Medial Axis Transform Research Articles

Geometry of 3D MAT and its application to moulding surfaces

This paper investigates the differential geometry of 3D MAT (medial axis transform) using the moving frame and differential form. After constructing the mapping relation and moving frames around both the MA (medial axis) point and the associated boundary points, various curves are defined to serve as carriers for the study. Based on analysis of the infinitesimal translation and rotation of the moving frames, the relations of distance differentials, rotation vectors and differential invariants are derived. Furthermore, a special case in the 3D MAT, the normal form, is defined for the moulding surfaces, where the 3D problem can be converted into a 2D one.

Toward BIM-Enabled Decision Making for In-Building Response Missions

Decision making for rescue and evacuation is critical for disaster response operations not only in open spaces but also in buildings. For infrastructures with large and complex geometrical layouts, decision making could be facilitated with computer-aided approaches for better accuracy and efficiency. This paper aims to respond to fire in buildings. We combined network analysis with building information modeling (BIM) to facilitate the decision making for response operations. Building geometry is retrieved from the BIM model for graph construction and route finding. In this paper, the visibility graph (VG) and medial axis transform (MAT) are evaluated for graph construction. A hybrid method that combines VG and MAT is proposed, and encouraging results have been shown. Risks based on building materials and traffic of pedestrians are to be adapted for network edge costs to enable the lowest utility route finding in the future. The accuracy and efficiency for emergency decisions are expected to be improved for in-building rescue and evacuation operations.

Extraction of microcracks in rock images based on heuristic graph searching and application

In this paper, we propose a new method, based on a graph searching technique, for microcrack extraction from scanning electron microscopic images of rocks. This method mainly focuses on how to detect the crack and extract it, and then quantify some basic geometrical features. The crack can be detected automatically with the aid of two endpoints of the crack. The algorithm involves the following process: the A⁎ graph searching technique is first used to find a path throughout the crack region, defined by the initial two endpoints; the pixels of the path will be used as the seeds for the region growing method to restore the primary crack area; then, an automatic filling holes’ operation is used to remove the possible holes in the region growing result; the medial axis and distance transformation of the crack area are acquired, and then the final crack is rebuilt by painting disks along a medial axis without branches. The crack result is separated without interaction. In the remaining parts, the crack features are quantified, such as the length, width, angle and area, and error analysis shows that the error percentage of the proposed approach reduces to a low level with actual width increases, and results of some example images are illustrated. The algorithm is efficient and can also be used for image detection of other linear structural objects.

Average curve of [formula omitted] smooth planar curves

We define the Average Curve (AC) of a compatible set of two or more smooth and planar, Jordan curves. It is independent of their order and representation. We compare two variants: the valley AC (vAC), defined in terms of the valley of the field that sums the squared distances to the input curves, and the zero AC (zAC), defined as the zero set of the field that sums the signed distances to the input curves. Our formulation provides an orthogonal projection homeomorphism from the AC to each input curve. We use it to define compatibility. We propose a fast tracing algorithm for computing a polygonal approximation (PAC) of the AC and for testing compatibility. We provide a linear-cost implementation for tracing the PAC of polygonal approximations of smooth input curves. We also define the inflation of the AC and use it to visualize the local variability in the set of input curves. We argue that the AC and its inflation form a natural extension of the Medial Axis Transform to an arbitrary number of curves. We propose extensions to open curves and to weighted averages of curves, which can be used to design animations.

Recognition of Monochrome Thermal Images of Synchronous Motor with the Application of Skeletonization and Classifier Based on Words

AbstractThermography is a technology that enables recognition of objects in the specific area. The goal of using thermographic techniques for ironworks is to diagnose electrical equipment. These techniques can be also use to increase safety and quality control in ironworks. Faulty equipment can be dangerous for engineers. Article describes the method of the recognition of imminent failure states of synchronous motor. Thermal images of the stator are used for an analysis of electrical machine. Researches of image processing techniques have been carried out for three states of motor. Proposed approach uses patterns recognition. Using of medial axis transformation and classifier based on words gave good results. In the future electrical machines and metallurgical equipment will use diagnostic systems based on recognition of thermal images.

Canal surfaces with rational contour curves and blends bypassing the obstacles

In this paper, we will present an algebraic condition, see (20), which guarantees that a canal surface, given by its rational medial axis transform (MAT), possesses rational generalized contours (i.e., contour curves with respect to a given viewpoint). The remaining computational problem of this approach is how to find the right viewpoint. The canal surfaces fulfilling this distinguished property are suitable for being taken as modeling primitives when some rational approximations of canal surfaces are required. Mainly, we will focus on the low-degree cases such as quadratic and cubic MATs that are especially useful for applications. To document a practical usefulness of the presented approach, we designed and implemented two simple algorithms for computing rational offset blends between two canal surfaces based on the contour method which do not need any further advanced formalism (as e.g. interpolations with MPH curves). A main advantage of the designed blending technique is its simplicity and also an adaptivity to choose a suitable blend satisfying certain constrains (avoiding obstacles, bypassing other objects, etc.). Compared to other similar methods, our approach requires only one SOS decomposition for the whole family of rational canal surfaces sharing the same silhouette, which significantly simplifies the computational complexity.

A practical path planning methodology for wire and arc additive manufacturing of thin-walled structures

This paper presents a novel methodology to generate deposition paths for wire and arc additive manufacturing (WAAM). The medial axis transformation (MAT), which represents the skeleton of a given geometry, is firstly extracted to understand the geometry. Then a deposition path that is based on the MAT is efficiently generated. The resulting MAT-based path is able to entirely fill any given cross-sectional geometry without gaps. With the variation of step-over distance, material efficiency alters accordingly for both solid and thin-walled structures. It is found that thin-walled structures are more sensitive to step-over distance in terms of material efficiency. The optimal step-over distance corresponding to the maximum material efficiency can be achieved for various geometries, allowing the optimization of the deposition parameters. Five case studies of complex models including solid and thin-walled structures are used to test the developed methodology. Experimental comparison between the proposed MAT-based path patterns and the traditional contour path patterns demonstrate significant improved performance in terms of gap-free cross-sections. The proposed path planning strategy is shown to be particularly beneficial for WAAM of thin-walled structures. A novel path planning methodology based on the Medial Axis Transformation (MAT) of the geometry is proposed.Gap-free paths can be obtained for any arbitrarily shaped geometry.Relationships between step-over distance and material efficiency are analysed.Optimal step-over distances for different Additive Manufacturing (AM) systems are discussed.The proposed path planning strategy is particularly useful for wire and arc additive manufacturing of thin-walled structures.

Modeling Macromolecular Bodies using 3D Medial Axis Transforms and Normal Mode Analysis

Many large protein or protein/DNA machines are difficult to simulate on time scales long enough for complete turnover cycles. One way to overcome this general problem is to treat the protein at a (much) lower level of detail. In the approach described here, the protein complex is modeled as a collection of interacting flexible bodies, with low levels of detail over most of the protein surface (and interior), and high levels of detail only where necessary. The bulk shapes of all protein components are described with a low-resolution, purely repulsive potential, together with local high-resolution sites of interaction. The low-resolution potential function is built using the three-dimensional analog of the Medial Axis Transform (MAT) to generate an efficient set of basis functions that can represent the protein's repulsive isopotential surface.In addition to the general theory, a model for small DNA polymerases (specifically, the HIV Reverse Transcriptase) interacting with a coarse-grained DNA will be presented. As above, the polymerase model treats the protein as a single continuum body decorated with interaction sites. The system energy has several components: a) the repulsive body potential based on the MAT; b) a set of low order protein normal modes (from all-atom MD runs) whose amplitudes act as coordinates for the deformation energy function; c) an elastic energy function that includes both harmonic and non-harmonic terms, and accounts for stress/strain energy as the polymerase undergoes conformatioinal changes; d) a set of interaction sites (roughly corresponding to key individual amino acids) that give local (usually attractive) interactions with DNA, with nucleotides, and between sites on the polymerase body.

LayTracks3D: A New Approach to Meshing General Solids using Medial Axis Transform

This paper presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex and hex- dominant meshes of 3D assembly models. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D are similar to tunnels with no branches and are symmetric, non-intersecting, orthogonal to the boundary, and the shortest path from the MA to the boundary. These properties of tracks result in desired meshes with near cube shape elements at the boundary, structured mesh along the boundary normal with any irregular nodes restricted to the MA, and sharp boundary feature preservation. The algorithm has been tested on a few industrial CAD models and hex-dominant meshes are shown in the result section. The paper also describes how this algorithm can be extended to produce all-hex meshes in general geometries.

Analysis of human chromosome classification using centromere position

Automated homologous classification of human chromosomes from the metaphase spread of a cell is an essential task to identify various genetic disorders. Karyotyping is the process of visualizing and categorizing the chromosomes within a cell. It is very important to have a good feature extraction scheme for proper chromosome classification. Chromosome classification is performed by identifying the morphological features which mainly include the centromere location. The parameter is essential for classification which helps in determining a karyogarm. In this paper, a comparative analysis of two algorithms for identification of centromere position is done. The two approaches make use of the Medial Axis Transformation and Projection Vector. The analysis helps us to identify the algorithm that performs better in the identification of centromere position. The projection vector approach performs well in obtaining the centromere location in the chromosome with an efficiency of 90%.

Fast 3D inverse simulation of hot forging processes via Medial Axis Transformation: an approach for preform estimation in hot die forging

In hot die forging processes, the selection of an ideal preform is of great importance with respect to cavity filling and mechanical load. The common procedure in order to define an adequate preform is the usage of Finite-Element-Analysis (FEA), usually as an iterative process in which various preforms are tested with regard to their suitability. An approach that aims at reducing the number of trials by proposing a first estimation of a suitable preform is presented in this paper. It is conjectured that the material flow paths and resistance can be described by the cavity shape using the Medial Axis Transformation. Based on this, a local inverse material flow for time discrete steps is calculated. The result is a first estimation of an adequate preform shape within a few minutes as an input for further FEA. FE-based parametric design optimization procedure is then presented and compared to the inverse approach, which is identified as a useful complement for the forward simulation technique.

Virtual Prototype Design and Test-Simplifying the CAD/Analysis Interface

The design of mechanical structural parts is now predominantly a digital process. As an important element of the virtual design cycle, these parts must be tested for their structural integrity using finite element analysis (FEA) software. However, the interface between CAD and FEA is imperfect. The process of preparing CAD models for FEA consumes a great deal of the stress analyst’s time. Existing “automatic” CAD to FEA translators tend to treat all part features as “solid”; this leads to longer computation times and less accurate results for features that can be better characterized as “thin” or “long.” In addition, many features of CAD parts (e.g. fillets and chamfers) are important for their size and shape in the manufactured product, but have relatively little impact on the strength of the part and needlessly complicate the stress analysis—these features are usually removed by the analyst prior to FEA; they may need to be evaluated with additional analyses to test if it is safe to remove them. The Automatic CAD-FEA Interface Project (ACFI), is developing algorithms to make the translation from CAD to FEA seamless and automatic; these algorithms are based on mathematical theory and the principles of theoretical mechanics. This paper presents the latest ACFI advances for (i) automatically evaluating and reworking three dimensional CAD part geometries to prepare them for finite element meshing, (ii) exporting the revised geometries to a preprocessor, and (iii) identifying element type to be associated with each feature geometry. The algorithms used in this work approximate the medial axis transform (MAT) of the CAD part, a “power shape” that represents the three-dimensional solid part. This part can then be evaluated for its geometric properties. This approach has been shown to be a robust method for shape interrogation of three dimensional geometries.

Medial Axis Transformation based Skeletonzation of Image Patterns using Image Processing Techniques

The medial axis of an image pattern is the loci of all inscribed disks that touch two or more boundary points without crossing any of the boundaries. The medial axis transform (MAT) is a powerful representation for objects with inherent symmetry or near-symmetry. The medial axis of 2-D image patterns provides a conceptual design base, with transition to a detailed design occurring when the radius function is added to the medial axis or surface. To make such a design tool practicable, however, it is essential to be able to convert from an MAT format to a boundary representation of an object. In the proposed work, the medial axis transform has been extracted using the Euclidean distance transform based computation. The image pattern u prepared initially in binary form and then distance of each non-zero pixel to its closest zeroed pixel is computed. This process continues till the entire image pattern is scanned to its core.

Profile Tolerance Verification for Free-form Surfaces Using Medial Axis Transform

Tolerances for freeform surfaces are specified using profile tolerance that controls form or combination of size, form, orientation and location of a feature(s) relative to a true profile. Freeform surfaces are generally inspected by using fixtures on a coordinate measuring machine (CMM). The combination of fixtures and the CMM enables the establishment of correspondence between points on the machined and nominal surface for tolerance verification. To respond to the market quickly, it has become inevitable to use 3D scanners that can scan an object rapidly and provide dense unorganized points as an output without maintaining any correspondence with the nominal CAD model. Current state of art uses the shortest distance criterion to establish correspondence and verify the profile tolerances. This results in acceptance of parts that ought to be rejected and vice versa.A novel, alternative approach is proposed to overcome this deficiency and verify tolerances specified on a free-form surface. The technique establishes the correct one to one correspondence between the machined surface and CAD model using the Medial axis transform (MAT). The MAT of both the nominal surface and the measured points respectively, are discretised to obtain grids. Corresponding points on the two grids are then used to verify the deviation of the machined surface from the nominal surface. Results of preliminary experiments with simulated data are presented.

The hidden geometries of the Arabidopsis thaliana epidermis.

The quest for the discovery of mathematical principles that underlie biological phenomena is ancient and ongoing. We present a geometric analysis of the complex interdigitated pavement cells in the Arabidopsis thaliana (Col.) adaxial epidermis with a view to discovering some geometric characteristics that may govern the formation of this tissue. More than 2,400 pavement cells from 10, 17 and 24 day old leaves were analyzed. These interdigitated cells revealed a number of geometric properties that remained constant across the three age groups. In particular, the number of digits per cell rarely exceeded 15, irrespective of cell area. Digit numbers per 100 µm2 cell area reduce with age and as cell area increases, suggesting early developmental programming of digits. Cell shape proportions as defined by length∶width ratios were highly conserved over time independent of the size and, interestingly, both the mean and the medians were close to the golden ratio 1.618034. With maturity, the cell area∶perimeter ratios increased from a mean of 2.0 to 2.4. Shape properties as defined by the medial axis transform (MAT) were calculated and revealed that branch points along the MAT typically comprise one large and two small angles. These showed consistency across the developmental stages considered here at 140° (± 5°) for the largest angles and 110° (± 5°) for the smaller angles. Voronoi diagram analyses of stomatal center coordinates revealed that giant pavement cells (≥500 µm2) tend to be arranged along Voronoi boundaries suggesting that they could function as a scaffold of the epidermis. In addition, we propose that pavement cells have a role in spacing and positioning of the stomata in the growing leaf and that they do so by growing within the limits of a set of ‘geometrical rules’.

SMAT 알고리즘을 이용한 위상학적 모델 추출 방법

본 연구는 실내 GIS 모델을 구축하기 위한 위상학적 모델이 객체의 기하학적 특징을 반영할 필요성에 의해, 기하적 정보를 갖는 위상학적 모델인 기하 네트워크 모델을 자동 구축하는 알고리즘을 개발하는 것을 목적으로 한다. GNM의 요소 중 기하 정보를 갖는 요소를 자동 추출하기 위한 중심 알고리즘으로서 직선 중심축 추출 알고리즘을 개발하였다. 개발된 SMAT 알고리즘은 기존의 S-MAT 알고리즘을 활용하여 일반화되었고, 해당되는 객체의 범위를 단순 폴리곤에서 내부 폐색 구역을 갖는 폴리곤으로 확장하였다. 자동 구축된 GNM은 타 시스템에서의 활용 및 용이한 접근을 위해 최종적으로 .csv 파일로 출력된다. GNM 자동 추출 알고리즘은 최단 경로 탐색, 위급 상황 발생 시 대피로 안내, 상황에 따른 차별적 분석 등 다양한 경우에 효율적으로 활용될 수 있다. The purpose of this study is to develop the auto-building algorithm of the Geometric Network Model(GNM), a topology model including geometric information because of the need to reflect the features' geometric characteristic into the topology model, which is for development of indoor 3D virtual model enabling queries. As the critical algorithm, the Straight Medial Axis Transformation(SMAT) algorithm is proposed in order to automatically extract the medial axis of features. The SMAT algorithm is generalized from the existing S-MAT algorithm and a range of target features where applicable is extended from simple polygons to weakly simple polygons which mean the polygons containing the inner ring inside. The GNM built automatically is finally printed out as the .csv file for easy access and w ide application in other systems. This auto-building algorithm of the GNM is available for plenty of cases such as finding a shortest path, guiding a route in emergency situation, and semantic analysis.

Medial Axis Transformation based Skeletonzation of Image Patterns using Image Processing Techniques

Medial Axis Transformation based Skeletonzation of Image Patterns using Image Processing Techniques

A Statistical Method on Meridional Profiles of Centrifugal Pumps

A method based on the medial axis transform (MAT) theory is presented to explore the laws of meridional profiles versus specific speeds for centrifugal pumps. Through extracting each pump’s MAT and transforming to two newly introduced variables, striking features emerge. Based on these features, statistics are carried out on the two variables versus specific speeds. A series of pumps is used to verify this method. According to the laws gained from the statistical results, the meridional profile at any specific speed within this series of pumps can be directly drawn through calculations.

Extração de vias combinando métodos de detecção de regiões e linhas em imagens de intensidade de pulso laser

Este trabalho tem por objetivo extrair os eixos de vias a partir de regiões de vias isoladas previamente, tendo por base uma imagem de intensidade de pulso laser. Neste tipo de imagem, as vias são facilmente identificadas, pois se apresentam como faixas alongadas e em tonalidade bem escura e homogênea, contrastando com os outros objetos da imagem. A imagem de intensidade é segmentada através da técnica de crescimento de regiões, gerando regiões que representam as vias. A partir dessas regiões, os eixos das vias são extraídos de duas formas. Uma delas combina o método de detecção de linhas de Steger com um procedimento de limiarização por comprimento das linhas, visando a reduzir a ocorrência de linhas espúrias. A outra se baseia no método de esqueletização de regiões pela Transformada do Eixo Médio, seguido de um processo de poda para eliminar o máximo possível as ramificações. A partir dos experimentos realizados é possível comparar os eixos extraídos pelas duas formas descritas, e aquela que utiliza o método de detecção de linhas de Steger apresenta melhores resultados do que a baseada no método de esqueletização.

Goodness of spatial structure in Japanese rock gardens1

In this study, we examined pattern goodness in natural scenes using stone arrangements in a Japanese rock garden. The results showed that the stone arrangement simulating the rock garden at the Ryoan-ji Temple and arrangements with a single stone deleted from that simulation were evaluated highly. These arrangements had a self-similar spatial structure, namely, covert regularity, or had simple structures in medial axis transformation. These arrangements also produced impressions of greater width and depth than other arrangements. In contrast, sector arrangements, which gave the most regular impression, were evaluated the lowest for goodness. This suggests that the pattern goodness of natural scenes or the artistic evaluation does not always correspond to overt regularity, often considered to determine pattern goodness. The most important finding is that two types of sector arrangement and two types of random arrangement were classified in their respective groups by integrated multiple impressions, although they did not have similar perceptual appearances. An intuitive judgment based on integrated impressions may allow us to notice the hidden order in spatial structures and obtain substantial understanding of the structure.