Topological Regularization for Dense Prediction

TL;DR

This paper introduces a topological regularization method based on persistent homology for dense prediction tasks in computer vision, improving convergence and performance by regularizing internal neural network activations.

Contribution

It proposes a novel topological regularization technique using persistent homology that applies to both outputs and internal activations in neural networks for dense prediction.

Findings

Topological regularization improves convergence in training.

Regularization of internal activations reduces computational costs.

Enhanced performance on benchmark dense prediction tasks.

Abstract

Dense prediction tasks such as depth perception and semantic segmentation are important applications in computer vision that have a concrete topological description in terms of partitioning an image into connected components or estimating a function with a small number of local extrema corresponding to objects in the image. We develop a form of topological regularization based on persistent homology that can be used in dense prediction tasks with these topological descriptions. Experimental results show that the output topology can also appear in the internal activations of trained neural networks which allows for a novel use of topological regularization to the internal states of neural networks during training, reducing the computational cost of the regularization. We demonstrate that this topological regularization of internal activations leads to improved convergence and test benchmarks on several problems and architectures.