LSMAT Least Squares Medial Axis Transform

by   Daniel Rebain, et al.

The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers, perturbations and/or noise along the boundary of objects. To overcome this limitation, we introduce a new formulation of the medial axis transform which is naturally robust in the presence of these artifacts. Unlike previous work which has approached the medial axis from a computational geometry angle, we consider it from a numerical optimization perspective. In this work, we follow the definition of the medial axis transform as "the set of maximally inscribed spheres". We show how this definition can be formulated as a least squares relaxation where the transform is obtained by minimizing a continuous optimization problem. The proposed approach is inherently parallelizable by performing independant optimization of each sphere using Gauss-Newton, and its least-squares form allows it to be significantly more robust compared to traditional computational geometry approaches. Extensive experiments on 2D and 3D objects demonstrate that our method provides superior results to the state of the art on both synthetic and real-data.


page 1

page 5

page 6

page 8

page 9

page 10

page 13

page 14


Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape

We present a full pipeline for computing the medial axis transform of an...

Pole recovery from noisy data on imaginary axis

This note proposes an algorithm for identifying the poles and residues o...

Cosine-Pruned Medial Axis: A new method for isometric equivariant and noise-free medial axis extraction

We present the CPMA, a new method for medial axis pruning with noise rob...

SEG-MAT: 3D Shape Segmentation Using Medial Axis Transform

Segmenting arbitrary 3D objects into constituent parts that are structur...

Robust Ellipsoid-specific Fitting via Expectation Maximization

Ellipsoid fitting is of general interest in machine vision, such as obje...

Coverage Axis: Inner Point Selection for 3D Shape Skeletonization

In this paper, we present a simple yet effective formulation called Cove...

Treating Bugs as Features: A compositional guide to the statistical analysis of the microbiome-gut-brain axis

There has been a growing acknowledgement of the involvement of the gut m...

Please sign up or login with your details

Forgot password? Click here to reset