Discriminative learning is challenging when examples are sets of features, and the sets vary in cardinality and lack any sort of meaningful ordering. Kernel-based classification methods can learn complex decision boundaries, but a kernel over unordered set inputs must somehow solve for correspondences – generally a computationally expensive task that becomes impractical for large set sizes. We present a new fast kernel function which maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in this space. This “pyramid match ” computation is linear in the number of features, and it implicitly finds correspondences based on the finest resolution histogram cell where a matched pair first appears. Since the kernel does not penalize the presence of extra features, it is robust to clutter. We show the kernel function is positive-definite, making it valid for use in learning algorithms whose optimal solutions are guaranteed only for Mercer kernels. We demonstrate our algorithm on object recognition tasks and show it to be accurate and dramatically faster than current approaches. 1.

sminchisescu.ins.uni-bonn.de In visual recognition, the images are frequently modeled as unordered collections of local features (bags). We show that bag-of-words representations commonly used in conjunction with linear classifiers can be viewed as special match kernels, which count 1 if two local features fall into the same regions partitioned by visual words and 0 otherwise. Despite its simplicity, this quantization is too coarse, motivating research into the design of match kernels that more accurately measure the similarity between local features. However, it is impractical to use such kernels for large datasets due to their significant computational cost. To address this problem, we propose efficient match kernels (EMK) that map local features to a low dimensional feature space and average the resulting vectors to form a setlevel feature. The local feature maps are learned so their inner products preserve, to the best possible, the values of the specified kernel function. Classifiers based on EMK are linear both in the number of images and in the number of local features. We demonstrate that EMK are extremely efficient and achieve the current state of the art in three difficult computer vision datasets: Scene-15, Caltech-101 and Caltech-256. 1

haibin.ling @ siemens.com We propose using the proximity distribution of vectorquantized

The design of low-level image features is critical for computer vision algorithms. Orientation histograms, such as those in SIFT [16] and HOG [3], are the most successful and popular features for visual object and scene recognition. We highlight the kernel view of orientation histograms, and show that they are equivalent to a certain type of match kernels over image patches. This novel view allows us to design a family of kernel descriptors which provide a unified and principled framework to turn pixel attributes (gradient, color, local binary pattern, etc.) into compact patch-level features. In particular, we introduce three types of match kernels to measure similarities between image patches, and construct compact low-dimensional kernel descriptors from these match kernels using kernel principal component analysis (KPCA) [23]. Kernel descriptors are easy to design and can turn any type of pixel attribute into patch-level features. They outperform carefully tuned and sophisticated features including SIFT and deep belief networks. We report superior performance on standard image classification benchmarks: Scene-15, Caltech-101, CIFAR10 and CIFAR10-ImageNet. 1

Abstract. Recent research has shown the effectiveness of using sparse coding(Sc) to solve many computer vision problems. Motivated by the fact that kernel trick can capture the nonlinear similarity of features, which may reduce the feature quantization error and boost the sparse coding performance, we propose Kernel Sparse Representation(KSR). KSR is essentially the sparse coding technique in a high dimensional feature space mapped by implicit mapping function. We apply KSR to both image classification and face recognition. By incorporating KSR into Spatial Pyramid Matching(SPM), we propose KSRSPM for image classification. KSRSPM can further reduce the information loss in feature quantization step compared with Spatial Pyramid Matching using Sparse Coding(ScSPM). KSRSPM can be both regarded as the generalization of Efficient Match Kernel(EMK) and an extension of ScSPM. Compared with sparse coding, KSR can learn more discriminative sparse codes for face recognition. Extensive experimental results show that KSR outperforms sparse coding and EMK, and achieves state-of-the-art performance for image classification and face recognition on publicly available datasets. 1

A popular approach to problems in image classification is to represent the image as a bag of visual words and then employ a classifier to categorize the image. Unfortunately, a significant shortcoming of this approach is that the clustering and classification are disconnected. Since the clustering into visual words is unsupervised, the representation does not necessarily capture the aspects of the data that are most useful for classification. More seriously, the semantic relationship between clusters is lost, causing the overall classification performance to suffer. We introduce “discriminative cluster refinement” (DCR), a method that explicitly models the pairwise relationships between different visual words by exploiting their co-occurrence information. The assigned class labels are used to identify the co-occurrence patterns that are most informative for object classification. DCR employs a maximum-margin approach to generate an optimal kernel matrix for classification. One important benefit of DCR is that it integrates smoothly into existing bag-of-words information retrieval systems by employing the set of visual words generated by any clustering method. While DCR could improve a broad class of information retrieval systems, this paper focuses on object category recognition. We present a direct comparison with a state-of-the art method on the PASCAL 2006 database and show that cluster refinement results in a significant improvement in classification accuracy given a small number of training examples. 1.

This paper presents an extension to category classification with bag-of-features, which represents an image as an orderless distribution of features. We propose a method to exploit spatial relations between features by utilizing object boundaries provided during supervised training. We boost the weights of features that agree on the position and shape of the object and suppress the weights of background features, hence the name of our method — “spatial weighting”. The proposed representation is thus richer and more robust to background clutter. Experimental results show that our approach improves the results of one of the best current image classification techniques. Furthermore, we propose to apply the spatial model to object localization. Initial results are promising. 1.

The success of kernel methods including support vector networks (SVMs) strongly depends on the design of appropriate kernels. While initially kernels were designed in order to handle fixed-length data, their extension to unordered, variable-length data became more than necessary for real pattern recognition problems such as object recognition and bioinformatics. We focus in this paper on object recognition using a new type of kernel referred to as “context-dependent”. Objects, seen as constellations of local features (interest points, regions, etc.), are matched by minimizing an energy function mixing (1) a fidelity term which measures the quality of feature matching, (2) a neighborhood criteria which captures the object geometry and (3) a regularization term. We will show that the fixed-point of this energy is a “contextdependent” kernel (“CDK”) which also satisfies the Mercer condition. Experiments conducted on object recognition show that when plugging our kernel in SVMs, we clearly outperform SVMs with “context-free ” kernels. 1.

We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m × n matrices A, for m ≪ n, such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD distance. We also provide an empirical evaluation of the method that, in some scenarios, shows its advantages over the “usual ” recovery in the ℓp norms. 1

The success of kernel methods including support vector machines (SVMs) strongly depends on the design of appropriate kernels. While initially kernels were designed in order to handle fixed-length data, their extension to unordered, variable-length data became more than necessary for real pattern recognition problems such as object recognition and bioinformatics. We focus in this paper on object recognition using a new type of kernel referred to as “context-dependent”. Objects, seen as constellations of local features (interest points, regions, etc.), are matched by minimizing an energy function mixing (1) a fidelity term which measures the quality of feature matching, (2) a neighborhood criterion which captures the object geometry and (3) a regularization term. We will show that the fixedpoint of this energy is a “context-dependent” kernel (“CDK”) which also satisfies the Mercer condition. Experiments conducted on object recognition show that when plugging our kernel in SVMs, we clearly outperform SVMs with “context-free ” kernels. 1.