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Spatial relations between objects in an image have proved useful forstructural object recognition. Structural constraints can act as regularizationin neural network training, improving generalization capability with smalldatasets. Several relations can be modeled as a morphological dilation of areference object with a structuring element representing the semantics of therelation, from which the degree of satisfaction of the relation between anotherobject and the reference object can be derived. However, dilation is notdifferentiable, requiring an approximation to be used in the context ofgradient-descent training of a network. We propose to approximate dilationsusing convolutions based on a kernel equal to the structuring element. We showthat the proposed approximation, even if slightly less accurate than previousapproximations, is definitely faster to compute and therefore more suitable forcomputationally intensive neural network applications.

Approximation of dilation-based spatial relations to add structural constraints in neural networks