Zhongwen Zhang

Zhongwen Zhang, Yuri Boykov

We propose "collision cross-entropy" as a robust alternative to Shannon's cross-entropy (CE) loss when class labels are represented by soft categorical distributions y. In general, soft labels can naturally represent ambiguous targets in classification. They are particularly relevant for self-labeled clustering methods, where latent pseudo-labels are jointly estimated with the model parameters and uncertainty is prevalent. In case of soft labels, Shannon's CE teaches the model predictions to reproduce the uncertainty in each training example, which inhibits the model's ability to learn and generalize from these examples. As an alternative loss, we propose the negative log of "collision probability" that maximizes the chance of equality between two random variables, predicted class and unknown true class. We show that it has the properties of a generalized CE. The proposed collision CE agrees with Shannon's CE for one-hot labels, but the training from soft labels differs. For example, unlike Shannon's CE, data points where y is a uniform distribution have zero contribution to the training. Collision CE significantly improves classification supervised by soft uncertain targets. Unlike Shannon's, collision CE is symmetric for y and network predictions, which is particularly relevant when both distributions are estimated in the context of self-labeled clustering. Focusing on discriminative deep clustering where self-labeling and entropy-based losses are dominant, we show that the use of collision CE improves the state-of-the-art. We also derive an efficient EM algorithm that significantly speeds up the pseudo-label estimation with collision CE.

Zhongwen Zhang, Yuri Boykov

Maximization of mutual information between the model's input and output is formally related to "decisiveness" and "fairness" of the softmax predictions, motivating these unsupervised entropy-based criteria for clustering. First, in the context of linear softmax models, we discuss some general properties of entropy-based clustering. Disproving some earlier claims, we point out fundamental differences with K-means. On the other hand, we prove the margin maximizing property for decisiveness establishing a relation to SVM-based clustering. Second, we propose a new self-labeling formulation of entropy clustering for general softmax models. The pseudo-labels are introduced as auxiliary variables "splitting" the fairness and decisiveness. The derived self-labeling loss includes the reverse cross-entropy robust to pseudo-label errors and allows an efficient EM solver for pseudo-labels. Our algorithm improves the state of the art on several standard benchmarks for deep clustering.

Zhongwen Zhang, Yuri Boykov

We consider weakly supervised segmentation where only a fraction of pixels have ground truth labels (scribbles) and focus on a self-labeling approach optimizing relaxations of the standard unsupervised CRF/Potts loss on unlabeled pixels. While WSSS methods can directly optimize such losses via gradient descent, prior work suggests that higher-order optimization can improve network training by introducing hidden pseudo-labels and powerful CRF sub-problem solvers, e.g. graph cut. However, previously used hard pseudo-labels can not represent class uncertainty or errors, which motivates soft self-labeling. We derive a principled auxiliary loss and systematically evaluate standard and new CRF relaxations (convex and non-convex), neighborhood systems, and terms connecting network predictions with soft pseudo-labels. We also propose a general continuous sub-problem solver. Using only standard architectures, soft self-labeling consistently improves scribble-based training and outperforms significantly more complex specialized WSSS systems. It can outperform full pixel-precise supervision. Our general ideas apply to other weakly-supervised problems/systems.

Zhongwen Zhang, Dmitrii Marin, Maria Drangova et al.

We are interested in unsupervised reconstruction of complex near-capillary vasculature with thousands of bifurcations where supervision and learning are infeasible. Unsupervised methods can use many structural constraints, e.g. topology, geometry, physics. Common techniques use variants of MST on geodesic tubular graphs minimizing symmetric pairwise costs, i.e. distances. We show limitations of such standard undirected tubular graphs producing typical errors at bifurcations where flow "directedness" is critical. We introduce a new general concept of confluence for continuous oriented curves forming vessel trees and show how to enforce it on discrete tubular graphs. While confluence is a high-order property, we present an efficient practical algorithm for reconstructing confluent vessel trees using minimum arborescence on a directed graph enforcing confluence via simple flow-extrapolating arc construction. Empirical tests on large near-capillary sub-voxel vasculature volumes demonstrate significantly improved reconstruction accuracy at bifurcations. Our code has also been made publicly available.

Zhongwen Zhang, Egor Chesakov, Dmitrii Marin et al.

We propose a new geometric regularization principle for reconstructing vector fields based on prior knowledge about their divergence. As one important example of this general idea, we focus on vector fields modelling blood flow pattern that should be divergent in arteries and convergent in veins. We show that this previously ignored regularization constraint can significantly improve the quality of vessel tree reconstruction particularly around bifurcations where non-zero divergence is concentrated. Our divergence prior is critical for resolving (binary) sign ambiguity in flow orientations produced by standard vessel filters, e.g. Frangi. Our vessel tree centerline reconstruction combines divergence constraints with robust curvature regularization. Our unsupervised method can reconstruct complete vessel trees with near-capillary details on synthetic and real 3D volumes.