We propose a data structure obtained by hierarchically averaging bag-of-word descriptors during a sequence of views that achieves average speedups in large-scale loop closure applications ranging from 4 to 20 times on benchmark datasets. Although simple, the method works as well as sophisticated agglomerative schemes at a fraction of the cost with minimal loss of performance.
We define the relevant information in a signal @math as being the information that this signal provides about another signal @math . Examples include the information that face images provide about the names of the people portrayed, or the information that speech sounds provide about the words spoken. Understanding the signal @math requires more than just predicting @math , it also requires specifying which features of @math play a role in the prediction. We formalize this problem as that of finding a short code for @math that preserves the maximum information about @math . That is, we squeeze the information that @math provides about @math through a bottleneck' formed by a limited set of codewords @math . This constrained optimization problem can be seen as a generalization of rate distortion theory in which the distortion measure @math emerges from the joint statistics of @math and @math . This approach yields an exact set of self consistent equations for the coding rules @math and @math . Solutions to these equations can be found by a convergent re-estimation method that generalizes the Blahut-Arimoto algorithm. Our variational principle provides a surprisingly rich framework for discussing a variety of problems in signal processing and learning, as will be described in detail elsewhere. 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 epsivnerally 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   We present a new approach for tracking roads from satellite images, and thereby illustrate a general computational strategy ("active testing") for tracking 1D structures and other recognition tasks in computer vision. Our approach is related to recent work in active vision on "where to look next" and motivated by the "divide-and-conquer" strategy of parlour games. We choose "tests" (matched filters for short road segments) one at a time in order to remove as much uncertainty as possible about the "true hypothesis" (road position) given the results of the previous tests. The tests are chosen online based on a statistical model for the joint distribution of tests and hypotheses. The problem of minimizing uncertainty (measured by entropy) is formulated in simple and explicit analytical terms. At each iteration new image data are examined and a new entropy minimization problem is solved (exactly), resulting in a new image location to inspect, and so forth. We report experiments using panchromatic SPOT satellite imagery with a ground resolution of ten meters. This paper presents a method for recognizing scene categories based on approximate global geometric correspondence. This technique works by partitioning the image into increasingly fine sub-regions and computing histograms of local features found inside each sub-region. The resulting "spatial pyramid" is a simple and computationally efficient extension of an orderless bag-of-features image representation, and it shows significantly improved performance on challenging scene categorization tasks. Specifically, our proposed method exceeds the state of the art on the Caltech-101 database and achieves high accuracy on a large database of fifteen natural scene categories. The spatial pyramid framework also offers insights into the success of several recently proposed image descriptions, including Torralbas "gist" and Lowes SIFT descriptors.