Related Experiment Video
Updated: May 31, 2026
05:33
Three-Dimensional Shape Modeling and Analysis of Brain Structures
Published on: November 14, 2019
Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves
Shantanu H Joshi1, Eric Klassen, Anuj Srivastava
1Dept. of Electrical Engineering, Florida State University, Tallahassee, FL 32310, USA.
Proceedings. IEEE Computer Society Conference on Computer Vision and Pattern Recognition
|September 28, 2011
Summary
The square-root-elastic (SRE) framework efficiently studies closed curve shapes using elastic metrics and path-straightening. This study extends SRE by removing rotation and re-parameterization to analyze curve shapes more effectively.
Area of Science:
- Computational geometry
- Computer vision
- Differential geometry
Background:
- Studying shapes of closed curves is crucial in various scientific fields.
- Existing frameworks may not adequately handle shape transformations like rotations and re-parameterizations.
- The square-root-elastic (SRE) framework offers a robust approach by combining elastic shape metrics and path-straightening.
Purpose of the Study:
- To extend the square-root-elastic (SRE) framework for analyzing closed curve shapes.
- To incorporate the removal of shape-preserving transformations (rotations and re-parameterizations) into the SRE framework.
- To demonstrate the enhanced framework's effectiveness on 2D and 3D curve data.
Main Methods:
- Development of quotient spaces to handle shape transformations.
- Construction of geodesics on these quotient spaces within the SRE framework.
- Application of the extended SRE framework to experimental datasets of 2D and 3D curves.
Main Results:
- Successfully extended the SRE framework to account for the removal of rotations and re-parameterizations.
- Demonstrated the framework's capability to find meaningful geodesic paths in shape spaces of curves.
- Validated the approach through experimental analysis on diverse 2D and 3D curve datasets.
Conclusions:
- The extended SRE framework provides a more comprehensive method for shape analysis of closed curves.
- Removing shape-preserving transformations enhances the robustness and applicability of geodesic analysis in shape spaces.
- The presented methods offer significant advancements for shape comparison and analysis in computational and geometric applications.
Related Concept Videos
01:23Curvilinear Motion: Rectangular Components
Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...
01:10Residual Stresses in Circular Shafts
In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experience plastic deformation. This deformation arises from either high levels of shearing stress or significant strains. Residual stresses are internal stresses that persist within a material after removing the external force causing deformation. This phenomenon is demonstrated when observing the behavior of a shaft under torque; notably, the shaft's...
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...
01:23Equation of the Elastic Curve
The concept of curvature in plane curves, crucial in structural engineering, defines how sharply a beam bends under load. This curvature is determined using the curve's first and second derivatives.
Consider a cantilever beam with a point load at its free end (for instance, a diving board). When analyzing beam deflection with small slopes, the shape of the beam's elastic curve becomes key. The governing equation for this analysis involves the bending moment and the beam's flexural rigidity,...
Consider a cantilever beam with a point load at its free end (for instance, a diving board). When analyzing beam deflection with small slopes, the shape of the beam's elastic curve becomes key. The governing equation for this analysis involves the bending moment and the beam's flexural rigidity,...
01:12Elasticity
Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
The elasticity of an object can be described by a stress-strain curve, which represents the relationship between stress...
The elasticity of an object can be described by a stress-strain curve, which represents the relationship between stress...
01:18Residual Stresses in Bending
In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...