… space of tree-like shapes along with a metric that gives locally unique geodesics. We review
the basics of metric geometry in spaces … prove that unique means exist in such spaces in sec…

… Starting from a purely geometric point of view, we define a shape space for treelike shapes.
… We define two metrics on this shape space, QED and TED, which give the shape space a …

… a shape space for rooted tree-like shapes and studied different metrics on this space. The
… In this section, we extend the Elastic Shape Framework to define a distance between trees. …

… the characteristic internal spacings of spaces bathed by streams. … This means that the number
of points on the circle (N) is fixed… , which are organized in tree-like fashion at the larger and …

… 1 is tree-like if and only if it coincides with the relation II* defined in terms of the clusters
associated with 11 (see Proposition 3). Certainly (I is tree-like … of tree-like metric spaces or how to …

… and the definition of a self-dual tree structure for the shapes of … Next section is devoted to
define the notions of saturation … In Section 3 we prove that the shapes of an image, defined as …

… elastic trajectories in the SRVF space, where elasticity refers … of tree-like 3D shapes in
the extended SRVF space, we … Here, we mathematically define the shape space Cα of such …

… The semantics of this logic are tree-like spaces which are a … through common properties of
extensional objects. Apart from … way of understanding the meaning of quantifiers in varying (…

… spaces and non-expanding maps is isomorphic to a category LAT* of complete, atomic,
tree-like, real … We define a real valued non-negative function ∆(x, y) on A(L) ⊗ A(L) as follows: …

… analysis and modeling of the geometry and topology of a collection of tree shapes, we
need to define a distance metric in the shape space of trees and a mechanism for computing …