The design of low-level image features is critical for computer vision algorithms. Orientation histograms, such as those in SIFT \cite{Lowe2004Distinctive} and HOG \cite{Dalal2005Histograms}, 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) \cite{Scholkopf1998Nonlinear}.

The design of low-level image features is critical for computer vision algorithms. Orientation histograms, such as those in SIFT \cite{Lowe2004Distinctive} and HOG \cite{Dalal2005Histograms}, 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) \cite{Scholkopf1998Nonlinear}.

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 thekernel 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 frameworkto 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 componentanalysis (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.

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 wordsand 0 otherwise. Despite its simplicity, this quantization is too coarse, motivating research into the design of match kernels that more accurately measure thesimilarity 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. Wedemonstrate 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.