The Scale Axis Transform

The scale axis transform is a generalization of the medial axis transform. It introduces a shape representation that uses a family of skeletons to capture the dominant geometric features of a shape and yields a hierarchy of successively simplified skeletons. See the Definition and Theory – SoCG 2009 tab for the formal mathematical definitions and properties and the 3D Computation Algorithm – SIGGRAPH 2010 tab for practical computation algorithm for 3D shapes.

The Scale Axis Transform

For any question/request about the scale axis feel free to contact Bálint Miklós at the email address:

The Scale Axis Transform

This paper defines the scale axis transform in the general high dimensional euclidean setting. By using a new adaptive distance function induced by the shape, the multiplicative distance, topological properties of the scale axis are be derived.

The Scale Axis Transform

Joachim Giesen, Balint Miklos, Mark Pauly, Camille Wormser: The Scale Axis Transform, ACM Symposium on Computational Geometry 2009   BibTeX PDF

For any question/request about the scale axis feel free to contact Bálint Miklós at the email address:

The Scale Axis Picture Show

The seven minutes long video below is a visual exploration of the scale axis construction and a 2d algorithm for a practical skeleton computation based on the scale axis. The results are compared to other stable medial axis structures. This video has been presented at the multimedia session of SoCG 2009.

The video has been produced with an extended version of Mesecina (the binary you can download, does not contain all the algorithms presented in the video). The two pages abstract below gives references and an overview of the algorithm used to genereate the results in the video.

Joachim Giesen, Balint Miklos, Mark Pauly, Camille Wormser: The Scale Axis Picture Show, Video/multimedia session of Symposium on Computational Geometry 2009   BibTeX  PDF

Video download: The Scale Axis Picture Show.mp4 - H.264 - 1280x720 - 73.4 MB

More examples

To see how the topology of the scale axis evolves in comparison to other methods click on the image below



Click on the thumbnails below to download large (approx. 8000x800 resolution) images showing the evolution of the approximation of the scale axis.



Joachim Giesen, Bálint Miklós, Mark Pauly, Camille Wormser