💻 computer science

SCKAN: Structural Consensus-based KAN Prototype Learning for Semi-Supervised Pancreas Segmentation

The paper proposes SCKAN, a novel semi-supervised learning framework that integrates Kolmogorov-Arnold Networks with structural consensus mechanisms to overcome supervision bias and improve generalizability in pancreas segmentation under sparse annotation conditions.

Original authors: Yuqi Liu, Yufei Chen, Wei Fu, Xiaodong Yue, Shuo Li

Published 2026-05-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yuqi Liu, Yufei Chen, Wei Fu, Xiaodong Yue, Shuo Li

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Finding the Pancreas in a Crowd

Imagine you are trying to teach a computer to find the pancreas (a small, tricky organ) inside thousands of 3D CT scan images. This is crucial for spotting cancer early.

The Problem:
You have a huge pile of images, but only a tiny few have "answer keys" (doctors have drawn the pancreas on them). The rest are blank. This is called Semi-Supervised Learning.

The pancreas is a shape-shifter. In one person, it looks like a long snake; in another, it's a short, fat blob. Because the shapes vary so much, the computer gets confused. When it only has a few "answer keys" to learn from, it develops a bad habit called "Supervision Bias."

The Analogy: Imagine a student who only studies three specific practice exams. If the real test looks slightly different, the student panics and guesses wrong. They memorized the examples instead of understanding the concept. The computer ends up either cutting off parts of the pancreas (under-segmentation) or grabbing too much surrounding tissue (over-segmentation).

The Solution: SCKAN (The "Smart Group Study" Method)

The authors propose a new method called SCKAN. Think of it as organizing a "group study session" where the computer learns not just from the few answer keys, but by finding the shared structural rules that apply to everyone, regardless of how their pancreas looks.

They use a new type of math engine called a KAN (Kolmogorov-Arnold Network).

The Analogy: Traditional AI is like a rigid ruler; it tries to force every shape to fit a straight line. A KAN is like a flexible, stretchy rubber band. It can bend and twist to fit complex, wiggly shapes perfectly, filtering out the "noise" (random differences) to find the "signal" (the true shape).

SCKAN works in two main steps:

1. SPCL: The "Anatomy Map" (Structure-constrained Prototype Learning)

Instead of looking at the whole pancreas as one big, confusing blob, SCKAN breaks it down into three logical parts: the Head, the Body, and the Tail.

How it works: Even though every pancreas is shaped differently, they all have a head, a body, and a tail in roughly the same order.
The Analogy: Imagine trying to recognize a friend in a crowd. Instead of memorizing their exact face (which might change with a hat or glasses), you focus on the structure: "They have a head on top, a body in the middle, and legs at the bottom."
The Magic: The system forces the computer to learn that the "Head" of Person A must look like the "Head" of Person B, even if Person A is tall and Person B is short. This creates a "structural consensus" (an agreement on the rules) across all the images, preventing the computer from getting biased by just the few labeled examples.

2. CKaF: The "Noise Filter" (Consensus-based KAN Fusion)

Once the computer has identified these Head/Body/Tail parts, it needs to combine the information from the few "labeled" images and the many "unlabeled" images.

How it works: The unlabeled images are full of noise and confusion. The KAN acts as a super-smart filter.
The Analogy: Imagine a noisy classroom where 99 students are whispering random things, and only 1 student has the correct answer. A normal teacher might get distracted by the noise. The KAN is like a super-teacher who can instantly tune out the 99 whispers, find the common thread of truth among them, and combine it with the one correct answer to create a perfect, clear lesson.
The Result: It filters out the "weird" shapes of individual samples and keeps only the stable, shared knowledge.

Why This Matters (According to the Paper)

The authors tested this on two public datasets of pancreas scans.

The Result: When they gave the computer very few "answer keys" (as few as 3 or 5% of the data), SCKAN performed significantly better than all previous methods.
The Proof: In the visualizations, other methods left holes in the pancreas or grabbed too much background. SCKAN produced clean, complete outlines that looked very close to the doctor's drawings.

Summary

SCKAN is a new way to teach computers to find pancreases in medical scans when there are very few examples to learn from.

It stops the computer from just memorizing specific examples (which causes errors).
It breaks the organ down into logical parts (Head, Body, Tail) to find shared rules.
It uses a flexible, smart math tool (KAN) to filter out the noise and combine what it learns from everyone.

The result is a computer that understands the structure of the pancreas, not just the pictures it was shown, leading to much more accurate medical diagnoses.

Technical Summary: SCKAN – Structural Consensus-based KAN Prototype Learning for Semi-Supervised Pancreas Segmentation

Problem Statement
Accurate pancreas segmentation is vital for early cancer diagnosis but is hindered by the scarcity of annotated medical data, necessitating Semi-Supervised Learning (SSL). Existing SSL methods, particularly those relying on Consistency Regularization (CR) or Prototype Learning (PL), face severe generalizability limitations when applied to pancreas data. This is due to significant inter-sample morphological variability (differences in shape and size across patients). These limitations lead to a "Supervision Bias" problem: models fail to generalize beyond the limited labeled guidance, resulting in under- or over-segmentation. Current methods lack shared structural knowledge across samples; they treat samples in isolation or rely on prototypes constrained by sparse supervision, failing to capture the analogous structural semantics (head, body, tail) that exist across diverse morphologies.

Methodology: SCKAN
The authors propose Structural Consensus-based KAN Prototype Learning (SCKAN), the first framework to integrate Kolmogorov-Arnold Networks (KANs) with cross-sample structural consensus learning for Semi-Supervised Pancreas Segmentation (SSPS). Built upon a Mean-Teacher framework, SCKAN employs two core components to address supervision bias:

Structure-constrained Prototype Consistency Learning (SPCL):
- Structure-aware Spatial Decomposition (SSD): This module decomposes the pancreas into spatially coherent subregions (head, body, tail) using anatomy-guided K-means clustering on spatial coordinates. This establishes a reliable cross-sample structural correspondence, ensuring that prototypes from different samples represent analogous anatomical parts.
- Positional Consistency Calibration (PCC): To refine these prototypes, PCC introduces two mechanisms:
  - Position-weighted Contrastive Learning: Assigns specific weights to prototype pairs based on whether they share the same class and region, optimizing cross-sample alignment and inter-class discriminability.
  - Positional Decorrelation Regularization: Imposes a penalty on intra-sample prototypes to ensure diversity among subregions (e.g., ensuring the head prototype remains distinct from the tail prototype within the same sample).
Consensus-based Kolmogorov-Arnold Fusion (CKaF):
- This module leverages the superior nonlinear fitting capabilities of KANs to aggregate stable structural consensus while filtering sample-specific noise.
- It utilizes KAN's adaptive B-spline functions with local support to model complex, nonlinear cross-sample relationships. By processing labeled and unlabeled prototypes through KAN layers and performing batch-level averaging, CKaF synthesizes a "Structural Consensus Prototype." This process effectively filters morphology-specific noise and aggregates stable knowledge shared across high-variability samples, reducing bias.
Consensus-Guided Synergetic Learning:
- The segmentation network and the prototype space are bridged via consistency regularization. A hybrid loss (combining Dice and Cross-Entropy) is applied to both the segmentation predictions and the prototype-based predictions. A time-dependent Gaussian warming-up function gradually increases the contribution of consensus learning during training.

Key Contributions

First Cross-Sample Structural Consensus with KANs: The paper introduces the first application of KANs to construct cross-sample structural consensus learning in the context of SSPS, specifically targeting the supervision bias caused by pancreatic morphological diversity.
Novel SPCL Mechanism: The authors design an anatomy-guided prototype-level consistency mechanism that promotes unbiased structural representations by enforcing cross-sample alignment at the subregion level (head, body, tail).
Novel CKaF Strategy: A KAN-enhanced cross-sample fusion strategy is proposed to aggregate stable consensus and filter sample-wise noise, thereby reducing morphology-specific bias.

Experimental Results
The method was evaluated on two public datasets: NIH-PAN (80 CT scans) and MSD-PAN (281 annotated cases).

Performance: SCKAN achieved state-of-the-art results on both datasets. On the NIH-PAN dataset with only 5% labeled data (3 samples), SCKAN achieved a Dice score of 78.91%, significantly outperforming previous SSL methods like BCP (74.90%) and MPER (74.88%).
Robustness: On the more challenging MSD-PAN dataset, SCKAN maintained competitive performance with consistently low variance, achieving a Dice of 63.72% at 20% supervision.
Visual Quality: Qualitative results demonstrated that SCKAN effectively preserves structural completeness and reduces holes or over-segmentation common in other methods.
Ablation Studies:
- Removing SPCL components (SSD and PCC) resulted in a drop in Dice score, confirming the necessity of anatomy-guided structural correspondence.
- Replacing the KAN fusion (CKaF) with standard MLP or Average Fusion strategies increased the gap between labeled and unlabeled data performance, validating that KANs are superior at filtering noise and aggregating consensus.
- The diversity loss coefficient ( $\lambda_{div}$ ) was found to be optimal at 0.5, balancing cross-sample alignment and intra-sample diversity.

Significance and Claims
The paper claims that SCKAN fundamentally addresses the "Supervision Bias" problem in semi-supervised pancreas segmentation. By moving beyond sample-wise consistency to cross-sample structural consensus, the method enables models to learn shared anatomical knowledge despite significant morphological variability. The integration of KANs is highlighted as a critical innovation, as their adaptive B-spline nonlinearity provides a strong basis for modeling complex cross-sample relationships and filtering local noise. The authors assert that this approach leads to more generalizable and accurate segmentation, particularly in scenarios with extreme annotation scarcity. The code is made publicly available to facilitate further research.