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Polar matching is a recently developed shift and rotation invariant object detection method that is based upon dual-tree complex wavelet transforms or equivalent multiscale directional filterbanks. It can be used to facilitate both keypoint matching, neighborhood search detection, or detection and tracking with particle filters. The theory is extended here to incorporate an allowance for local spatial and dilation perturbations. With experiments, we demonstrate that the robustness of the polar matching method is strengthened at modest computational cost.