perturbations --- although not without some error --- when compared with conventional methods. We also demonstrate mathematically that even a single point correspondence suffices, theoretically at least, to recover affine parameters via the differential method.