Deep Image Prototype Learning with Geometric Heat-Kernel Priors
Authors: Jiarui Xing, Tal Zeevi, Nian Wu, Jian Wang
Organizations: Yale School of Medicine, New Haven CT, 06510, USA · University of Virginia, Charlottesville, VA, 22903, USA · Harvard Medical School, Boston MA, 02115, USA
Abstract
Learning unsupervised representations of medical imaging cohorts can reveal anatomically meaningful prototypes without expert labels, which are often noisy and fail to capture true pathological heterogeneity. However, existing deep latent-variable models estimate Gaussian mixture priors via Euclidean averaging, producing prototypes that drift off the curved data manifold and degenerate as the number of sub-populations grows. We propose a manifold-anchored variational framework built on a geometry-aware Expectation-Maximization (EM) algorithm, whose M-step selects each sub-population prototype as the graph medoid with the highest diffusion centrality on a heat-kernel-weighted latent graph, ensuring that every prototype remains on-manifold. A Dirichlet energy regularizer enforces geometric smoothness of the latent space, and a per-sub-population uncertainty score enables label-free quality assessment. The manifold-anchored EM is a general-purpose geometric tool that extends standard EM and applies readily to other latent-variable models beyond this setting. On cardiac scar and brain MRI benchmarks, our framework attains the highest accuracy among all compared methods, produces the sharpest prototypes reported to date, and remains stable at large sub-population counts where all baselines degenerate. Code and implementation details are available at https://github.com/jr-xing/On-Manifold-Variational-Learning-with-Heat-Kernel-Priors.
Anomaly detection in medical images is challenging due to limited annotations and the domain gap. Existing reconstruction-based methods often rely on frozen pre-trained encoders, restricting adaptation to domain-specific patterns and degrading localization accuracy. Meanwhile, prototype-based learning offers interpretable representations but commonly suffers from prototype collapse, where a few prototypes dominate training and reduce diversity. To address these issues, we propose DNP-ConFormer, a unified framework that integrates a trainable encoder with prototype-guided reconstruction and a Diversity-Aware Alignment Loss. A momentum encoder enables stable domain-adaptive representation learning, while a lightweight Prototype Extractor discovers informative normal prototypes and injects them into the decoder via attention to guide reconstruction. The proposed alignment objective further encourages balanced feature-to-prototype assignments, effectively mitigating prototype collapse. Extensive experiments on multiple medical imaging benchmarks demonstrate improved representation quality and anomaly localization compared with prior methods. Visualization and prototype assignment analyses further validate the effectiveness and interpretability of our approach. The code is available at https://github.com/liluhu0/DNP-ConFormer.
Numerous medical imaging problems must be solved under limited labels and constrained compute, yet it remains unclear whether performance gains are driven mainly by more expressive models or by better representation of clinically meaningful anatomy. We study this question through a low-data anatomy-aware benchmark for 5-class cardiac pathology prediction on the public ACDC MRI dataset. Using segmentation-derived patient descriptors from the right ventricle, myocardium, and left ventricle, we compare anatomy-specific and multi-structure representations across linear, kernel, and tree-based classifiers. We find that under limited label settings, representation dominates complexity. These results suggest that in resource-constrained healthcare settings, identifying and representing the most informative anatomy may matter more than the increasing complexity of the model alone.
Few-Shot Medical Image Segmentation (FSMIS) aims to delineate novel anatomical targets from one or a few annotated support images, addressing the annotation scarcity in medical imaging. Notwithstanding recent advancements, current prototype-based methods are bottlenecked by two coupled limitations: 1) cue entanglement, where a single spatial-domain prototype is forced to summarise organ silhouette, parenchymal texture and boundary appearance simultaneously, so any support-query mismatch on one cue propagates indiscriminately to the others; and 2) topology-blind matching, where cosine similarity measures distance in the ambient Euclidean space and ignores the connectivity of the underlying feature manifold, causing fragmented activations inside low-contrast organs and leakage into neighbouring tissues. To this end, we propose Spectral-Geodesic Prototype Network (SGP-Net), built around a Spectral-Geodesic Prototype Module with two coupled components. A Spectral Prototype Bank (SPB) decomposes support and query features into low-, mid- and high-frequency bands via learnable radial Fourier filters, yielding three disentangled prototypes per class that separately encode shape, texture and boundary cues. A Geodesic Matcher (GM) then replaces cosine similarity with a differentiable heat-diffusion approximation of geodesic distance, propagating matching signals along a feature affinity graph so that on-manifold pixels accumulate consistent responses while off-manifold look-alikes are suppressed. Experiments on three public FSMIS benchmarks demonstrate that SGP-Net achieves competitive performance against recent state-of-the-art methods.