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Green Image
Issue No. 06 - June (2013 vol. 35)
ISSN: 0162-8828
pp: 1383-1396
Simon Lucey , Commonwealth Science and Industrial Research Organisation (CSIRO), Brisbane
Rajitha Navarathna , Queensland University of Technology, Brisbane
Ahmed Bilal Ashraf , University of Pennsylvania, Philadelphia
Sridha Sridharan , Queensland University of Technology, Brisbane
In this paper, we propose a framework for both gradient descent image and object alignment in the Fourier domain. Our method centers upon the classical Lucas & Kanade (LK) algorithm where we represent the source and template/model in the complex 2D Fourier domain rather than in the spatial 2D domain. We refer to our approach as the Fourier LK (FLK) algorithm. The FLK formulation is advantageous when one preprocesses the source image and template/model with a bank of filters (e.g., oriented edges, Gabor, etc.) as 1) it can handle substantial illumination variations, 2) the inefficient preprocessing filter bank step can be subsumed within the FLK algorithm as a sparse diagonal weighting matrix, 3) unlike traditional LK, the computational cost is invariant to the number of filters and as a result is far more efficient, and 4) this approach can be extended to the Inverse Compositional (IC) form of the LK algorithm where nearly all steps (including Fourier transform and filter bank preprocessing) can be precomputed, leading to an extremely efficient and robust approach to gradient descent image matching. Further, these computational savings translate to nonrigid object alignment tasks that are considered extensions of the LK algorithm, such as those found in Active Appearance Models (AAMs).
Active appearance model, Jacobian matrices, Integrated circuits, Vectors, Robustness, Linear programming, Lighting

S. Lucey, R. Navarathna, A. B. Ashraf and S. Sridharan, "Fourier Lucas-Kanade Algorithm," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 35, no. 6, pp. 1383-1396, 2013.
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