Computer Vision and Image Understanding
SKETCH: an interface for sketching 3D scenes
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Assisted articulation of closed polygonal models
ACM SIGGRAPH 98 Conference abstracts and applications
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shock Graphs and Shape Matching
International Journal of Computer Vision
Tracking and modeling people in video sequences
Computer Vision and Image Understanding - Modeling people toward vision-based underatanding of a person's shape, appearance, and movement
Segmentation of Medical Image Objects Using Deformable Shape Loci
IPMI '97 Proceedings of the 15th International Conference on Information Processing in Medical Imaging
Fast Realistic Human Body Deformations for Animation and VR Applications
CGI '96 Proceedings of the 1996 Conference on Computer Graphics International
A shock grammar for recognition
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Boundary Smoothing via Symmetry Transforms
Journal of Mathematical Imaging and Vision
On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
A Formal Classification of 3D Medial Axis Points and Their Local Geometry
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognition of Shapes by Editing Their Shock Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Alternative 2D Shape Representations using the Symmetry Set
Journal of Mathematical Imaging and Vision
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
ALSBIR: A local-structure-based image retrieval
Pattern Recognition
Efficient Shape Modeling: ⋮-Entropy, Adaptive Coding, and Boundary Curves -vs- Blum's Medial Axis
International Journal of Computer Vision
Deriving the Medial Axis with geometrical arguments for planar shapes
Pattern Recognition Letters
Contour Grouping Based on Contour-Skeleton Duality
International Journal of Computer Vision
The global-local transformation for invariant shape representation
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part II
Measuring 3D shape similarity by graph-based matching of the medial scaffolds
Computer Vision and Image Understanding
The Global-Local transformation for noise resistant shape representation
Computer Vision and Image Understanding
Skeleton Search: Category-Specific Object Recognition and Segmentation Using a Skeletal Shape Model
International Journal of Computer Vision
Image skeletonization based on curve skeleton extraction
HCII'11 Proceedings of the 14th international conference on Human-computer interaction: design and development approaches - Volume Part I
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Essential loops and their relevance for skeletons and symmetry sets
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
The structure of shapes scale space aspects of the (pre-) symmetry set
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Bottom-up perceptual organization of images into object part hypotheses
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
On the Local Form and Transitions of Pre-symmetry Sets
Journal of Mathematical Imaging and Vision
Perceptually friendly shape decomposition by resolving segmentation points with minimum cost
Journal of Visual Communication and Image Representation
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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The main question we address is: What is the minimal information required to generate closed, nonintersecting planar boundaries? For this paper, we restrict 驴shape驴 to this meaning. More precisely, we examine whether the medial axis, together with dynamics, can serve as a language to design shapes and to effect shape changes, e.g., for modeling, to generate a morph sequence, etc. We represent the medial axis together with a direction of flow along the axis as the shock graph and examine the reconstruction of shape along each of the three types of medial axis points, (labeled A_1^2, A_1^3, A_3; see below for the A notation) and the associated six types of shock points. First, we show that the tangent and curvature of the medial axis and the speed and acceleration of the shock with respect to time of propagation, i.e., first and second order geometric and dynamic properties, are sufficient to determine the boundary tangent and curvature at corresponding points of the boundary. This implies that a rather coarse sampling of the symmetry axis, its tangent, curvature, speed, and acceleration is sufficient to regenerate accurately a local neighborhood of shape at regular axis points (A_1^2). We also show how higher order differential properties of the axis can be related to the higher-order differential properties of the boundary of the same order. Second, we examine the reconstruction of shape at branch points (A_1^3) where three regular branches are joined. We show that the three pairs of geometry (that is, curvature) and dynamics (that is, acceleration) must satisfy certain constraints. Finally, we derive similar results for the end points of shock branches (A_3 points). These formulas completely specify the local reconstruction of a shape from its shock-graph or medial axis and the conditions required to form a coherent shape from the medial axis.