Solid shape
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
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 shock grammar for recognition
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
On the Intrinsic Reconstruction of Shape from Its Symmetries
IEEE Transactions on Pattern Analysis and Machine Intelligence
Curvature Scale Space Representation: Theory, Applications, and MPEG-7 Standardization
Curvature Scale Space Representation: Theory, Applications, and MPEG-7 Standardization
Recognition of Shapes by Editing Their Shock Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Transitions of the Pre-Symmetry Set
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Curves vs. skeletons in object recognition
Signal Processing - Special section on content-based image and video retrieval
Matching 2D Shapes using their Symmetry Sets
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
Shape Representation and Classification Using the Poisson Equation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Alternative 2D Shape Representations using the Symmetry Set
Journal of Mathematical Imaging and Vision
Deep Structure, Singularities, and Computer Vision: First International Workshop, DSSCV 2005, Maastricht, The Netherlands, June 9-10, 2005, Revised Selected Papers (Lecture Notes in Computer Science)
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Contour Grouping Based on Contour-Skeleton Duality
International Journal of Computer Vision
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
Abstraction of 2D shapes in terms of parts
Proceedings of the 7th International Symposium on Non-Photorealistic Animation and Rendering
Computationally efficient matching of microRNA shapes using mutual symmetry
SIP '07 Proceedings of the Ninth IASTED International Conference on Signal and Image Processing
Skeleton Search: Category-Specific Object Recognition and Segmentation Using a Skeletal Shape Model
International Journal of Computer Vision
Describing and matching 2d shapes by their points of mutual symmetry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
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
Proceedings of the 5th international conference on Scale Space and PDE Methods in 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
PRIB'06 Proceedings of the 2006 international conference on Pattern Recognition in Bioinformatics
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Symmetry is an important cue in shape analysis. It has lead to the definition of popular shape descriptors like the medial axis. Its properties have been analyzed with a superset, called the symmetry set which represents the midpoints of circles that are at least bitangent to a shape.In this work we investigate the pre-symmetry set. This set considers the pairs of points at which the bitangent contact occurs. One thus obtains pairwise symmetric points of a 2D shape. A closed 2D shape has a parameterization P with finite length. Its pre-symmetry can therefore be represented by a symmetric diagram curves formed from the pairs of points (p i ,p j )驴S 1脳S 1.We discuss the properties of the pre-symmetry set visualized by this diagram. We firstly give the so-called transitions, changes caused by a perturbation of the shape and show the changes of the curves in the pre-symmetry set diagram. Secondly, we investigate curves that are spanned by all points on the shape. We name the curves essential loops and discuss their properties and transitions. As one important result we show that their are either zero or two essential loops. In the latter case a part of the medial axis is spanned by an essential loop and can therefore be considered as the main axis of the medial axis.As application of pre-symmetry sets, we discuss two possibilities for shape matching based on representations of the pre-symmetry set. The first shape descriptor we present is given by a circular diagram representing the shape, with a set of points representing the extrema of the curvature in the order they appear on the shape. They are pairwise connected and endowed with a length measure. This descriptor is directly related to the curves and their lengths in the pre-symmetry set diagram. The second descriptor is given by a binary array representing the areas enclosed by the curves in the pre-symmetry set diagram. It is area based and relates to the geometric derivation of the symmetry set.