Least-Squares Estimation of Transformation Parameters Between Two Point Patterns
IEEE Transactions on Pattern Analysis and Machine Intelligence
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
How Easy is Matching 2D Line Models Using Local Search?
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics)
SIAM Journal on Computing
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shock Graphs and Shape Matching
International Journal of Computer Vision
The Earth Mover's Distance as a Metric for Image Retrieval
International Journal of Computer Vision
Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Representation and Matching of Qualitative Shape at Multiple Scales
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Inexact Multisubgraph Matching Using Graph Eigenspace and Clustering Models
Proceedings of the Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The Earth Mover's Distance under Transformation Sets
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The geometry of graphs and some of its algorithmic applications
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Object Recognition as Many-to-Many Feature Matching
International Journal of Computer Vision
The representation and matching of categorical shape
Computer Vision and Image Understanding
The Representation and Matching of Images Using Top Points
Journal of Mathematical Imaging and Vision
Efficient many-to-many feature matching under the l1 norm
Computer Vision and Image Understanding
Probabilistic subgraph matching based on convex relaxation
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Discrete representation of top points via scale space tessellation
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
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Scale-space feature hierarchies can be conveniently represented as graphs, in which edges are directed from coarser features to finer features. Consequently, feature matching (or view-based object matching) can be formulated as graph matching. Most approaches to graph matching assume a one-to-one correspondence between nodes (features) which, due to noise, scale discretization, and feature extraction errors, is overly restrictive. In general, a subset of features in one hierarchy, representing an abstraction of those features, may best match a subset of features in another. We present a framework for the many-to-many matching of multi-scale feature hierarchies, in which features and their relations are captured in a vertex-labeled, edge-weighted graph. The matching algorithm is based on a metric-tree representation of labeled graphs and their low-distortion metric embedding into normed vector spaces. This two-step transformation reduces the many-to-many graph matching problem to that of computing a distribution-based distance measure between two such embeddings. To compute the distance between two sets of embedded, weighted vectors, we use the Earth Mover's Distance under transformation. To demonstrate the approach, we target the domain of multi-scale, qualitative shape description, in which an image is decomposed into a set of blobs and ridges with automatic scale selection. We conduct an extensive set of view-based matching trials, and compare the results favorably to matching under a one-to-one assumption.