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SVD and log-log frequency sampling with Gabor kernels for invariant pictorial recognition

This paper presents an efficient scheme for affine-invariant object recognition. Affine invariance is obtained by a representation which is based on a new sampling configuration in the frequency domain. We discuss the decomposition of affine transform into slant, tilt, swing, scale and 2D translation by applying singular value decomposition (SVD). The affine invariant spectral signatures (AISS) are derived from a set of Cartesian logarithmic-logarithmic (log-log) sampling configuration in the frequency domain. The AISS enables the recognition of image patches that correspond to roughly planar object surfaces-regardless of their poses in space. Unlike previous log-polar representations which are not invariant to slant (i.e. foreshortening only in one direction), the AISS yields a complete affine invariance. The proposed log-log configuration can be employed either by a global Fourier transform or by a local Gabor transform. Local representation enables one to recognize separately several objects in the same image. The actual signature recognition is performed by multi-dimensional indexing in a pictorial dataset. 3D pose information is also derived as a by-product.