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

Invariant Pictorial Recognition Zhiqian Wang and Jezekiel Ben-Arie EECS Department, University of Illinois at Chicago, Chicago, IL 60607 Abstract This paper presents an e cient scheme for a neinvariant object recognition. A ne invariance is obtained by a representation which is based on a new sampling con guration in the frequency domain. We discuss the decomposition of a ne transform into slant, tilt, swing, scale and 2D translation by applying Singular Value Decomposition (SVD). The Afne Invariant Spectral Signatures (AISS) are derived from a set of Cartesian logarithmic-logarithmic (loglog) sampling con guration in the frequency domain. 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), AISS yields a complete a ne invariance. The proposed log-log conguration can be employed either by a global Fourier transform or by a local Gabor transform. Local representation enables 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 byproduct.