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In this paper, we examine the properties of the  radial distance  which has been used as a tool to compare the shape of simple surfacic objects. We give a rigorous definition of the  radial distance  and derive its theoretical properties, and in particular under which conditions it satisfies the distance properties. We show how the computation of the  radial distance  can be implemented in practice and made faster by the use of an analytical formula and a Fast Fourier Transform. Finally, we conduct experiments to measure how the  radial distance  is impacted by perturbation and generalization and we give abacuses and thresholds to deduce when buildings are likely to be homologous or non-homologous given their  radial distance .

Is the radial distance really a distance? An analysis of its properties and interest for the matching of polygon features