Multi-layer Tree Matching Using HSTs
Matching two images by mapping image features play a fundamental role in many computer vision task. Due to noisy nature of feature extraction, establishing a one-to-one matching of features may not always be possible. Although many-to-many matching techniques establishes the desired multi map between features, they ignore the spatial structure of the nodes. In this paper, we propose a novel technique that utilizes both the individual node features and the clustering information of nodes for image matching where image features are represented as hierarchically well-separated trees (HSTs). Our method uses the fact that non-leaf nodes of an HST represent a constellation of nodes in the original image and obtains a matching by finding a mapping between non-leaf nodes among the two HSTs. Empirical evaluation of the method on an extensive set of recognition tests shows the robustness and efficiency of the overall approach.
KeywordsHierarchically well-separated tree HST Metric embedding Graph matching Tree matching
Unable to display preview. Download preview PDF.
- 3.Bartal, Y.: Probabilistic approximation of metric spaces and its algorithmic applications. In: Proceedings of the 37th Annual Symposium on Foundations of Computer Science, FOCS 1996, p. 184. IEEE Computer Society, Washington, DC (1996)Google Scholar
- 4.Bartal, Y.: On approximating arbitrary metrices by tree metrics. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, STOC 1998, pp. 161–168. ACM, New York (1998)Google Scholar
- 8.Charikar, M., Chekuri, C., Goel, A., Guha, S., Plotkin, S.: Approximating a finite metric by a small number of tree metrics. In: Proceedings of the 39th Annual Symposium on Foundations of Computer Science, FOCS 1998, pp. 379–388. IEEE Computer Society, Washington, DC (1998)Google Scholar
- 9.Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing, pp. 151–158. ACM (1971)Google Scholar
- 11.Fakcharoenphol, J., Rao, S., Talwar, K.: A tight bound on approximating arbitrary metrics by tree metrics. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, STOC 2003, pp. 448–455. ACM, New York (2003)Google Scholar
- 12.Richard, M.: Karp. A 2k-competitive algorithm for the circle (August 5, 1989) (manuscript)Google Scholar
- 16.Nene, S.A., Nayar, S.K., Murase, H., et al.: Columbia object image library (coil-20). Technical report, Technical Report CUCS-005-96 (1996)Google Scholar
- 17.Shapiro, L.G., Haralick, R.M.: Structural descriptions and inexact matching. IEEE Transactions on Pattern Analysis and Machine Intelligence (5), 504–519 (1981)Google Scholar
- 18.Wildman, J., Osmanlioglu, Y., Weber, S., Shokoufandeh, A.: Delay minimizing user association in cellular networks via hierarchically well-separated trees. arXiv preprint arXiv:1501.02419 (2015)Google Scholar