Kartezio: Evolutionary Design of Explainable Pipelines for Biomedical Image Analysis

An unresolved issue in contemporary biomedicine is the overwhelming number and diversity of complex images that require annotation, analysis and interpretation. Recent advances in Deep Learning have revolutionized the field of computer vision, creating algorithms that compete with human experts in image segmentation tasks. Crucially however, these frameworks require large human-annotated datasets for training and the resulting models are difficult to interpret. In this study, we introduce Kartezio, a modular Cartesian Genetic Programming based computational strategy that generates transparent and easily interpretable image processing pipelines by iteratively assembling and parameterizing computer vision functions. The pipelines thus generated exhibit comparable precision to state-of-the-art Deep Learning approaches on instance segmentation tasks, while requiring drastically smaller training datasets, a feature which confers tremendous flexibility, speed, and functionality to this approach. We also deployed Kartezio to solve semantic and instance segmentation problems in four real-world Use Cases, and showcase its utility in imaging contexts ranging from high-resolution microscopy to clinical pathology. By successfully implementing Kartezio on a portfolio of images ranging from subcellular structures to tumoral tissue, we demonstrated the flexibility, robustness and practical utility of this fully explicable evolutionary designer for semantic and instance segmentation.

Sparse regular variation

Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure-the spectral measure-defined on the positive orthant of the unit sphere. This measure gathers information on the localization of extreme events and is often sparse since severe events do not occur in all directions. Unfortunately, it is defined through weak convergence which does not provide a natural way to capture its sparse structure. In this paper, we introduce the notion of sparse regular variation, which allows to better learn the sparse structure of extreme events. This concept is based on the euclidean projection onto the simplex for which efficient algorithms are known. We show several results for sparsely regularly varying random vectors. Finally, we prove that under mild assumptions sparse regular variation and regular variation are two equivalent notions.