Curve Matching Tools project definition
Public web page of
CurveMatch
Overview
This page is a preliminary definition of a collection of tools to match curves. Given a collection of curves, the matching tools will compute a resampling of the curves that defines a anatomically homologous parameterization of the curves. These tools will be a port of Matlab and C++ routines to Java.
Restrictions, Exclusions, Limitations
People Affected
| Person | Initials | Role | Notes |
|---|
| Ryan Cabeen | RC | Java implementer and application architect | |
| Shantanu Joshi | SJ | Designer and Matlab implementer | |
| Craig Schwartz | CS | project supervisor | |
| Roger Woods | RW | project sponsor | |
Version
1.0
Requirements
- Java 1.5 is used to implement this reader
- The tools will perform the same procedures as the original code
- Necessary matlab routines will be implemented
Command line Options
Requirements Change Procedure
- Changes and their date will be entered in a 'requirements change' list.
Requirements Changes
Products
The result of this project will be tools that will generate a mean curve and a collection of curves that have anatomically homologous vertices.
Approach
The method of this approach was outlined in the following two papers published in IEEE CVPR, as well as EMMCVPR 2007.
*
S. H. Joshi et al, A Novel Representation for Riemannian Analysis of Elastic Curves in R^n , IEEE CVPR 2007.
*
S.H. Joshi et al, Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves, EMMCVPR, Springer Lecture Notes in CS 4679, 2007.
Notes
This approach represents parameterized curves as functions in an abstract shape space. Curves can be either open or closed. Closed curves specify the boundary of a ROI or an object of interest. Open curves generally arise as features or delineations of important anatomical landmarks either manually traced or automatically extracted from intensity images or surfaces. The representation of shapes is invariant to rigid motions as well as scaling of curves. Additionally the shape of a curve is also invariant to the change in parameterization. Our approach endows the shape space with a Riemannian metric on the tangent space, and computes efficient geodesics between shapes in a parameterization-invariant manner. An interesting aspect of the shape space is that the uniform scaling constraint on the curves, makes it an infinite-dimensional Hilbert sphere. Alternately, closed curves lie in the subset of the Hilbert sphere. On account of this, geodesics can be specified analytically and computed very efficiently.
The Riemannian metric on the shape space also presents a natural framework for computing statistics on the shape space. We use the notion of Karcher mean (intrinsic) to compute averages of a collection of shapes. The computation of the mean shape is an iterative procedure, and is also efficient due to the spherical nature of the shape space.
The optimization procedure while computing geodesics relies on a gradient descent approach that works quite well. However, if one is interested in an approximate global solution to a geodesic, we also provide a way of computing geodesics using Dynamic Programming.
Lessons Learned
