Related Experiment Video
Updated: May 29, 2026
12:59
Three and Four-Dimensional Visualization and Analysis Approaches to Study Vertebrate Axial Elongation and Segmentation
Published on: February 28, 2021
Medial axis transformation of a planar shape
1MEMBER, IEEE, Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60201.
IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
Summary
This paper introduces an efficient O(n log n) algorithm for computing the medial axis transformation of simple polygons. This method improves upon existing techniques for shape description and analysis.
Area of Science:
- Computational Geometry
- Computer Graphics
- Shape Analysis
Background:
- The medial axis transformation (MAT) is a fundamental tool for shape representation, first proposed by Blum.
- Existing methods for computing the MAT of polygons often lack efficiency or exactness.
Purpose of the Study:
- To present a novel algorithm for computing the medial axis of planar shapes represented by simple polygons.
- To improve the efficiency and exactness of medial axis computation.
Main Methods:
- Developed an O(n log n) algorithm for medial axis computation.
- The algorithm is designed for n-edge simple polygons.
- Implemented the algorithm in Fortran.
Main Results:
- The proposed algorithm achieves a time complexity of O(n log n).
- Demonstrated improvements in efficiency and exactness compared to previous methods.
- Successful implementation and testing of the algorithm.
Conclusions:
- The O(n log n) algorithm provides an efficient and exact method for computing the medial axis of simple polygons.
- The developed algorithm represents a significant advancement in computational geometry for shape analysis.
- The practical implementation showcases the algorithm's viability.
Related Concept Videos
01:16Perpendicular-Axis Theorem
The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body.
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...
01:12Transformation of Plane Strain
When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
01:21Plastic Deformations of Members with a Single Plane of Symmetry
When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
01:18Transformation of Plane Stress
Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's faces...
01:29Three-Dimensional Analysis of Strain
Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
01:20Transformations of Functions III
Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...