In this paper, we present a novel method for 2D shape extraction based on the Hough Transform. The method is applicable under similarity transformations while maintaining the dimensionality of the problem as that of the original GHT. This is possible due to the use of a set of Fourier based descriptors which remain invariant under translation, scale and rotation. In contrast with other invariants used in the same context, the descriptors we present here are local, and therefore our method is specially tolerant to noise and occlusion. Experimental results are presented demonstrating performance on highly occluded scenes and showing significantly superior performance of our method, related to the GHT, in the presence of global unmodelled deformations.