DeDA: Deep Directed Accumulator

Chronic active multiple sclerosis lesions, also termed as rim+ lesions, can be characterized by a hyperintense rim at the edge of the lesion on quantitative susceptibility maps. These rim+ lesions exhibit a geometrically simple structure, where gradients at the lesion edge are radially oriented and a greater magnitude of gradients is observed in contrast to rim- (non rim+) lesions. However, recent studies have shown that the identification performance of such lesions remains unsatisfied due to the limited amount of data and high class imbalance. In this paper, we propose a simple yet effective image processing operation, deep directed accumulator (DeDA), that provides a new perspective for injecting domain-specific inductive biases (priors) into neural networks for rim+ lesion identification. Given a feature map and a set of sampling grids, DeDA creates and quantizes an accumulator space into finite intervals, and accumulates feature values accordingly. This DeDA operation is a generalized discrete Radon transform and can also be regarded as a symmetric operation to the grid sampling within the forward-backward neural network framework, the process of which is order-agnostic, and can be efficiently implemented with the native CUDA programming. Experimental results on a dataset with 177 rim+ and 3986 rim- lesions show that 10.1% of improvement in a partial (false positive rate<0.1) area under the receiver operating characteristic curve (pROC AUC) and 10.2% of improvement in an area under the precision recall curve (PR AUC) can be achieved respectively comparing to other state-of-the-art methods. The source code is available online at https://github.com/tinymilky/DeDA