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In this paper, we present a registration approach for images having arbitrarily-shaped locally variant illuminations. These variations tend to degrade the performance of geometric registration precision (GRP) and impact subsequent processing. Traditional registration approaches typically use a least-squares estimator that is sensitive to outliers. Instead, we propose using a robust bisquare M-estimator, as it differently penalizes the small and large residuals. The proposed approach shows clear improvements over competing approaches in terms of GRP and illumination correction, using simulated and real image pairs.