Efficient computation of a simplified medial axis

Abstract

Applications of of the medial axis have been limited because of its instability and algebraic complexity. In this paper, we use a simplification of the medial axis, the θ-SMA, that is parameterized by a separation angle (θ) formed by the vectors connecting a point on the medial axis to the closest points on the boundary. We present a formal characterization of the degree of simplification of the θ-SMA as a function of θ, and we quantify the degree to which the simplified medial axis retains the features of the original polyhedron.We present a fast algorithm to compute an approximation of the θ-SMA. It is based on a spatial subdivision scheme, and uses fast computation of a distance field and its gradient using graphics hardware. The complexity of the algorithm varies based on the error threshold that is used, and is a linear function of the input size. We have applied this algorithm to approximate the SMA of models with tens or hundreds of thousands of triangles. Its running time varies from a few seconds, for a model consisting of hundreds of triangles, to minutes for highly complex models.

Medial Spheres for Shape Approximation

“…Our goal is to locate a few medial spheres such that the volume of their union approximates the volume of Ω well. As proven in [16], removal of spheres having a small object angle has a small impact on the volume of the reconstructed object (refer to Fig. 2, right).…”

Extended grassfire transform on medial axes of 2D shapes

“…measures have been proposed for identifying portions of the medial axis that depict prominent shape features, in 2D [15] and 3D [17], which can be classified into local or global ones [14,16]. Local measures rate a medial axis point by the boundary geometry in its immediate neighborhood, such as the angle formed by the medial axis point and its two closest boundary points [2,7,17,9] or the Euclidean distance between the two boundary points [1,6]. However, without knowledge of the shape in a larger neighborhood, local features cannot easily distinguish between noisy features on the boundary and a meaningful shape part that is thin.…”

Developing a line-of-sight based algorithm for urban street network generalization

“…Since then many algorithms for medial-axis computation have been proposed. Foskey et al (2003) classified those algorithms into four general categories: thinning algorithms, distance field based algorithms, algebraic methods, and surface-sampling approaches.…”

“…One well-known -feature‖ of the medial axis is its sensitivity to the object's shape, meaning that even a minor perturbation in the boundary may cause spurious deviation on the path of the medial axis (Foskey et al 2003;Jiang & Liu 2010;Tam & Heidrich 2003). Although this means the medial axis can accurately reflect the shape of an object, this also means the medial axis is unstable and thus undesirable as a tool for shape analysis in that it may carry plenty of noises.…”