Medial Axis Algorithm Research Articles

Medial axis-based machine-vision system for orchard robot navigation

In this paper, we propose a novel medial axis-based machine vision technique for autonomous path tracking and navigation of an agricultural robot in orchards. In the proposed method, the raw color image captured by the onboard camera is converted to grayscale using the color index of vegetation extraction. The gray image is run through Gabor filters to extract the texture features before applying Principal Component Analysis technique to minimize the computational load during path coordinate extraction. The resulting image is clustered using K-means clustering algorithm with k = 2 as proved best based on Silhouette method. Navigation path is then extracted using medial axis algorithm from the binary image generated after k-means clustering. Fuzzy logic controller with two inputs, heading and offset, is used to smoothly track the medial axis during navigation. Experiment is carried out in an orchard environment to gauge the performance of the system. The results of field experiment clearly demonstrate that the proposed medial axis technique has the potential to accurately extract guidance path for robot navigation. The navigation performance of the system is quite satisfactory with a maximum trajectory tracking error and standard deviation of 14.6 mm and 6.8 mm respectively. The average root mean square error (RMSE) for the lateral deviation was 45.3 mm.

Q-MAT+: An error-controllable and feature-sensitive simplification algorithm for medial axis transform

The medial axis transform (MAT), as an intrinsic shape representation, plays an important role in shape approximation, recognition and retrieval. Q-MAT is a state-of-the-art algorithm driven by quadratic error minimization to compute a geometrically precise, structurally concise, and compact representation of the MAT for 3D shapes. In this work we extend the technique to make it more robust, controllable, and name it Q-MAT+. Combining shape diameter function (SDF) and other mesh information, Q-MAT+ gets a more complete and accurate initial MAT than Q-MAT, even for extreme thin features, such as wires and sheets. Q-MAT+ could quickly remove insignificant branches while preserving significant ones to get a simple and faithful piecewise linear approximation of the MAT. Moreover, it performs the medial axis simplification with explicit maintenance and the control of Hausdorff error, which is not originally supported in Q-MAT. We further demonstrate the outstanding efficiency and accuracy of our method compared with other existing approaches for MAT generation and simplification.

The algorithm of central axis in surface reconstruction

Reverse engineering is an important technique means of product imitation and new product development. Its core technology -- surface reconstruction is the current research for scholars. In the various algorithms of surface reconstruction, using axis reconstruction is a kind of important method. For the various reconstruction, using medial axis algorithm was summarized, pointed out the problems existed in various methods, as well as the place needs to be improved. Also discussed the later surface reconstruction and development of axial direction.

Set Voronoi diagrams of 3D assemblies of aspherical particles

Several approaches to quantitative local structure characterization for particulate assemblies, such as structural glasses or jammed packings, use the partition of space provided by the Voronoi diagram. The conventional construction for spherical mono-disperse particles, by which the Voronoi cell of a particle is that of its centre point, cannot be applied to configurations of aspherical or polydisperse particles. Here, we discuss the construction of a Set Voronoi diagram for configurations of aspherical particles in three-dimensional space. The Set Voronoi cell of a given particle is composed of all points in space that are closer to the surface (as opposed to the centre) of the given particle than to the surface of any other; this definition reduces to the conventional Voronoi diagram for the case of mono-disperse spheres. An algorithm for the computation of the Set Voronoi diagram for convex particles is described, as a special case of a Voronoi-based medial axis algorithm, based on a triangulation of the particles’ bounding surfaces. This algorithm is further improved by a pre-processing step based on morphological erosion, which improves the quality of the approximation and circumvents the problems associated with small degrees of particle–particle overlap that may be caused by experimental noise or soft potentials. As an application, preliminary data for the volume distribution of disordered packings of mono-disperse oblate ellipsoids, obtained from tomographic imaging, is computed.

A simple algorithm for medial axis transform computation

Although medial axis transform is introduced as a shape description for many engineering applications, the computational algorithm is still challenging. This is especially true for the shape with free form boundary. This paper presents an algorithm for medial axis transform computation from a perspective of minimum distance between the points in a two-dimensional shape and its boundary. The minimum distance is given by a resultant distance function which is a superposition of the individual distance function between a point within a shape and each boundary point. By elaborating the resultant distance function, the medial axis transform will be obtained naturally. The distance function is modeled as a solid cone and the superposition is equivalent to the union Boolean set operation. The implementation of the approach is simplified using a solid modeling kernel. Several examples of two-dimensional shapes with free form boundaries are raised to illustrate the concept and algorithm.

COMPUTATIONAL AND STRUCTURAL ADVANTAGES OF CIRCULAR BOUNDARY REPRESENTATION

Boundary approximation of planar shapes by circular arcs has quantitative and qualitative advantages compared to using straight-line segments. We demonstrate this by way of three basic and frequent computations on shapes – convex hull, decomposition, and medial axis. In particular, we propose a novel medial axis algorithm that beats existing methods in simplicity and practicality, and at the same time guarantees convergence to the medial axis of the original shape.

Pore-scale Observation of Microsphere Deposition at Grain-to-Grain Contacts over Assemblage-scale Porous Media Domains Using X-ray Microtomography

The prevalence of colloid deposition at grain-to-grain contacts in two porous media (spherical glass beads and angular quartz sand, 710-850 microm) was examined using X-ray microtomography (XMT) under conditions where the colloid-grain surface interaction was solely attractive (lacking an energy barrier to deposition), and under fluid velocity conditions representative of engineered filtration systems. XMT allows pore-scale observation of colloid deposition over assemblage-scale porous media domains. Colloids visible in reconstructed images were prepared by coating gold on hollow ceramic microspheres (36 microm in size) (to render densities only slightly higher than water). A significant fraction of the deposited microspheres were deposited at grain-to-grain contacts (about 20% in glass beads, 40% in quartz sand) under the conditions examined. The deposited microsphere concentrations decreased log-linearly with increasing transport distance regardless of the environment of deposition (grain-to-grain contact versus single-contact deposition). The profile shape was, therefore, consistent with filtration theory, and the observed deposition rate coefficients were also well predicted by filtration theory. The ability of filtration theory to predict the magnitude and spatial distribution of deposition demonstrates that filtration theory captures the essential elements of deposition in the absence of an energy barrier despite a lack of accounting for grain-to-grain contacts. The observed factor of 2 greater deposition at grain-to-grain contacts in quartz sand relative to equivalently sized glass beads is consistent with greater grain-to-grain contact lengths and greater fraction of small pores in the quartz sand relative to the glass beads, as determined via a pore structure analysis algorithm (medial axis algorithm).

Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I. Theoretical foundations

In this first installment of a two-part paper, the underlying theory for an algorithm that computes the Voronoi diagram and medial axis of a planar domain bounded by free-form (polynomial or rational) curve segments is presented. An incremental approach to computing the Voronoi diagram is used, wherein a single boundary segment is added to an existing boundary-segment set at each step. The introduction of each new segment entails modifying the Voronoi regions of the existing boundary segments, and constructing the Voronoi region of the new segment. We accomplish this by (i) computing the bisector of the new segment with each of the current boundary segments; (ii) updating the Voronoi regions of the current boundary segments by partitioning them with these bisectors; and (iii) constructing the Voronoi region of the new segment as a union of regions obtained from the partitioning in (ii). When all boundary segments are included, and their Voronoi regions have been constructed, the Voronoi diagram of the boundary is obtained as the union of the Voronoi polygons for each boundary segment. To construct the medial axis of a planar domain, we first compute the Voronoi diagram of its boundary. The medial axis is then obtained from the Voronoi diagram by (i) removing certain edges of the Voronoi diagram that do not belong to the medial axis, and (ii) adding certain edges that do belong to the medial axis but are absent from the Voronoi diagram; unambiguous characterizations for edges in both these categories are given. Details of algorithms based on this theory are deferred to the second installment of this two-part paper.

Voronoi diagram and medial axis algorithm for planar domains with curved boundaries — II: Detailed algorithm description

Details of algorithms to construct the Voronoi diagrams and medial axes of planars domain bounded by free-form (polynomial or rational) curve segments are presented, based on theoretical foundations given in the first installment Ramamurthy and Farouki, J. Comput. Appl. Math. (1999) 102 119–141 of this two-part paper. In particular, we focus on key topological and computational issues that arise in these constructions. The topological issues include: (i) the data structures needed to represent various geometrical entities — bisectors, Voronoi regions, etc., and (ii) the Boolean operations (i.e., union, intersection, and difference) on planar sets required by the algorithm. Specifically, representations for the Voronoi polygons of boundary segments, and for individual Voronoi diagram or medial axis edges, are proposed. Since these edges may be segments of (a) nonrational algebraic curves (curve/curve bisectors); (b) rational curves (point/curve bisectors); or (c) straight lines (point/point bisectors), data structures tailored to each of these geometrical entities are introduced. The computational issues addressed include the curve intersection algorithms required in the Boolean operations, and iterative schemes used to precisely locate bifurcation or “ n-prong” points ( n ⩾ 3) of the Voronoi diagram and medial axis. A selection of computed Voronoi diagram and medial axis examples is included to illustrate the capabilities of the algorithm.

New Algorithm for Medial Axis Transform of Plane Domain

In this paper, we present a new approximate algorithm for medial axis transform of a plane domain. The underlying philosophy of our approach is the localization idea based on the Domain Decomposition Lemma, which enables us to break up the complicated domain into smaller and simpler pieces. We then develop tree data structure and various operations on it to keep track of the information produced by the domain decomposition procedure. This strategy enables us to isolate various important points such as branch points and terminal points. Because our data structure guarantees the existence of such important points—in fact, our data structure is devised with this in mind—we can zoom in on those points. This makes our algorithm efficient. Our algorithm is a “from within” approach, whereas traditional methods use a “from-the-boundary” approach. This “from within” nature of our algorithm and the localization scheme help mitigate various instability phenomena, thereby making our algorithm reasonably robust.