This paper provides an introduction to support vector machines (SVMs), kernel Fisher discriminant analysis, and

We consider visual category recognition in the framework of measuring similarities, or equivalently perceptual distances, to prototype examples of categories. This approach is quite flexible, and permits recognition based on color, texture, and particularly shape, in a homogeneous framework. While nearest neighbor classifiers are natural in this setting, they suffer from the problem of high variance (in bias-variance decomposition) in the case of limited sampling. Alternatively, one could use support vector machines but they involve time-consuming optimization and computation of pairwise distances. We propose a hybrid of these two methods which deals naturally with the multiclass setting, has reasonable computational complexity both in training and at run time, and yields excellent results in practice. The basic idea is to find close neighbors to a query sample and train a local support vector machine that preserves the distance function on the collection of neighbors. Our method can be applied to large, multiclass data sets for which it outperforms nearest neighbor and support vector machines, and remains efficient when the problem becomes intractable for support vector machines. A wide variety of distance functions can be used and our experiments show state-of-the-art performance on a number of benchmark data sets for shape and texture classification (MNIST, USPS, CUReT) and object recognition (Caltech-101). On Caltech-101 we achieved a correct classification rate of 59.05%(±0.56%) at 15 training images per class, and 66.23%(±0.48%) at 30 training images. 1.

We investigate the problem of learning optimal descriptors for a given classification task. Many hand-crafted descriptors have been proposed in the literature for measuring visual similarity. Looking past initial differences, what really distinguishes one descriptor from another is the tradeoff that it achieves between discriminative power and invariance. Since this trade-off must vary from task to task, no single descriptor can be optimal in all situations. Our focus, in this paper, is on learning the optimal tradeoff for classification given a particular training set and prior constraints. The problem is posed in the kernel learning framework. We learn the optimal, domain-specific kernel as a combination of base kernels corresponding to base features which achieve different levels of trade-off (such as no invariance, rotation invariance, scale invariance, affine invariance, etc.) This leads to a convex optimisation problem with a unique global optimum which can be solved for efficiently. The method is shown to achieve state-of-the-art performance on the UIUC textures, Oxford flowers and Caltech 101 datasets. 1.

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Abstract We develop a distance metric for clustering and classification algorithms which is invariant to affine transformations and includes priors on the transformation parameters. Such clustering requirements are generic to a number of problems in computer vision. We extend existing techniques for affine-invariant clustering, and show that the new distance metric outperforms existing approximations to affine invariant distance computation, particularly under large transformations. In addition, we incorporate prior probabilities on the transformation parameters. This further regularizes the solution, mitigating a rare but serious tendency of the existing solutions to diverge. For the particular special case of corresponding point sets we demonstrate that the affine invariant measure we introduced may be obtained in closed form. As an application of these ideas we demonstrate that the faces of the principal cast of a feature film can be generated automatically using clustering with appropriate invariance. This is a very demanding test as it involves detecting and clustering over tens of thousands of images with the variances including changes in viewpoint, lighting, scale and expression. 1

This paper describes a novel multi-view matching framework based on a new type of invariant feature. Our features are located at Harris corners in discrete scale-space and oriented using a blurred local gradient. This defines a rotationally invariant frame in which we sample a feature descriptor, which consists of an 8 × 8 patch of bias/gain normalised intensity values. The density of features in the image is controlled using a novel adaptive non-maximal suppression algorithm, which gives a better spatial distribution of features than previous approaches. Matching is achieved using a fast nearest neighbour algorithm that indexes features based on their low frequency Haar wavelet coefficients. We also introduce a novel outlier rejection procedure that verifies a pairwise feature match based on a background distribution of incorrect feature matches. Feature matches are refined using RANSAC and used in an automatic 2D panorama stitcher that has been extensively tested on hundreds of sample inputs. 1

Invariance is an important aspect in image object recognition. We present results obtained with an extended tangent distance incorporated in a kernel density based Bayesian classifier to compensate for affine image variations. An image distortion model for local variations is introduced and its relationship to tangent distance is considered. The proposed classification algorithms are evaluated on databases of different domains. An excellent result of 2.2% error rate on the original USPS handwritten digits recognition task is obtained. On a database of radiographs from daily routine, best results are obtained by combining tangent distance and the proposed distortion model.

We propose a complex wavelet domain image similarity measure, which is simultaneously insensitive to luminance change, contrast change and spatial translation. The key idea is to make use of the fact that these image distortions lead to consistent magnitude and/or phase changes of local wavelet coefficients. Since small scaling and rotation of images can be locally approximated by translation, the proposed measure also shows robustness to spatial scaling and rotation when these geometric distortions are small relative to the size of the wavelet filters. Compared with previous methods, the proposed measure is computationally efficient, and can evaluate the similarity of two images without a precise registration process at the front end. 1.

We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinearized variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher's discriminant and oriented PCA using support vector kernel functions. Extensive simulations show the utility of our approach.

We wish to match sets of images to sets of images where both sets are undergoing various distortions such as viewpoint and lighting changes.