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Direct object recognition using no higher than second order statistics of the image

Novel algorithms for object recognition are described that directly recover the transformations relating the image to its model. Unlike methods fitting the 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 corresponding regions in the model and data (2D views)-which are from planar surfaces of the 3D objects-these methods allow direct computation 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 order moments of the image, the other via a combination of the affine properties of geometrical and differential attributes of the image. Empirical results on natural images demonstrate the effectiveness of the proposed algorithms. We demonstrate in particular that the differential method is quite stable against perturbations-although not without some error-when compared with conventional methods.