• Publications
  • Influence
Recognition of shapes by editing their shock graphs
tl;dr
This paper presents a novel framework for the recognition of objects based on their silhouettes. Expand
  • 736
  • 72
On Aligning Curves
tl;dr
This paper presents a novel method to find the optimal correspondence or alignment between 2D curves using their intrinsic properties. Expand
  • 403
  • 27
Symmetry-Based Indexing of Image Databases
tl;dr
We propose a graph-based representation of relational structure of components of shape that allows for deformations by changing attributes of this relational graph. Expand
  • 311
  • 21
On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks
  • P. Giblin, B. Kimia
  • Computer Science, Mathematics
  • International Journal of Computer Vision
  • 2004
tl;dr
We explore the local geometry of the medial axis (MA) and shocks (SH), and their structural changes under deformations, by viewing these symmetries as subsets of the symmetry set (SS) and present two results. Expand
  • 94
  • 13
Euler Spiral for Shape Completion
tl;dr
In this paper we address the curve completion problem, e.g., the geometric continuation of boundaries of objects which are temporarily interrupted by occlusion. Expand
  • 164
  • 13
On the evolution of curves via a function of curvature
tl;dr
We prove an existence theorem for the curve shortening problem and prove the existence of lemmas for the classical solution. Expand
  • 176
  • 12
On the role of medial geometry in human vision
  • B. Kimia
  • Medicine, Biology
  • Journal of Physiology-Paris
  • 1 March 2003
A key challenge underlying theories of vision is how the spatially restricted, retinotopically represented feature analysis can be integrated to form abstract, coordinate-free object models. AExpand
  • 82
  • 12
Parts of visual form: computational aspects
tl;dr
A proposed general principle of form from function motivates a particular partitioning scheme involving two types of parts, neck-based and limb-based, which lead to natural and intuitive parts which can be used for recognition. Expand
  • 104
  • 11
Shapes, shocks, and deformations I: The components of two-dimensional shape and the reaction-diffusion space
tl;dr
We undertake to develop a general theory of two-dimensional shape by elucidate several principles which any such theory should meet. Expand
  • 537
  • 10
On solving 2D and 3D puzzles using curve matching
  • W. Kong, B. Kimia
  • Computer Science
  • Proceedings of the IEEE Computer Society…
  • 8 December 2001
tl;dr
We approach the problem of 2D and 3D puzzle solving by matching the geometric features of puzzle pieces three at a time. Expand
  • 188
  • 10