HyperTopo-Adapters: Geometry- and Topology-Aware Segmentation of Leaf Lesions on Frozen Encoders

TL;DR

This work addresses topology-sensitive leaf-lesion segmentation by introducing HyperTopo-Adapters, a lightweight head that projects frozen encoder features onto a product manifold $\\mathbb{H} \\oplus \\mathbb{E} \\oplus \\mathbb{S}$ to capture hierarchical structure, local detail, and boundary closure. A topology-aware objective combines a hyperbolic geodesic contrastive loss with a differentiable Soft Euler Characteristic, complemented by warmups and per-sample structure-aware metrics to stabilize training and surface topology preservation. On a 2,940-image Kaggle leaf dataset, the method yields consistent improvements in boundary and topology metrics (notably reducing $\\Delta \\\beta_1$ hole errors by around 9%) while maintaining competitive Dice/IoU, with ablations validating the contribution of curvature learning, latent dimensions, and surrogate settings. The work provides an open, reproducible train/eval suite that isolates geometric/topological priors and offers a practical pathway to topology-preserving architectures for biological segmentation.

Abstract

Leaf-lesion segmentation is topology-sensitive: small merges, splits, or false holes can be biologically meaningful descriptors of biochemical pathways, yet they are weakly penalized by standard pixel-wise losses in Euclidean latents. I explore HyperTopo-Adapters, a lightweight, parameter-efficient head trained on top of a frozen vision encoder, which embeds features on a product manifold -- hyperbolic + Euclidean + spherical (H + E + S) -- to encourage hierarchical separation (H), local linear detail (E), and global closure (S). A topology prior complements Dice/BCE in two forms: (i) persistent-homology (PH) distance for evaluation and selection, and (ii) a differentiable surrogate that combines a soft Euler-characteristic match with total variation regularization for stable training. I introduce warm-ups for both the hyperbolic contrastive term and the topology prior, per-sample evaluation of structure-aware metrics (Boundary-F1, Betti errors, PD distance), and a min-PD within top-K Dice rule for checkpoint selection. On a Kaggle leaf-lesion dataset (N=2,940), early results show consistent gains in boundary and topology metrics (reducing Delta beta_1 hole error by 9%) while Dice/IoU remain competitive. The study is diagnostic by design: I report controlled ablations (curvature learning, latent dimensions, contrastive temperature, surrogate settings), and ongoing tests varying encoder strength (ResNet-50, DeepLabV3, DINOv2/v3), input resolution, PH weight, and partial unfreezing of late blocks. The contribution is an open, reproducible train/eval suite (available at https://github.com/ChimdiWalter/HyperTopo-Adapters) that isolates geometric/topological priors and surfaces failure modes to guide stronger, topology-preserving architectures.

Figures (8)

• Figure 1: The HyperTopo Architecture pipeline I designed. Features are extracted by DINOv2 and projected into three distinct geometric manifolds before decoding.
• Figure 2: Figure 2: Qualitative results from the Euclidean Baseline. Note the fragmentation (confetti-like predictions) in the red masks on the right, indicating high $\beta_0$ error.
• Figure 3: Figure 3: Comparison of Euclidean vs. Naive HES. Note that while HES improves hole detection ($\Delta \beta_1$), it initially degrades Dice scores due to feature space fragmentation caused by the aggressive hyperbolic constraint ($\tau=0.1$).
• Figure 4: Figure 4: Comparison of Euclidean vs. Tuned HyperTopo (HES High). With $\tau=0.2$ and optimized weights, the HyperTopo model (Green) recovers performance, beating the baseline in Dice and maintaining superior topological metrics.
• Figure 5: Figure 5: Qualitative results for Naive H$\oplus$E$\oplus$S. While it captures necrotic holes (improved $\beta_1$), the overall mask integrity is poor, leading to lower Dice scores.

Theorems & Definitions (1)

• Proposition 2.1