title: Analysis of planar shapes using geodesic paths on shape spaces.
abstract: For analyzing shapes of planar, closed curves, we propose differential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier basis to represent tangents to the shape spaces and then use a gradient-based shooting method to solve for the tangent that connects any two shapes via a geodesic. Using the Surrey fish database, we demonstrate some applications of this approach: 1) interpolation and extrapolations of shape changes, 2) clustering of objects according to their shapes, 3) statistics on shape spaces, and 4) Bayesian extraction of shapes in low-quality images.
authors.affiliation: Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA. klassen@math.fsu.edu
authors.forename: Eric
authors.initials: E
authors.lastname: Klassen
authors.forename: Anuj
authors.initials: A
authors.lastname: Srivastava
authors.forename: Washington
authors.initials: W
authors.lastname: Mio
authors.forename: Shantanu H
authors.initials: SH
authors.lastname: Joshi
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D001499:Bayes Theorem; D003196:Computer Graphics; D005556:Form Perception; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique