AbstractÐNearly all super-resolution algorithms are based on the fundamental constraints that the super-resolution image should generate the low resolution input images when appropriately warped and down-sampled to model the image formation process. �These reconstruction constraints are normally combined with some form of smoothness prior to regularize their solution.) In the first part of this paper, we derive a sequence of analytical results which show that the reconstruction constraints provide less and less useful information as the magnification factor increases. We also validate these results empirically and show that, for large enough magnification factors, any smoothness prior leads to overly smooth results with very little high-frequency content �however, many low resolution input images are used). In the second part of this paper, we propose a super-resolution algorithm that uses a different kind of constraint, in addition to the reconstruction constraints. The algorithm attempts to recognize local features in the low-resolution images and then enhances their resolution in an appropriate manner. We call such a super-resolution algorithm a hallucination or recogstruction algorithm. We tried our hallucination algorithm on two different data sets, frontal images of faces and printed Roman text. We obtained significantly better results than existing reconstruction-based algorithms, both qualitatively and in terms of RMS pixel error. Index TermsÐSuper-resolution, analysis of reconstruction constraints, learning, faces, text, hallucination, recogstruction. 1

Many different low-level feature detectors exist and it is widely agreed that the evaluation of detectors is important. In this paper we introduce two evaluation criteria for interest points: repeatability rate and information content. Repeatability rate evaluates the geometric stability under different transformations. Information content measures the distinctiveness of features. Different interest point detectors are compared using these two criteria. We determine which detector gives the best results and show that it satisfies the criteria well.

Abstract—The problem of finding the closest point in high-dimensional spaces is common in pattern recognition. Unfortunately, the complexity of most existing search algorithms, such as k-d tree and R-tree, grows exponentially with dimension, making them impractical for dimensionality above 15. In nearly all applications, the closest point is of interest only if it lies within a user-specified distance e. We present a simple and practical algorithm to efficiently search for the nearest neighbor within Euclidean distance e. The use of projection search combined with a novel data structure dramatically improves performance in high dimensions. A complexity analysis is presented which helps to automatically determine e in structured problems. A comprehensive set of benchmarks clearly shows the superiority of the proposed algorithm for a variety of structured and unstructured search problems. Object recognition is demonstrated as an example application. The simplicity of the algorithm makes it possible to construct an inexpensive hardware search engine which can be 100 times faster than its software equivalent. A C++ implementation of our algorithm is available upon request to search@cs.columbia.edu/CAVE/.

In computer vision and image processing, edge detection concerns the localization of significant variations of the grey level image and the identification of the physical phenomena that originated them. This information is very useful for applications in 3D reconstruction, motion, recognition, image enhancement and restoration, image registration, image compression, and so on. Usually, edge detection requires smoothing and differentiation of the image. Differentiation is an ill-conditioned problem and smoothing results in a loss of information. It is difficult to design a general edge detection algorithm which performs well in many contexts and captures the requirements of subsequent processing stages. Consequently, over the history of digital image processing a variety of edge detectors have been devised which differ in their mathematical and algorithmic properties. This paper is an account of the current state of our understanding of edge detection. We propose an overview of research...

Computing the weighted average of the pixel values in a window is a basic module in many computer vision operators. The process is reformulated in a linear vector space and the role of the different subspaces is emphasized. Within this framework well known artifacts of the gradient based edge detectors, such as large spurious responses can be explained quantitatively. It is also shown that template matching with a template derived from the input data is meaningful since it provides an independent measure of confidence in the presence of the employed edge model. The widely used three-step edge detection procedure: gradient estimation, nonmaxima suppression, hysteresis thresholding; is generalized to include the information provided by the confidence measure. The additional amount of computation is minimal and experiments with several standard test images show the ability of the new procedure to detect weak edges. Keywords: edge detection, performance assessment, gradient estimation, window operators 1

Abstract: Autonomous long range navigation in partially known planetary-like terrain is an open challenge for robotics. Navigating several hundreds of meters without any human intervention requires the robot to be able to build various representations of its environment, to plan and execute trajectories according to the kind of terrain traversed, to localize itself as it moves, and to schedule, start, control and interrupt these various activities. In this paper, we brie y describe some functionalities that are currently running on board the Marsokhod model robot Lama at LAAS/CNRS. We then focus on the necessity tointegrate various instances of the perception and decision functionalities, and on the di culties raised by this integration. 1.

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semi-definite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semi-definite Gram matrix, either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across 5 poses (left and right profiles, left and right half profiles, and frontal view) with 2 different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gaborbased Chengjun Liu is with the Department of Computer Science, New J...

Weinvestigate the use of linear and nonlinear principal manifolds for learning lowdimensional representations for visual recognition. Three techniques: Principal Component Analysis #PCA#, Independent Component Analysis #ICA# and Nonlinear PCA #NLPCA# are examined and tested in a visual recognition experiment using a large gallery of facial images from the #FERET" database. We compare the recognition performance of a nearest-neighbour matching rule with each principal manifold representation to that of a maximum aposteriori #MAP# matching rule using a Bayesian similarity measure derived from probabilistic subspaces and demonstrate the superiority of the latter.

In contrast to the traditional approach, the recognition problem is formulated as one of matching appearance rather than shape. For any given vision task, all possible appearance variations define its visual workspace. A set of images is obtained by coarsely sampling the workspace. The image set is compressed to obtain a low-dimensional subspace, called the eigenspace, in which the visual workspace is represented as a continuous appearance manifold. Given an unknown input image, the recognition system first projects the image to eigenspace. The parameters of the vision task are recognized based on the exact position of the projection on the appearance manifold. The proposed appearance representation has several applications in visual perception. As examples, a real-time recognition system with 20 complex objects, an illumination planning technique for robust object recognition, and a real-time visual positioning and tracking system are described. The simplicity and generality of the pr...

Abstract. Local feature approaches to vision geometry and object recognition are based on selecting and matching sparse sets of visually salient image points, known as ‘keypoints ’ or ‘points of interest’. Their performance depends critically on the accuracy and reliability with which corresponding keypoints can be found in subsequent images. Among the many existing keypoint selection criteria, the popular Förstner-Harris approach explicitly targets geometric stability, defining keypoints to be points that have locally maximal self-matching precision under translational least squares template matching. However, many applications require stability in orientation and scale as well as in position. Detecting translational keypoints and verifying orientation/scale behaviour post hoc is suboptimal, and can be misleading when different motion variables interact. We give a more principled formulation, based on extending the Förstner-Harris approach to general motion models and robust template matching. We also incorporate a simple local appearance model to ensure good resistance to the most common illumination variations. We illustrate the resulting methods and quantify their performance on test images.