Topological Regularization for Dense Prediction
This work addresses computer vision applications by providing an incremental improvement in regularization techniques for neural networks.
The paper tackles the problem of improving dense prediction tasks like depth perception and semantic segmentation by introducing a topological regularization method based on persistent homology, which reduces computational cost and leads to improved convergence and test benchmarks.
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.