Approximation of dilation-based spatial relations to add structural constraints in neural networks
This work addresses the need for structural constraints in neural networks to improve generalization with small datasets, but it is incremental as it builds on existing approximations for dilation.
The authors tackled the problem of incorporating non-differentiable spatial relations into neural networks by approximating morphological dilation with convolutions, resulting in a method that is faster to compute and suitable for neural network applications, though slightly less accurate than previous approximations.
Spatial relations between objects in an image have proved useful for structural object recognition. Structural constraints can act as regularization in neural network training, improving generalization capability with small datasets. Several relations can be modeled as a morphological dilation of a reference object with a structuring element representing the semantics of the relation, from which the degree of satisfaction of the relation between another object and the reference object can be derived. However, dilation is not differentiable, requiring an approximation to be used in the context of gradient-descent training of a network. We propose to approximate dilations using convolutions based on a kernel equal to the structuring element. We show that the proposed approximation, even if slightly less accurate than previous approximations, is definitely faster to compute and therefore more suitable for computationally intensive neural network applications.