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DiffKillR: Killing and Recreating Diffeomorphisms for Cell Annotation in Dense Microscopy Images

Chen Liu, Danqi Liao, Alejandro Parada-Mayorga, Alejandro Ribeiro, Marcello DiStasio, Smita Krishnaswamy

TL;DR

DiffKillR tackles the challenge of dense cell annotation in microscopy by reframing labeling as archetype matching followed by diffeomorphic image registration. It introduces two networks: DiffeoInvariantNet, which learns a diffeomorphism-invariant cell representation for robust archetype matching, and DiffeoMappingNet, which computes forward and inverse warping fields $\,\mathcal{W}$ and $\mathcal{W}^{-1}$ to recreate and transfer pixel-level annotations between matched cells. Theoretical guarantees from algebraic-signal processing establish that a finite set of deformations suffices to represent bandlimited diffeomorphisms and provide an error bound for cell matching, while empirical results demonstrate strong performance on cell counting, orientation prediction, and few-shot segmentation with reduced labeling. The approach enables versatile, label-efficient annotation across diverse microscopy tasks and offers practical impact for histology analysis and clinical diagnostics.

Abstract

The proliferation of digital microscopy images, driven by advances in automated whole slide scanning, presents significant opportunities for biomedical research and clinical diagnostics. However, accurately annotating densely packed information in these images remains a major challenge. To address this, we introduce DiffKillR, a novel framework that reframes cell annotation as the combination of archetype matching and image registration tasks. DiffKillR employs two complementary neural networks: one that learns a diffeomorphism-invariant feature space for robust cell matching and another that computes the precise warping field between cells for annotation mapping. Using a small set of annotated archetypes, DiffKillR efficiently propagates annotations across large microscopy images, reducing the need for extensive manual labeling. More importantly, it is suitable for any type of pixel-level annotation. We will discuss the theoretical properties of DiffKillR and validate it on three microscopy tasks, demonstrating its advantages over existing supervised, semi-supervised, and unsupervised methods. The code is available at https://github.com/KrishnaswamyLab/DiffKillR.

DiffKillR: Killing and Recreating Diffeomorphisms for Cell Annotation in Dense Microscopy Images

TL;DR

DiffKillR tackles the challenge of dense cell annotation in microscopy by reframing labeling as archetype matching followed by diffeomorphic image registration. It introduces two networks: DiffeoInvariantNet, which learns a diffeomorphism-invariant cell representation for robust archetype matching, and DiffeoMappingNet, which computes forward and inverse warping fields and to recreate and transfer pixel-level annotations between matched cells. Theoretical guarantees from algebraic-signal processing establish that a finite set of deformations suffices to represent bandlimited diffeomorphisms and provide an error bound for cell matching, while empirical results demonstrate strong performance on cell counting, orientation prediction, and few-shot segmentation with reduced labeling. The approach enables versatile, label-efficient annotation across diverse microscopy tasks and offers practical impact for histology analysis and clinical diagnostics.

Abstract

The proliferation of digital microscopy images, driven by advances in automated whole slide scanning, presents significant opportunities for biomedical research and clinical diagnostics. However, accurately annotating densely packed information in these images remains a major challenge. To address this, we introduce DiffKillR, a novel framework that reframes cell annotation as the combination of archetype matching and image registration tasks. DiffKillR employs two complementary neural networks: one that learns a diffeomorphism-invariant feature space for robust cell matching and another that computes the precise warping field between cells for annotation mapping. Using a small set of annotated archetypes, DiffKillR efficiently propagates annotations across large microscopy images, reducing the need for extensive manual labeling. More importantly, it is suitable for any type of pixel-level annotation. We will discuss the theoretical properties of DiffKillR and validate it on three microscopy tasks, demonstrating its advantages over existing supervised, semi-supervised, and unsupervised methods. The code is available at https://github.com/KrishnaswamyLab/DiffKillR.
Paper Structure (29 sections, 2 theorems, 6 equations, 4 figures, 4 tables)

This paper contains 29 sections, 2 theorems, 6 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Cell Segmentation
  4. Traditional methods for cell segmentation
  5. Supervised learning for cell segmentation
  6. Self-supervised and weakly-supervised cell segmentation
  7. Instance segmentation techniques
  8. Diffeomorphism in Medical Image Analysis
  9. Image registration
  10. Atlas-based image segmentation
  11. Methods
  12. DiffeoInvariantNet: learning diffeomorphism invariance
  13. Data augmentation with realistic diffeomorphisms
  14. "Killing" diffeomorphisms
  15. DiffeoMappingNet: mapping pairwise diffeomorphisms
  16. ...and 14 more sections

Key Result

Theorem 4.1

pesenson2000sampling Let $G$ be a Lie group and $\widehat{G}$ a finite subset of $G$. Then there exists a constant $C_{0}>0$ such that every deformation in $\mathcal{PW}_{\omega}(\boldsymbol{S})$ is uniquely determined by its values on $\widehat{G}$ as long as

Figures (4)

  • Figure 1: Proposed DiffKillR framework. (A) A small set of annotated cells forms a cell bank. (B) DiffeoInvariantNet learns a latent space that is invariant to common diffeomorphisms. For each new cell, it finds the closest archetypal cell within the cell bank. (C) DiffeoMappingNet transforms the label to the new cell using the pairwise diffeomorphism computed via image registration.
  • Figure 2: Realistic diffeomorphisms, illustrated using a square and an ellipse.
  • Figure 3: Mapping diffeomorphisms of synthetic shapes with DiffeoMappingNet. Qualitatively, VM-Diff VM_diff is the most competitive architecture for DiffeoMappingNet.
  • Figure 4: Few-shot cell segmentation performance on histology images MoNuSeg.

Theorems & Definitions (4)

  • Definition 4.1
  • Definition 4.2
  • Theorem 4.1
  • Theorem 4.2