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

arXiv: https://arxiv.org/abs/2102.10923 · HTML: https://mlsanity.com/paper/2102.10923/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 8 references that are in the map.
- First posted on arXiv 22 Feb 2021.

## Builds on (most cited first, 1 of 1)

- [Psi-Net: Shape and boundary aware joint multi-task deep network for medical image segmentation](https://mlsanity.com/paper/1902.04099/) (2019)

## Abstract (arXiv)

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.