Pictorial recognition using affine-invariant spectral signatures

This paper describes an efficient approach to pose invariant object recognition employing pictorial recognition of image patches. A complete affine invariance is achieved by a representation which is based on a new sampling configuration in the frequency domain. Employing Singular Value Decomposition (SVD), the affine transform is decomposed into slant, tilt, swing, scale and 2D translation. From this decomposition, we derive an affine invariant representation that allows to recognize image patches that correspond to object surfaces which are roughly planar-invariant to their pose in space. The representation is in the form of Spectral Signatures that are derived from a set of Cartesian logarithmic-logarithmic (log-log) sampling configuration in the frequency domain. Unlike previous log-polar representations which are not invariant to slant (i.e. foreshortening only in one direction), our new configuration yields complete affine invariance. The proposed log-log configuration can be employed both globally or locally by a Gabor or Fourier transforms. Local representation enables to recognize separately several objects in the same image. The actual signature recognition is performed by multidimensional indexing in a pictorial dataset represented in the frequency domain. The recognition also provides 3D pose information.