Homeomorphism Prior for False Positive and Negative Problem in Medical Image Dense Contrastive Representation Learning

TL;DR

Medical image dense contrastive learning faces large-scale FP&N pairs due to intrinsic image properties. GEMINI addresses this by embedding a homeomorphism prior through Deformable Homeomorphism Learning (DHL) and Geometric Semantic Similarities (GSS), enabling reliable pixel-wise correspondence and soft negative-pair learning. The framework is instantiated in two practical variants: GEMINI-Semi for few-shot semi-supervised segmentation and GEMINI-MIP for self-supervised pre-training, achieving state-of-the-art results across seven datasets and demonstrating strong data efficiency and transferability. By combining topology-preserving deformation with semantic-aware similarity, GEMINI significantly mitigates FP&N issues and enhances dense representation learning in MIDP tasks, with potential for broad clinical impact.

Abstract

Dense contrastive representation learning (DCRL) has greatly improved the learning efficiency for image-dense prediction tasks, showing its great potential to reduce the large costs of medical image collection and dense annotation. However, the properties of medical images make unreliable correspondence discovery, bringing an open problem of large-scale false positive and negative (FP&N) pairs in DCRL. In this paper, we propose GEoMetric vIsual deNse sImilarity (GEMINI) learning which embeds the homeomorphism prior to DCRL and enables a reliable correspondence discovery for effective dense contrast. We propose a deformable homeomorphism learning (DHL) which models the homeomorphism of medical images and learns to estimate a deformable mapping to predict the pixels' correspondence under topological preservation. It effectively reduces the searching space of pairing and drives an implicit and soft learning of negative pairs via a gradient. We also propose a geometric semantic similarity (GSS) which extracts semantic information in features to measure the alignment degree for the correspondence learning. It will promote the learning efficiency and performance of deformation, constructing positive pairs reliably. We implement two practical variants on two typical representation learning tasks in our experiments. Our promising results on seven datasets which outperform the existing methods show our great superiority. We will release our code on a companion link: https://github.com/YutingHe-list/GEMINI.

Figures (19)

• Figure 1: The DCRL with the large-scale FP&N problem. A) The DCRL pulls and pushes the positive and negative feature pairs for consistent or distinct representation. However, B) medical images' properties cause unreliable correspondence discovery, resulting in the open problem of large-scale FP&N features pairs in DCRL and extremely limiting the representation learning ability.
• Figure 2: The homeomorphism prior enables the pixel-wise correspondence discovery under the condition of medical images' inherent topology, promoting its reliability. A) In topologie, the homeomorphic objects are able to align their topologies via a homeomorphism mapping for point-to-point correspondence with topological preservation. B) Due to the consistency of human body, the medical images are homeomorphic in image space. This provides prior knowledge to construct a deformable mapping for the pixels' correspondence under the condition of their inherent topology, which will effectively reduce the searching space of pairing. C) This gives a potential to enable a reliable pixel-wise correspondence discovery in the medical image DCRL.
• Figure 3: Our GEMINI embedded the homeomorphism prior in medical images achieves a reliable correspondence discovery in DCRL. It has two aspects: a) The DHL (Sec.\ref{['sec:dhl']}) learns a deformable mapping for soft learning of negative pairs. b) The GSS (Sec.\ref{['sec:gss']}) fuses semantic similarity into the measurement of correspondence degree to construct the positive pairs reliably. The "opt" is the optimization. More details are described in Sec.D of our Supplementary Materials.
• Figure 4: The gradients from the loss of our GSS simultaneously train the explicit contrast of positive pairs and drive the implicit and soft learning in our DHL.
• Figure 5: Intuitions on behavior. a) The two optimization objectives in Equ.\ref{['equ:opt']} for $\theta$ drive the reliable learning of positive and implicit learning of negative pairs. b) The feature pairs are learned softly via the gradient from the DHL.