International Journal of Computer Vision
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Intrinsic Bayesian Active Contours for Extraction of Object Boundaries in Images
International Journal of Computer Vision
Elastic Shape Models for Face Analysis Using Curvilinear Coordinates
Journal of Mathematical Imaging and Vision
New Possibilities with Sobolev Active Contours
International Journal of Computer Vision
New possibilities with Sobolev active contours
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Towards segmentation based on a shape prior manifold
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Variational segmentation using dynamical models for rigid motion
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Deform PF-MT: particle filter with mode tracker for tracking nonaffine contour deformations
IEEE Transactions on Image Processing
Converting level set gradients to shape gradients
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
SIAM Journal on Imaging Sciences
A Continuum Mechanical Approach to Geodesics in Shape Space
International Journal of Computer Vision
SIAM Journal on Imaging Sciences
An integral solution to surface evolution PDEs via geo-cuts
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Almost Local Metrics on Shape Space of Hypersurfaces in $n$-Space
SIAM Journal on Imaging Sciences
3D human motion analysis framework for shape similarity and retrieval
Image and Vision Computing
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We wish to endow the manifold M of smooth curves in 驴驴 with a Riemannian metric that allows us to treat continuous morphs (homotopies) between two curves c驴 and c驴 as trajectories with computable lengths which are independent of the parameterization or representation of the two curves (and the curves making up the morph between them). We may then define the distance between the two curves using the trajectory of minimal length (geodesic) between them, assuming such a minimizing trajectory exists. At first we attempt to utilize the metric structure implied rather unanimously by the past twenty years or so of shape optimization literature in computer vision. This metric arises as the unique metric which validates the common references to a wide variety of contour evolution models in the literature as "gradient flows" to various formulated energy functionals. Surprisingly, this implied metric yields a pathological and useless notion of distance between curves. In this paper, we show how this metric can be minimally modified using conformal factors the depend upon a curve驴s total arclength. A nice property of these new conformal metrics is that all active contour models that have been called "gradient flows" in the past will constitute true gradient flows with respect to these new metrics under specfic time reparameterizations.