Abstract
Computer vision researchers have developed several learning methods based on the bag-of-words model for image related tasks, such as image retrieval or image categorization. For such an approach, images are represented as histograms of visual words from a codebook that is usually obtained with a simple clustering method. Next, kernel methods are used to compare such histograms. Popular choices, besides the linear SVM, are the intersection, Hellinger’s, χ 2 and Jensen-Shannon kernels.
This paper aims at introducing a kernel for histograms of visual words, namely the PQ kernel. This kernel is inspired from a class of similarity measures for ordinal variables, more precisely Goodman and Kruskals gamma and Kendalls tau. A proof that PQ is actually a kernel is also given in this work. The proof is based on building its feature map.
Object recognition experiments are conducted to compare the PQ kernel with other state of the art kernels on two benchmark datasets. The PQ kernel has the best mean average precision (AP) on both datasets. In one of the experiments, PQ and Jensen-Shannon kernels are combined to improve the mean AP score even further. In conclusion, the PQ kernel can be used with success, alone or in combination with other kernels, for image retrieval, image classification or other related tasks.
Chapter PDF
Similar content being viewed by others
Keywords
References
Bosch, A., Zisserman, A., Munoz, X.: Image Classification using Random Forests and Ferns. In: ICCV, pp. 1–8. IEEE Computer Society Press (2007)
Csurka, G., Dance, C.R., Fan, L., Willamowski, J., Bray, C.: Visual categorization with bags of keypoints. In: Workshop on Statistical Learning in Computer Vision, ECCV, pp. 1–22 (2004)
Dalal, N., Triggs, B.: Histograms of Oriented Gradients for Human Detection. In: CVPR, vol. 1, pp. 886–893. IEEE Computer Society, Washington, DC (2005)
Everingham, M., van Gool, L., Williams, C.K., Winn, J., Zisserman, A.: The Pascal Visual Object Classes (VOC) Challenge. IJCV 88(2), 303–338 (2010)
Fei-Fei, L., Fergus, R., Perona, P.: Learning generative visual models from few training examples: An incremental Bayesian approach tested on 101 object categories. CVIU 106(1), 59–70 (2007)
Fei-Fei, L., Perona, P.: A Bayesian Hierarchical Model for Learning Natural Scene Categories. In: CVPR, vol. 2, pp. 524–531. IEEE Computer Society (2005)
Lazebnik, S., Schmid, C., Ponce, J.: A Maximum Entropy Framework for Part-Based Texture and Object Recognition. In: ICCV 2005, vol. 1, pp. 832–838. IEEE Computer Society, Washington, DC (2005)
Lazebnik, S., Schmid, C., Ponce, J.: Beyond Bags of Features: Spatial Pyramid Matching for Recognizing Natural Scene Categories. In: CVPR 2006, vol. 2, pp. 2169–2178. IEEE Computer Society, Washington, DC (2006)
Leung, T., Malik, J.: Representing and Recognizing the Visual Appearance of Materials using Three-dimensional Textons. IJCV 43(1), 29–44 (2001)
Lowe, D.G.: Object Recognition from Local Scale-Invariant Features. In: ICCV, vol. 2, pp. 1150–1157. IEEE Computer Society, Washington, DC (1999)
Philbin, J., Chum, O., Isard, M., Sivic, J., Zisserman, A.: Object retrieval with large vocabularies and fast spatial matching. In: CVPR 2007, pp. 1–8 (2007)
Shalev-Shwartz, S., Singer, Y., Srebro, N.: Pegasos: Primal Estimated sub-GrAdient SOlver for SVM. In: ICML, pp. 807–814. ACM (2007)
Sivic, J., Russell, B.C., Efros, A.A., Zisserman, A., Freeman, W.T.: Discovering Objects and their Localization in Images. In: Proceedings of ICCV, pp. 370–377 (2005)
Upton, G., Cook, I.: A Dictionary of Statistics. Oxford University Press (2004)
Vedaldi, A., Fulkerson, B.: VLFeat: An Open and Portable Library of Computer Vision Algorithms (2008), http://www.vlfeat.org/
Vedaldi, A., Zisserman, A.: Efficient additive kernels via explicit feature maps. In: CVPR, pp. 3539–3546. IEEE Computer Society, San Francisco (2010)
Winn, J., Criminisi, A., Minka, T.: Object Categorization by Learned Universal Visual Dictionary. In: ICCV, vol. 2, pp. 1800–1807. IEEE Computer Society (2005)
Yagnik, J., Strelow, D., Ross, D.A., Lin, R.S.: The power of comparative reasoning. In: ICCV, pp. 2431–2438. IEEE (2011)
Zhang, J., Marszalek, M., Lazebnik, S., Schmid, C.: Local Features and Kernels for Classification of Texture and Object Categories: A Comprehensive Study. IJCV 73(2), 213–238 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ionescu, R.T., Popescu, M. (2013). Kernels for Visual Words Histograms. In: Petrosino, A. (eds) Image Analysis and Processing – ICIAP 2013. ICIAP 2013. Lecture Notes in Computer Science, vol 8156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41181-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-41181-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41180-9
Online ISBN: 978-3-642-41181-6
eBook Packages: Computer ScienceComputer Science (R0)