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

• URL: http://arxiv.org/abs/2601.06067v1
• Date: Mon, 29 Dec 2025 04:27:26 GMT
• Title: HyperTopo-Adapters: Geometry- and Topology-Aware Segmentation of Leaf Lesions on Frozen Encoders
• Authors: Chimdi Walter Ndubuisi, Toni Kazic,
• Abstract summary: Leaf-lesion segmentation is topology-sensitive; small merges, splits, or false holes can be meaningful descriptors of biochemical pathways.<n>I explore HyperTopo-Adapters, a lightweight, parameter-efficient head trained on top of a frozen vision encoder.<n>Early results show consistent gains in boundary and topology metrics on a Kaggle leaf-lesion dataset.
• Score: 0.14323566945483493
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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