## Mercer kernels for object recognition with local features (2005)

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Venue: | In IEEE CVPR |

Citations: | 40 - 0 self |

### BibTeX

@INPROCEEDINGS{Lyu05mercerkernels,

author = {Siwei Lyu},

title = {Mercer kernels for object recognition with local features},

booktitle = {In IEEE CVPR},

year = {2005},

pages = {223--229}

}

### Years of Citing Articles

### OpenURL

### Abstract

A new class of kernels for object recognition based on local image feature representations are introduced in this paper. Formal proofs are given to show that these kernels satisfy the Mercer condition. In addition, multiple types of local features and semilocal constraints are incorporated. Experimental results of SVM classifiers coupled with the proposed kernels are reported on recognition tasks with the COIL-100 database and compared with existing methods. The proposed kernels achieved competitive performance and were robust to changes in object configurations and image degradations.

### Citations

8952 | The Nature of Statistical Learning Theory
- Vapnik
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(Show Context)
Citation Context ...ust to changes in object configurations and image degradations. 1. Introduction Kernel methods received attention originally as a “trick” to introduce non-linearity into support vector machines (SVM) =-=[21]-=-. Evaluating a kernel function between two data is equivalent to computing the scalar product of their images in a non-linearly mapped space (usually termed as feature space). It is realized later tha... |

5086 | Distinctive image features from Scale-Invariant keypoints
- Lowe
- 2004
(Show Context)
Citation Context ...under changes in object configurations (e.g., translation and scaling). Recent years have seen impressive developments in using local features computed at interest points for matching and recognition =-=[9, 17, 16, 10, 2]-=-. Such approaches lead to robust and compact image representations that lend themselves to powerful pattern analysis algorithms. However, the local feature representations pose several challenges to k... |

3423 | LIBSVM: a Library for Support Vector Machine
- Chang, Lin
- 2008
(Show Context)
Citation Context ... and their kernels. The kernel parameter, p, was set to 9 in all cases. For the global features, a Gaussian kernel, Equation (2) was employed. The SVM classifiers were implemented with package LIBSVM =-=[3]-=-, which was enhanced to work with kernels on local feature representations. As a standard preprocessing step in the literature, we used the normalized kernel evaluation in building the SVM classifier,... |

1715 | A combined corner and edge detector
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- 1988
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Citation Context ... specific positions in an image that carry distinctive features of the object being studied. Interest points are found by an interest point detector, popular choices for which are the Harris detector =-=[6]-=- and multi-resolution based detectors [19]. In this paper, we denote pi = (xi, yi) as the coordinate (in the image plane) of the i-th interest point detected in the image, and vector Fi as the local f... |

1153 | A Performance Evaluation of Local Descriptors
- Mikolajczyk, Schmid
- 2003
(Show Context)
Citation Context ...al features have proved to be very successful in appearance based object matching and recognition, as they are distinctive, robust to image degradation and transformation, and require no segmentation =-=[11]-=-. Local features are usually collected at or in the neighboring region around interest points, which are specific positions in an image that carry distinctive features of the object being studied. Int... |

782 |
Kernel Method for Pattern Analysis
- Shawe-Taylor, Cristianini
- 2004
(Show Context)
Citation Context ... with kernel evaluations, these algorithms can discover non-linear patterns in data. At the same time, they are still computationally efficient, as the kernel function is evaluated in the input space =-=[20]-=-. Instead of using general-purpose kernels (e.g., Gaussians), recent effort has been put on designing kernels tailored to the requirements of a specific application. Such kernels better reflect the si... |

460 | R.: Local Grayvalue Invariants for Image Retrieval
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(Show Context)
Citation Context ...under changes in object configurations (e.g., translation and scaling). Recent years have seen impressive developments in using local features computed at interest points for matching and recognition =-=[9, 17, 16, 10, 2]-=-. Such approaches lead to robust and compact image representations that lend themselves to powerful pattern analysis algorithms. However, the local feature representations pose several challenges to k... |

319 | Indexing based on scale invariant interest points
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- 2001
(Show Context)
Citation Context ...under changes in object configurations (e.g., translation and scaling). Recent years have seen impressive developments in using local features computed at interest points for matching and recognition =-=[9, 17, 16, 10, 2]-=-. Such approaches lead to robust and compact image representations that lend themselves to powerful pattern analysis algorithms. However, the local feature representations pose several challenges to k... |

296 | Evaluation of interest point detectors
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- 2000
(Show Context)
Citation Context ... 1+|x||z| constructed as K(x, z) = (C(x, z) + 1) q . For each of these local features, interest points were found by a Harris corner detector, showed to have high repeatability and robust performance =-=[18]-=-. Interest points too close to the boundary were ignored to avoid image border effects. The parameters of the interest point detector were set so that, on average, approximately 100 interest points we... |

178 | Support vector machines for 3-d object recognition
- Pontil, Verri
- 1998
(Show Context)
Citation Context ...st a few of the complicated problems a recognition system has to face. Many applications of kernel methods to object recognition are based on global image features (e.g., global grayvalue histograms) =-=[14, 4, 15]-=-. Though promising performance has been reported, these methods are plagued by the deficiencies of the global features, such as being sensitive to image degradations (e.g., noise, occlusion and backgr... |

147 | Columbia Object Image Library (COIL-100
- Nene, Nayar, et al.
- 1996
(Show Context)
Citation Context ...d”, i.e., depending on data through their scalar products. SVM was chosen for its performance and generalization ability. 3.1. Experimental setup We performed our experiments on the COIL-100 database =-=[13]-=-, a standard test benchmark for object recognition. The COIL-100 database contains 7200 color images of 100 different objects. All images are 128 × 128 pixels in size. They were obtained by placing th... |

132 | Recognition with local features: the kernel recipe
- Wallraven, Caputo
- 1998
(Show Context)
Citation Context ...nts should also be incorporated. Finally, to guarantee unique global optimal solutions for the SVM algorithm, the kernel must also satisfy the Mercer condition. Unfortunately, existing methods (e.g., =-=[1, 22, 23, 12, 8]-=-) are not satisfactory in that they do not meet all of these require2 ments. The major contribution of this paper is the definition of a new class of kernels for object recognition, based on local fea... |

97 | A kernel between sets of vectors
- Kondor, Jebara
- 2004
(Show Context)
Citation Context ...nts should also be incorporated. Finally, to guarantee unique global optimal solutions for the SVM algorithm, the kernel must also satisfy the Mercer condition. Unfortunately, existing methods (e.g., =-=[1, 22, 23, 12, 8]-=-) are not satisfactory in that they do not meet all of these require2 ments. The major contribution of this paper is the definition of a new class of kernels for object recognition, based on local fea... |

91 | A Kullback-Leibler divergence based kernel for SVM classification in multimedia applications
- Moreno, Ho, et al.
(Show Context)
Citation Context ...nts should also be incorporated. Finally, to guarantee unique global optimal solutions for the SVM algorithm, the kernel must also satisfy the Mercer condition. Unfortunately, existing methods (e.g., =-=[1, 22, 23, 12, 8]-=-) are not satisfactory in that they do not meet all of these require2 ments. The major contribution of this paper is the definition of a new class of kernels for object recognition, based on local fea... |

89 | Viewpoint invariant texture matching and wide baseline stereo
- Schaffalitzky, Zisserman
- 2001
(Show Context)
Citation Context |

41 |
Building kernels from binary strings for image matching
- Odone, Barla, et al.
- 2005
(Show Context)
Citation Context ...st a few of the complicated problems a recognition system has to face. Many applications of kernel methods to object recognition are based on global image features (e.g., global grayvalue histograms) =-=[14, 4, 15]-=-. Though promising performance has been reported, these methods are plagued by the deficiencies of the global features, such as being sensitive to image degradations (e.g., noise, occlusion and backgr... |

34 | Phase-based local features
- Carneiro, Jepson
- 2002
(Show Context)
Citation Context |

29 | Evaluation of salient point techniques
- Sebe, Tian, et al.
- 2003
(Show Context)
Citation Context ...y distinctive features of the object being studied. Interest points are found by an interest point detector, popular choices for which are the Harris detector [6] and multi-resolution based detectors =-=[19]-=-. In this paper, we denote pi = (xi, yi) as the coordinate (in the image plane) of the i-th interest point detected in the image, and vector Fi as the local feature computed at or around pi. An image ... |

24 | Object Categorization with SVM: Kernels for Local Features
- Eichborn, Chapelle
- 2004
(Show Context)
Citation Context ...In [23], a Mercer kernel is proposed for sets of vectors based on the concept of principal angles between two linear subspaces. However, this kernel showed poor recognition performance as reported in =-=[5]-=-. In [8], the Bhattacharyya kernel is introduced where a set of vectors is represented as a multivariate Gaussian. Though provably satisfying the Mercer condition, evaluating this kernel is cubic in t... |

21 | Nonmercer kernels for svm object recognition
- Boughorbel, Tarel, et al.
- 2004
(Show Context)
Citation Context |

20 |
Svms for histogram based image classification
- Chapelle, Haffner, et al.
- 1999
(Show Context)
Citation Context ...st a few of the complicated problems a recognition system has to face. Many applications of kernel methods to object recognition are based on global image features (e.g., global grayvalue histograms) =-=[14, 4, 15]-=-. Though promising performance has been reported, these methods are plagued by the deficiencies of the global features, such as being sensitive to image degradations (e.g., noise, occlusion and backgr... |

2 |
Convolution kernel for structure data
- Haussler
- 1999
(Show Context)
Citation Context ...rnels, the following facts hold (i) (Proposition 2.22, [20]) The product of two Mercer kernels is a Mercer kernel. Thus, a monomial of any degree of a Mercer kernel is a Mercer kernel. (ii) (Lemma 1, =-=[7]-=-) Let K be a Mercer kernel defined on X × X , for any finite A, B ⊆ X , define � K(A, B) = � x∈A � y∈B K(x, y). Then � K is a Mercer kernel on 2 X × 2 X \ {∅}. (iii) (Proposition 11.75, [20]) For a da... |

2 | Kernel principle angles for classifiication machines with applications to image sequence interpretation - Wolf, Shashua - 2003 |