On 2D constrained discrete rigid transformations

Rigid transformations are involved in a wide range of digital image processing applications. In such a context, they are generally considered as continuous processes, followed by a digitization of the results. Recently, rigid transformations on ℤ2 have been alternatively formulated as a fully discrete process. Following this paradigm, we investigate – from a combinatorial point of view – the effects of pixel-invariance constraints on such transformations. In particular we describe the impact of these constraints on both the combinatorial structure of the transformation space and the algorithm leading to its generation.

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