Use of medial axis transforms for computing normals at boundary points (original) (raw)

Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces

Computer-aided Design, 2010

This paper presents an algorithm for generating the Interior Medial Axis Transform (iMAT) of 3D objects with free-form boundaries. The algorithm proposed uses the exact representation of the part and generates an approximate rational spline description of the iMAT. The algorithm generates the iMAT by a tracing technique that marches along the object's boundary. 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 points and the search for these junction points is done in an efficient way. The algorithm works for multiply-connected objects as well. Results of the implementation are provided.

Fast computation of cross-sections of 3D objects from their Medial Axis Transforms

Though Medial Axis Transform (MAT) is well known for object representation, its use in dierent kinds of computations remains unexplored till date. One of the main reasons is the popularity of other volumetric representations such as Octree for better data compression and ordered storage and retrieval facility, etc. In this paper an algorithm has been proposed based on Medial Axis Transform which allows one to visualize the internal structure of a 3D object across a cross-sectional plane given by its direction cosine vector. This not only enhances the computation speed but also improves the quality of the results compared to those obtained from the computation with direct voxel representation. Ó .in (J. Mukherjee). 0167-8655/00/$ -see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 -8 6 5 5 ( 0 0 ) 0 0 0 2 5 -8

Shape simplification based on the medial axis transform

2003

Abstract We present a new algorithm for simplifying the shape of 3D objects by manipulating their medial axis transform (MAT). From an unorganized set of boundary points, our algorithm computes the MAT, decomposes the axis into parts, then selectively removes a subset of these parts in order to reduce the complexity of the overall shape. The result is simplified MAT that can be used for a variety of shape operations.

A Medial Axis Transformation for Grayscale Pictures

IEEE Transactions on Pattern Analysis and Machine Intelligence, 1982

Blum's medial axis transformation (MAT) for binary pictures yields medial axis points that lie midway between opposite borders of a region, or along angle bisectors. This note discusses a generalization of the MAT in which a score is computed for each point P of a grayscale picture based on the gradient magnitudes at pairs of points that have P as their midpoint. These scores are high at points that lie midway between pairs of antiparallel edges, or along angle bisectors, so that they define a MAT-like "skeleton", which we may call the GRADMAT. However, this skeleton is rather sensitive to the presence of noise edges or to irregularities in the region edges.

A Tracing Algorithm for Constructing Medial Axis Transform of 3D Objects Bound by Free-Form Surfaces

2005

This paper presents an algorithm for generating the Medial Axis Transform(MAT) of 3D objects with free-form boundaries. 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 generates the MAT by a tracing technique that marches along the object boundary. 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 points and the search for these junction points is done in an efficient way. The algorithm works for multiplyconnected objects as well. Results of implementation are provided.

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

Computer-aided Design, 2005

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. q

Discrete Medial Axis Transform for Discrete Thin and Elongated Objects

Abstract: Skeletons are compact shape descriptions of discrete images. They have been extensively studied because of their utility in various applications such as data compression, shape abstraction, navigation and features detection. In this article, a new Euclidean skeletal definition for 2D discrete objects based on the Distance Map (DMAT) is being proposed. As a novel feature, it is shown that this skeleton is a connected subset of the discretization of the continuous medial axis of the object....

Differential and Topological Properties of Medial Axis Transforms

Graphical Models and Image Processing, 1996

It has several properties which neither B-Rep nor CSG directly provide. First, because it elicits important symmet-The medial axis transform is a representation of an object which has been shown to be useful in design, interrogation, aniries of an object, it facilitates the design and interrogation mation, finite element mesh generation, performance analysis, of symmetrical objects [6]. Second, the MAT exhibits dimanufacturing simulation, path planning, and tolerance specimensional reduction [14]; for example, it transforms a 3-D fication. In this paper, the theory of the medial axis transform solid region into a connected set of points, curves, and for 3-D objects is developed. For objects with piecewise C 2 boundsurfaces, along with an associated radius function described aries, relationships between the curvature of the boundary and in more detail below. Third, once a region is expressed the position of the medial axis are developed. For n-dimensional with the MAT, the skeleton and radius function themselves submanifolds of ᑬ ᑬ n with boundaries which are piecewise C 2 and may be manipulated, and the boundary will deform in a completely G 1 , a deformation retract is set up between each object natural way, suggesting applications in computer animaand its medial axis, which demonstrates that if the object is path tion. Fourth, the skeleton may be used to facilitate the connected, then so is its medial axis. Finally, it is proven that path connected polyhedral solids without cavities have path con-creation of coarse and fine finite element meshes of the nected medial axes.

Reconstruction of Shapes Based on Normals Analysis 1

Most mesh processing filters (including remeshing, simplification, and subdivision) affect vertices of the mesh. Vertices coordinates are modified, new vertices are added and some original ones are removed, with the result that the shape of the original surface is changed. While a great deal of research is concentrated on preservation of surface shape during some mesh processing, there is no general tool that can be used for surface reconstruction at post processing stage. To the best of our knowledge, this paper is the first one to present a restoring algorithm that allows to "repair" output of various mesh processing filters. The proposed scheme is straightforward way to put "off-surface" vertices of the deformed mesh back to the original smooth shape. It does not require any surface parameterization and is based on normal analysis. The procedure is demonstrated by using it as post processing tool after applying local node movement and simplification algorithms...

Medial Meshes -- A Compact and Accurate Representation of Medial Axis Transform

IEEE Transactions on Visualization and Computer Graphics, 2015

The medial axis transform has long been known as an intrinsic shape representation supporting a variety of shape analysis and synthesis tasks. However, for a given shape, it is hard to obtain its faithful, concise and stable medial axis, which hinders the application of the medial axis. In this paper, we introduce the medial mesh, a new discrete representation of the medial axis. A medial mesh is a 2D simplicial complex coupled with a radius function that provides a piecewise linear approximation to the medial axis. We further present an effective algorithm for computing a concise and stable medial mesh for a given shape. Our algorithm is quantitatively driven by a shape approximation error metric, and progressively simplifies an initial medial mesh by iteratively contracting edges until the approximation error reaches a predefined threshold. We further demonstrate the superior efficiency and accuracy of our method over existing methods for medial axis simplification.