# Appearance Shock Grammar for Fast Medial Axis Extraction from Real Images

arXiv: https://arxiv.org/abs/2004.02677 · HTML: https://mlsanity.com/paper/2004.02677/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2020.

## Built on by (most cited first, 5 of 5)

- [Shape-Biased Domain Generalization via Shock Graph Embeddings](https://mlsanity.com/paper/2109.05671/) (2021)
- [Medial Spectral Coordinates for 3D Shape Analysis](https://mlsanity.com/paper/2111.13295/) (2021)
- [Contour-guided Image Completion with Perceptual Grouping](https://mlsanity.com/paper/2111.11322/) (2021)
- [Average Outward Flux Skeletons for Environment Mapping and Topology Matching](https://mlsanity.com/paper/2111.13826/) (2021)
- [Contour Completion using Deep Structural Priors](https://mlsanity.com/paper/2302.04447/) (2023)

## Abstract (arXiv)

We combine ideas from shock graph theory with more recent appearance-based methods for medial axis extraction from complex natural scenes, improving upon the present best unsupervised method, in terms of efficiency and performance. We make the following specific contributions: i) we extend the shock graph representation to the domain of real images, by generalizing the shock type definitions using local, appearance-based criteria; ii) we then use the rules of a Shock Grammar to guide our search for medial points, drastically reducing run time when compared to other methods, which exhaustively consider all points in the input image;iii) we remove the need for typical post-processing steps including thinning, non-maximum suppression, and grouping, by adhering to the Shock Grammar rules while deriving the medial axis solution; iv) finally, we raise some fundamental concerns with the evaluation scheme used in previous work and propose a more appropriate alternative for assessing the performance of medial axis extraction from scenes. Our experiments on the BMAX500 and SK-LARGE datasets demonstrate the effectiveness of our approach. We outperform the present state-of-the-art, excelling particularly in the high-precision regime, while running an order of magnitude faster and requiring no post-processing.