Medial Axis Transform Research Articles

C1Continuous Toolpath Generation Toward 5-axis High Speed Machining

AbstractWe present a scheme to construct C1 continuous toolpath for 5-axis pocketing of high speed machining. A continuous toolpath synthesis is proposed, that forms out circular segments of maximally inscribed sizes and linear segments connecting these circular segments. Extending earlier work that employed the Medial Axis Transform to compute these maximally inscribed circles for 2D planar pockets, this work examines general pockets in ℜ3 represented as NURBS surfaces, and in 5-axis machining setup. Results are demonstrated by employing the proposed scheme toward the machining of impellers. Possible extensions toward a C2 continuous toolpath is discussed as well.

Domain connected graph: the skeleton of a closed 3D shape for animation

In previous research, three main approaches have been employed to solve the skeleton extraction problem: medial axis transform (MAT), generalized potential field and decomposition-based methods. These three approaches have been formulated using three different concepts, namely surface variation, inside energy distribution, and the connectivity of parts. By combining the above mentioned concepts, this paper creates a concise structure to represent the control skeleton of an arbitrary object.First, an algorithm is proposed to detect the end, connection and joint points of an arbitrary 3D object. These three points comprise the skeleton, and are the most important to consider when describing it. In order to maintain the stability of the point extraction algorithm, a prong-feature detection technique and a level iso-surfaces function-based on the repulsive force field was employed. A neighborhood relationship inherited from the surface able to describe the connection relationship of these positions was then defined. Based on this relationship, the skeleton was finally constructed and named domain connected graph (DCG). The DCG not only preserves the topology information of a 3D object, but is also less sensitive than MAT to the perturbation of shapes. Moreover, from the results of complicated 3D models, consisting of thousands of polygons, it is evident that the DCG conforms to human perception.

Visual Perception in Japanese Rock Garden Design

We present an investigation into the relation between design principles in Japanese gardens, and their associated perceptual effects. This leads to the realization that a set of design principles described in a Japanese gardening text by Shingen (1466), shows many parallels to the visual effects of perceptual grouping, studied by the Gestalt school of psychology. Guidelines for composition of rock clusters closely relate to perception of visual figure. Garden design elements are arranged into patterns that simplify figure-ground segmentation, while seemingly balancing the visual salience of subparts and the global arrangement. Visual ‘ground’ is analyzed via medial axis transformation (MAT), often associated with shape perception in humans. MAT analysis reveals implicit structure in the visual ground of a quintessential rock garden design. The MAT structure enables formal comparison of structure of figure and ground. They share some aesthetic qualities, with interesting differences. Both contain naturalistic asymmetric, self-similar, branching structures. While the branching pattern of the ground converges towards the viewer, that of the figure converges in the opposite direction.

Segmentation Of Photospheric And Chromospheric Solar Features

We describe the application of a multi-scale Laplacian-of-Gaussian (LoG) operator and of an iterative version of Medial Axis Transform (i-MAT) as tools for the segmentation of both photospheric and chromospheric solar features. We introduce the multi-scale LoG operator in order to extract compact structures in photospheric intensity or Doppler images. The second method, based on a i-MAT algorithm applied to gray level images, is introduced to recognize reticulated structures like chromospheric network or intergranular lanes. The developed numerical procedures allow a non-subjective segmentation of solar images in order to investigate morphological and topological properties of identified features. We discuss the output of the segmentation procedures when applied to real images.

Constructing medial axis transform of extruded and revolved 3D objects with free-form boundaries

This paper presents an algorithm for generating the Medial Axis Transform (MAT) of 3D objects with free form boundaries that are obtained by extrusion along a line or revolution about an axis. The algorithm proposed uses the exact representation of the part and generates an approximate rational spline description (to within a defined tolerance) of the MAT. The algorithm uses the 2D MAT of the profile being extruded or revolved to identify the limiting entities (junction points, seams and points of extremal maximum curvature) of the 3D MAT. It is shown that the MAT points of the profile face are sufficient to determine the topology and geometry of the MAT of this class of solids. The algorithm works for multiply-connected objects as well. Results of implementation are presented and use of the algorithm to handle general solids is discussed.

Computer implementation of Heuvers' circle method for thermal optimisation in castings

A method based on geometric reasoning techniques is presented to predict hot spots and use of geometric parameters of a casting to obtain effective interface boundary conditions. The proposed method combines Chvorinov's rule and Heuvers' circle method with the medial axis transformation technique to develop an elegant optimisation technique for the optimal feeding design of castings. The results are validated using a FE based solidification analysis. It has been shown that the method has the ability to constrain heat transfer coefficient values to yield more realistic predictions for foundry practices. The proposed method has a considerable potential to reduce the number of FE simulations that are otherwise needed to achieve an optimal thermal design.

Constructing Medial Axis Transform for Free-form Trimmed Surfaces

Indian Institute of Science, bgm@mecheng.iisc.ernet.in ABSTRACT This paper presents an algorithm for constructing Medial Axis Transform for free-form surfaces. The algorithm uses a combination of tracing and bisector based techniques. This algorithm finds bisector curves by a tracing method and then trims these bisector curves for finding the branch points and constructing the MAT. Results on typical free-form domains are presented. Keywords: Medial Axis Transform, Free-form surface, geodesic. 1. INTRODUCTION One of the fundamental issues in CAD has been to represent objects in a way that not only allows the user to create and modify their shape and other attributes but also enables reasoning about the shape for various tasks in the product design cycle. Objects are normally described by their boundaries, but they can also be described by shifting the description to the interior. This is done by representing the skeleton/symmetric axis of the shape. Various skeleton/symmetric axis representation of shapes like Medial Axis Transform (MAT), Voronoi diagrams, box skeletons, mid surfaces and 2.5D skeletons are possible. Of these MAT has shown to be useful in various applications such as finite element mesh generation, pattern analysis and image analysis, path generation for pocket machining, robot motion planning and more Work on MAT up to now has been restricted to planar 2D and 3D objects. Very little work has been reported on construction of the MAT for 2D free form surface domains. An algorithm to develop MAT on free form surfaces (exact representation) is presented in this paper. 1.1 Medial Axis Transform (MAT) The medial axis transform was first introduced by Blum [1] to describe biological shapes. It can be viewed as the locus of the center of a maximal disk as it rolls inside an object. 1.2 Definition of 2D MAT for Planar Domains The medial axis (MA) of the set D, denoted M(D), is defined as the locus of points inside D which lie at the centers of all closed disks which are maximal in D, together with the limit points of this locus. A closed disk is said to be maximal in a subset D of the 2D space if it is contained in D but is not a proper subset of any other disk contained in D. The radius function of the MA of D is a continuous, real-valued function defined on M(D) whose value at each point on the MA is equal to the radius of the associated maximal disk. The medial axis transform (MAT) of D is the MA along with its associated radius function [8]. Fig. 1. illustrates the MA segments corresponding to a simple convex domain.

Techniques for the calculation of medial surfaces of solids

The Medial Axis Transform (MAT) surface, or simply Medial Surface (MS), offers the possibility of mathematically-based volumetric reasoning about geometric models using global shape and proximity information. The MAT surface is an important tool which can be used for several applications, such as designing manufacturing applications, robot path planning and offsetting, but has the disadvantage that it is computationally intensive. This paper describes two techniques which have been developed to improve the efficiency of the calculation process of the MAT of planar polyhedral objects. The first is a thorough analysis of the cases which can arise when calculating the vertex positions of the MAT of an object as combinations of points, lines and planes. The second technique, presented here, is a divide-and-conquer method, which makes use of some properties of the MAT structure to subdivide the problem. The power of the algorithms is illustrated by some examples, which show the MAT of solid objects with complicated shape and structure.

Visualization of the internal carotid artery using MRA images

A virtual angioscopy system is implemented to visualize the inside of the internal carotid artery (ICA) for qualitative assessment of carotid artery stenosis using magnetic resonance angiography (MRA) images. The carotid artery is one of the body regions not accessible by real optical endoscopy but can be visualized with virtual endoscopy. In order to visualize the carotid artery, it is segmented using the region-growing algorithm after locating the initial seed on the presegmented binary image. The ICA is separated from the external carotid artery (ECA) using a priori knowledge of the anatomic structure after bifurcation. A fly-through path is computed based on the medial axis transform (MAT) to automatically move the virtual camera from the common carotid artery (CCA) to the ICA. Considering interactive rendering speed and usability of standard graphic hardware, the surface-rendering algorithm with the perspective projection method is used to generate an endoscopic view of the ICA. In addition, the endoscopic view with the raycasting algorithm is provided for off-line navigation of the carotid artery. Virtual angioscopy is highly recommended as a diagnostic tool for identifying the specific location of the stenosis and for analyzing the stenosis qualitatively. The virtual angioscopy system for carotid artery will benefit radiological diagnostics, medical education, surgical planning and postoperative assessment.

A Spatial Access-Oriented Implementation of a 3-D GIS Topological Data Model for Urban Entities

3-D analysis in GIS is still one of the most challenging topics for research. With the goal being to model possible movement within the built environment, this paper, therefore, proposes a new approach to handling connectivity relationships among 3-D objects in urban environments in order to implement spatial access analyses in 3-D space. To achieve this goal, this paper introduces a 3-D network data model called the geometric network model (GNM), which has been developed by transforming the combinatorial data model (CDM), representing a connectivity relationship among 3-D objects using a dual graph. For the transformation, this paper presents (1) an O(n2) algorithm for computing a straight medial axis transformation (MAT), (2) the processes for transforming phenomena from 3-D CDM to 3-D GNM, and (3) spatial access algorithms for the 3-D geometric network based upon the Dijkstra algorithm. Using the reconstructed geometric network generated from the transformations, spatial queries based upon the complex connectivity relationships between 3-D urban entities are implemented using Dijkstra algorithm. Finally, the paper presents the results of an experimental implementation of a 3-D network data model (GNM) using GIS data of an area in downtown Columbus, Ohio.

Alternative techniques for casting process simulation

Over the past 20 years, casting process simulation has been an active area of research. The simulation techniques are either based on solving governing partial differential equations using numerical schemes such as the finite element or finite difference methods, or a variety of heuristically based geometry driven methods. Numerical methods are more accurate, but geometry driven methods are computationally less expensive. This paper explores two alternative techniques to overcome some of the limitations of traditional numerical simulation schemes for the casting process simulation. The first technique uses a geometric transformation method known as the medial axis transformation, to predict hot spots whereas the second technique, based on meshless methods, is used for simulating the mould filling process.

Any open bounded subset of [formula omitted] has the same homotopy type as its medial axis

Medial axis Transform is sometimes used as an intermediate representation in algorithms for meshing or recognition of shapes from digitized data. This raises the question whether the Medial Axis captures fundamental topological invariants of the object. The (positive) answer has been known already in the case of smooth objects. The main result presented here is the homotopy equivalence of any bounded open subset ofRnwith its medial axis.

Clinical Usefulness of Virtual Angioscopy Using 3D MR Angiography DICOM Images

Objective : To evaluate of virtual angioscopy was implemented using MR(magnetic resonance) angiography image of carotid artery. Methods : The endoscopy system provides a 3D volume rendered image as a navigation map and has the multi planar reformation image along the path and a 2D axial image as a reference image. We segmented the common carotid artery and internal, external carotid artery from the MR angiography image. We used the coordinates as a navigation path for virtual camera that were calculated from medial axis transformation. We used the perspective projection and marching cube algorithm to render the surface from volumetric MR angiography image data. Results : The virtual angioscopy is highly recommended as a diagnosis tool with which the specific place of stenosis can be identified and the degree of stenosis can be measured qualitatively. Conclusion : Virtual angioscopy is one of the powerful tool for non-invasive carotid artery and many in-vitro, in-vivo studies have shown the artery stenosis detection. Inside of the carotid artery is one of the body region not accessible by real optical endoscopy but can be visualized with virtual endoscopy.

기관지질환 진단을 위한 가상내시경

본 논문은 흉부를 촬영한 CT(Computed Tomography) 영상을 이용하여 기관지 내부를 시각화(visualization)하기 위해 가상기관지경(virtual bronchoscopy)을 구현하였다. 실제 광학내시경은 침습(invasive)검사로 환자가 불편함을 감수해야하며 검사 전에 사전 준비 작업이 필요하고 절개, 감염, 출혈 등의 부작용을 수반하는데 비해 가상내시경은 CT 나 MRI 등과 같은 스캐너의 단면 영상을 사용하여 구현한다. 가상기관지경의 항해경로 결정을 위해 CT 단면 원천영상에서 기관지(trachea wall)만을 분리하였고, 분리된 기관지 영상을 이용하여 중앙축 변환(MAT : .Medial Axis Transformation)을 통해 구해진 좌표값을 가상 카메라의 운행 경로로 사용하였다. 원근투영(perspective projection) 및 볼륨 데이터의 표면을 렌더링하기 위해 마칭큐브(marching cube) 알고리즘을 사용하였다. 기관지질환은 기관지 내부의 염증(inflammation) 이나 폐암(lung cancer)으로 기인하여 기관지 통로가 좁아지는 기관지 협착증, 기관지 확장증 및 기관지암으로 분류된다. 가상기관지경은 기관지 내부의 질환 위치와 질환 정도를 정성적으로 파악 할 수 있으며 기관지질환의 진단과 교육에 사용될 수 있다. The virtual bronchoscopy was implemented using chest CT images to visualize inside of tracheo-bronchial wall. The optical endoscopy procedures are invasive, uncomfortable for patients and sedation or anesthesia may be required. Also, they have serious side effects such as perforation, infection and hemorrhage. In order to determine the navigation path, we segmented the tracheo-bronchial wall from the chest CT image. We used the coordinates as a navigation path for virtual camera that were calculated from medial axis transformation. We used the perspective projection and marching cube algorithm to render the surface from volumetric CT image data. The tracheobronchial disease was classified into tracheobronchial stenosis causing from inflammation or lung cancer, bronchiectasis and bronchial cancer. The virtual bronchoscopy is highly recommended as a diagnosis tool with which the specific place of tracheobronchial disease can be identified and the degree of tracheobronchial disease can be measured qualitatively, Also, the virtual bronchoscopy can be used as an education and training tool for endoscopist and radiologist.

A new method for analyzing local shape in three-dimensional images based on medial axis transformation

In this paper, we propose a new approach based on three-dimensional (3-D) medial axis transformation for describing geometrical shapes in three-dimensional images. For 3-D-images, the medial axis, which is composed of both curves and medial surfaces, provides a simplified and reversible representation of structures. The purpose of this new method is to classify each voxel of the three-dimensional images in four classes: boundary, branching, regular and arc points. The classification is first performed on the voxels of the medial axis. It relies on the topological properties of a local region of interest around each voxel. The size of this region of interest is chosen as a function of the local thickness of the structure. Then, the reversibility of the medial axis is used to deduce a labeling of the whole object. The proposed method is evaluated on simulated images. Finally, we present an application of the method to the identification of bone structures from 3-D very high-resolution tomographic images.

Linear one-sided stability of MAT for weakly injective 3D domain

Despite its usefulness in many applications, the medial axis transform (MAT) is very sensitive to the change of the boundary in the sense that, even if a shape is perturbed only slightly, the Hausdorff distance between the MATs of the original shape and the perturbed one may be large. However, it is known that MATs of 2D domains are stable if we view this phenomenon with the one-sided Hausdorff distance. This result depends on the fact that MATs are stable if the differences between them are measured with the recently introduced hyperbolic Hausdorff distance. In this paper, we extend the result for the one-sided stability of the MAT to a class of 3D domains called weakly injective, which contains many important 3D shapes typically appearing in solid modeling. Especially, the weakly injective 3D domains can have sharp features like corners or edges. In fact, by using the stability of the MAT under the hyperbolic Hausdorff distance, we obtain an explicit bound for the one-sided Hausdorff distance of the MAT of a weakly injective 3D domain with respect to that of a perturbed domain, which is linear with respect to the domain perturbation. We discuss some consequences of this result concerning the computation and the approximation of the MAT of 3D objects.

Untangling the Blum Medial Axis Transform

For over 30 years, Blum's Medial Axis Transform (MAT) has proven to be an intriguing tool for analyzing and computing with form, but it is one that is notoriously difficult to apply in a robust and stable way. It is well documented how a tiny change to an object's boundary can cause a large change in its MAT. There has also been great difficulty in using the MAT to decompose an object into a hierarchy of parts reflecting the natural parts-hierarchy that we perceive. This paper argues that the underlying cause of these problems is that medial representations embody both the substance of each part of an object and the connections between adjacent parts. A small change in an object's boundary corresponds to a small change in its substance but may involve a large change in its connection information. The problems with Blum's MAT are generated because it does not explicitly represent this dichotomy of information. To use the Blum MAT to it's full potential, this paper presents a method for separating the substance and connection information of an object. This provides a natural parts-hierarchy while eliminating instabilities due to small boundary changes. The method also allows for graded, fuzzy classifications of object parts to match the ambiguity in human perception of many objects.

An approach for casting defect analysis employing finite element design optimisation, media axis transformation and neural networks

Our experience of using an approach based on the defect-metacause-rootcause relationship coupled with other novel computational techniques for casting defect analysis, has been discussed in this paper. A rootcause is a design, process or material parameter, which may be controlled to minimise the occurrence of defective castings. A metacause is defined as a scientific rationale that governs the occurrence of defects and is influenced by controlling one or more rootcauses. The defect-metacause-rootcause relationship has been linked to Finite Element modelling, as in most circumstances the objective of any modelling exercise is to understand the influence of rootcauses on defects by numerically modelling one or two metacauses. It has been shown that an optimal specification of rootcauses can be predicted by coupling the numerical modelling techniques with optimisation techniques. Use of the medial axis transformation has been explored for defining objective functions within an optimisation analysis. The influence of process, design or material parameters on the occurrence of defects has been studied using the “learning from examples” strategy of neural networks. Current limitations of these techniques have also been highlighted.

Constructing medial axis transform of planar domains with curved boundaries

The paper describes an algorithm for generating an approximation of the medial axis transform (MAT) for planar objects with free form boundaries. The algorithm generates the MAT by a tracing technique that marches along the object boundary rather than the bisectors of the boundary entities. The level of approximation is controlled by the choice of the step size in the tracing procedure. Criteria based on distance and local curvature of boundary entities are used to identify the junction or branch points and the search for these branch points is more efficient than while tracing the bisectors. The algorithm works for multiply connected objects as well. Results of implementation are provided.

Use of medial axis transforms for computing normals at boundary points

Medial axis transform (MAT) is well known for object representation. It is interesting to explore its use in different kinds of computations. In this paper an algorithm has been proposed for computation of normals at the boundaries of two-dimensional objects based on their MATs. In this technique, there is no requirement of linking boundary points during the computation compared to other existing techniques. The added advantage in the computation is that the computation can be restricted purely in the integer domain.