TopoGO — Knot Detection from Images

中文版README

Introduction

This project recognizes knot images and computes their topological invariants (Alexander polynomials). It implements two detection pipelines:

Pipeline A — Sliding Window Method

Detects crossings by scanning the label image with a sliding window.

• Demo (single image): demo_window.py
• Batch (all images): batch_window.py

Pipeline B — Centerline Method

Extracts skeleton centerlines, finds their endpoints, and detects crossings geometrically.

• Demo (single image): demo_centerline.py
• Batch (all images): batch_centerline.py

Processing Pipeline

 Image → Binarize → Segment → Label → Classify → Detect Crossings → Alexander Polynomial
  (s0)     (s1)       (s2)     (s3)      (s4)     (s5a / s5b)            (s6)

Source modules in src/ are numbered by pipeline step:

Module	Step	Description
0_io.py	0	Image loading and saving
1_binarize.py	1	Threshold-based binarization
2_segment.py	2	Connected component labeling
3_label_utils.py	3	Label arrangement, separation, and merging
4_classify.py	4	Line segment classification
5a_cross_detect.py	5a	Sliding window crossing detection (Pipeline A)
5b_centerline.py	5b	Centerline-based crossing detection (Pipeline B)
5b_thinning.py	5b	Zhang-Suen thinning (reference implementation)
6_alexander.py	6	Alexander polynomial computation
viz.py	—	Visualization utilities

Setup

pip install -r requirements.txt

References

• TopoGO_Knot-Detection-of-Images.pdf — Project paper
• SUSTech_DIP_Poster_*.pdf — Conference posters
• Input images sourced from Knot Atlas

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TODO: Prove conversion relationships with other topological invariants; explore alternative methods for computing the Alexander polynomial.