# Unified Multiscale Planar, Surface, and Curve Skeletons

## Question

Skeletons, or medial axes, are structures that researchers have aimed to compute for more than half a century to concisely describe 2D and 3D shapes. There are two key problems for their computation:

*regularization*: How to eliminate the effects of small-scale noise on the shape to get clean, useful, skeletons;*generalization*: How to compute regularized skeletons of 2D and 3D shapes using the*same*principle.

## Solution

We have found the solution to both above problems (after elusive searches in the same direction for decades and by tens of researchers). Simply put: We model skeletonization as an *advection* process that moves mass, uniformly spread on a shape's boundary, inwards, following a **momentum-conservation** principle:

Mass flows from the shape boundary inwards along the gradient of the boundary's distance transform. When different mass particles collide (that is, on the *surface* skeleton), they move in the direction that obeys momentum conservation. Such mass particles collide again along the *curve* skeleton. Ultimately, all mass sinks in a single point, the shape's center.
**Skeletonization**, using a single principle and model, regardless of dimensionality!

## Results

Our method gives visually identical results to more complex, dimension-specific, skeletonization methods. See below an example in 2D:

Even more impressively, we get the same visually identical results for our method compared to 3D skeletonization techniques:

## Publications

An Unified Multiscale Framework for Planar, Surface, and Curve Skeletonization A. Jalba, A. Sobiecki, A. Telea. IEEE TPAMI, vol. 38, no. 1, pp. 38-45, 2015