Related Experiment Video
Updated: May 11, 2026
10:35
Precision Measurements and Parametric Models of Vertebral Endplates
Published on: September 17, 2019
Area-Based Medial Axis of Planar Curves
Marc Niethammer1, Santiago Betelu, Guillermo Sapiro
1Department of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250, USA.
International Journal of Computer Vision
|May 28, 2013
Summary
A novel affine invariant medial axis for planar curves is defined using area-based distances. This robust method simplifies computation and aids in detecting affine skew symmetry in images.
Area of Science:
- Computer Vision
- Computational Geometry
- Image Analysis
Background:
- Medial axis computation is crucial for shape analysis.
- Existing methods often lack affine invariance or robustness.
- Need for a stable medial axis definition under affine transformations.
Purpose of the Study:
- Introduce a new definition of affine invariant medial axis for planar closed curves.
- Develop a robust and computationally simple method for medial axis calculation.
- Apply the medial axis for detecting affine skew symmetry.
Main Methods:
- Defined medial axis points as equidistant from curve points via minimum area between curve and chords.
- Utilized affine erosion and shock positions for a dynamical interpretation.
- Proposed a straightforward algorithm for medial axis computation.
Main Results:
- Introduced a robust affine invariant medial axis definition.
- Demonstrated a simple and effective computation method.
- Successfully applied the medial axis to detect affine skew symmetry in real images.
Conclusions:
- The proposed affine invariant medial axis is robust and computationally efficient.
- This method offers a new tool for shape analysis and feature detection.
- The technique shows promise for applications in computer vision and image processing.
Related Concept Videos
01:16Bending of Curved Members - Neutral Surface
In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...
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...
01:14Bending of Curved Members - Strain Analysis
The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member is the...
The important part of bending analysis for such a member is the...
01:18Deformations in a Symmetric Member in Bending
When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
01:15Unsymmetric Bending - Angle of Neutral Axis
Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal centroidal axes. The...
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal centroidal axes. The...
01:17Curve Equations
Curves are essential geometric elements characterized by tangent distance, chord length, middle ordinate, and total arc length. These measurements are crucial in understanding a curve's geometric and spatial properties and are defined by the relationship between its radius and its central angle.The tangent distance (T) refers to the straight-line measurement from the intersection point of two tangents to either the start or end of the curve. This distance is influenced by the curve's radius (R)...