On the editing distance between unordered labeled trees
Information Processing Letters
On the complexity of finding iso- and other morphisms for partial k-trees
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
The Tree-to-Tree Correction Problem
Journal of the ACM (JACM)
A tree-edit-distance algorithm for comparing simple, closed shapes
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Shape matching using edit-distance: an implementation
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computing the Edit-Distance between Unrooted Ordered Trees
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Recognition of Shapes by Editing Their Shock Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
A survey on tree edit distance and related problems
Theoretical Computer Science
Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering
International Journal of Computer Vision
Skeletal Shape Abstraction from Examples
IEEE Transactions on Pattern Analysis and Machine Intelligence
Matching of anatomical tree structures for registration of medical images
Image and Vision Computing
Approximate graph edit distance computation by means of bipartite graph matching
Image and Vision Computing
The Representation and Matching of Images Using Top Points
Journal of Mathematical Imaging and Vision
An optimal decomposition algorithm for tree edit distance
ACM Transactions on Algorithms (TALG)
Geometries on spaces of treelike shapes
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
Skeleton Search: Category-Specific Object Recognition and Segmentation Using a Skeletal Shape Model
International Journal of Computer Vision
A linear tree edit distance algorithm for similar ordered trees
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Means in spaces of tree-like shapes
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Tree-space statistics and approximations for large-scale analysis of anatomical trees
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Geometric tree kernels: classification of COPD from airway tree geometry
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Hi-index | 0.00 |
Geometric trees can be formalized as unordered combinatorial trees whose edges are endowed with geometric information. Examples are skeleta of shapes from images; anatomical tree-structures such as blood vessels; or phylogenetic trees. An inter-tree distance measure is a basic prerequisite for many pattern recognition and machine learning methods to work on anatomical, phylogenetic or skeletal trees. Standard distance measures between trees, such as tree edit distance, can be readily translated to the geometric tree setting. It is well-known that the tree edit distance for unordered trees is generally NP complete to compute. However, the classical proof of NP completeness depends on a particular case of edit distance with integer edit costs for trees with discrete labels, and does not obviously carry over to the class of geometric trees. The reason is that edge geometry is encoded in continuous scalar or vector attributes, allowing for continuous edit paths from one tree to another, rather than finite, discrete edit sequences with discrete costs for discrete label sets. In this paper, we explain why the proof does not carry over directly to the continuous setting, and why it does not work for the important class of trees with scalar-valued edge attributes, such as edge length. We prove the NP completeness of tree edit distance and another natural distance measure, QED, for geometric trees with vector valued edge attributes.