5,270 research outputs found
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
arbitrary 2D shape. The instability of the medial axis transform is overcome by
a pruning algorithm guided by a user-defined Hausdorff distance threshold. The
stable medial axis transform is then approximated by spline curves in 3D to
produce a smooth and compact representation. These spline curves are computed
by minimizing the approximation error between the input shape and the shape
represented by the medial axis transform. Our results on various 2D shapes
suggest that our method is practical and effective, and yields faithful and
compact representations of medial axis transforms of 2D shapes.Comment: GMP14 (Geometric Modeling and Processing
MAP: Medial Axis Based Geometric Routing in Sensor Networks
One of the challenging tasks in the deployment of dense wireless networks (like sensor networks) is in devising a routing scheme for node to node communication. Important consideration includes scalability, routing complexity, the length of the communication paths and the load sharing of the routes. In this paper, we show that a compact and expressive abstraction of network connectivity by the medial axis enables efficient and localized routing. We propose MAP, a Medial Axis based naming and routing Protocol that does not require locations, makes routing decisions locally, and achieves good load balancing. In its preprocessing phase, MAP constructs the medial axis of the sensor field, defined as the set of nodes with at least two closest boundary nodes. The medial axis of the network captures both the complex geometry and non-trivial topology of the sensor field. It can be represented compactly by a graph whose size is comparable with the complexity of the geometric features (e.g., the number of holes). Each node is then given a name related to its position with respect to the medial axis. The routing scheme is derived through local decisions based on the names of the source and destination nodes and guarantees delivery with reasonable and natural routes. We show by both theoretical analysis and simulations that our medial axis based geometric routing scheme is scalable, produces short routes, achieves excellent load balancing, and is very robust to variations in the network model
A Scale-Space Medialness Transform Based on Boundary Concordance Voting
The Concordance-based Medial Axis Transform (CMAT) presented in this paper is a multiscale medial axis (MMA) algorithm that computes the medial response from grey-level boundary measures. This non-linear operator responds only to symmetric structures, overcoming the limitations of linear medial operators which create “side-lobe” responses for symmetric structures and respond to edge structures. In addition, the spatial localisation of the medial axis and the identification of object width is improved in the CMAT algorithm compared with linear algorithms. The robustness of linear medial operators to noise is preserved in our algorithm. The effectiveness of the CMAT is accredited to the concordance property described in this paper. We demonstrate the performance of this method with test figures used by other authors and medical images that are relatively complex in structure. In these complex images the benefit of the improved response of our non-linear operator is clearly visible
A Framework for Symmetric Part Detection in Cluttered Scenes
The role of symmetry in computer vision has waxed and waned in importance
during the evolution of the field from its earliest days. At first figuring
prominently in support of bottom-up indexing, it fell out of favor as shape
gave way to appearance and recognition gave way to detection. With a strong
prior in the form of a target object, the role of the weaker priors offered by
perceptual grouping was greatly diminished. However, as the field returns to
the problem of recognition from a large database, the bottom-up recovery of the
parts that make up the objects in a cluttered scene is critical for their
recognition. The medial axis community has long exploited the ubiquitous
regularity of symmetry as a basis for the decomposition of a closed contour
into medial parts. However, today's recognition systems are faced with
cluttered scenes, and the assumption that a closed contour exists, i.e. that
figure-ground segmentation has been solved, renders much of the medial axis
community's work inapplicable. In this article, we review a computational
framework, previously reported in Lee et al. (2013), Levinshtein et al. (2009,
2013), that bridges the representation power of the medial axis and the need to
recover and group an object's parts in a cluttered scene. Our framework is
rooted in the idea that a maximally inscribed disc, the building block of a
medial axis, can be modeled as a compact superpixel in the image. We evaluate
the method on images of cluttered scenes.Comment: 10 pages, 8 figure
The tangent cone, the dimension and the frontier of the medial axis
This paper establishes a relation between the tangent cone of
the medial axis of X at a given point a ∈ Rn and the medial axis of
the set of points m(a) in X realising the Euclidean distance d(a, X).
As a consequence, a lower bound for the dimension of the medial axis
of X in terms of the dimension of the medial axis of m(a) is obtained.
This formula appears to be the missing link to the full description of the
medial axis’ dimension. An extended study of potentially troublesome
points on the frontier of the medial axis is also provided, resulting in their
characterisation by the recently introduced by Birbrair and Denkowski
reaching radius whose definition we simplify
Modeling of multifunctional porous tissue scaffolds with continuous deposition path plan
A novel modeling technique for porous tissue scaffolds with targeting the functionally gradient variational porosity with continuous material deposition planning has been proposed. To vary the porosity of the designed scaffold
functionally, medial axis transformation is used. The medial axis of each layers of the scaffold is calculated and used as an internal feature. The medial axis is then used connected to the outer contour using an optimum matching. The desired pore size and hence the porosity have been achieved by discretizing the sub-regions along its peripheral direction based on the pore
size while meeting the tissue scaffold design constraints. This would ensure the truly porous nature of the structure in every direction as well as controllable porosity with interconnected pores. Thus the desired controlled variational porosity along the scaffold architecture has been achieved with the combination of two geometrically oriented consecutive layers. A continuous,
interconnected and optimized tool-path has been generated for successive layers for additive-manufacturing or solid free form fabrication process. The proposed methodology has been computationally implemented with illustrative examples.
Furthermore, the designed example scaffolds with the desired pore size and porosity has been fabricated with an extrusion based bio-fabrication process
Medial Axis Isoperimetric Profiles
Recently proposed as a stable means of evaluating geometric compactness, the
isoperimetric profile of a planar domain measures the minimum perimeter needed
to inscribe a shape with prescribed area varying from 0 to the area of the
domain. While this profile has proven valuable for evaluating properties of
geographic partitions, existing algorithms for its computation rely on
aggressive approximations and are still computationally expensive. In this
paper, we propose a practical means of approximating the isoperimetric profile
and show that for domains satisfying a "thick neck" condition, our
approximation is exact. For more general domains, we show that our bound is
still exact within a conservative regime and is otherwise an upper bound. Our
method is based on a traversal of the medial axis which produces efficient and
robust results. We compare our technique with the state-of-the-art
approximation to the isoperimetric profile on a variety of domains and show
significantly tighter bounds than were previously achievable.Comment: Code and supplemental available here:
https://github.com/pzpzpzp1/isoperimetric_profil
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