Abstract-A new method of farthest point strategy (FPS) for progressive image acquisition-an acquisition process that enables an approximation of the whole image at each sampling stage-is presented. Its main advantage is in retaining its uniformity with the increased density, providing efficient means for sparse image sampling and display. In contrast to previously presented stochastic approaches, the FPS guarantees the uniformity in a deterministic min-max sense. Within this uniformity criterion, the sampling points are irregularly spaced, exhibiting anti-aliasing properties comparable to those characteristic of the best available method (Poisson disk). A straightforward modification of the FPS yields an image-dependent adaptive sampling scheme. An efficient O(N log N) algorithm for both versions is introduced, and several applications of the FPS are discussed.

Abstract-Ants and other insects are known to use chemicals called pheromones for various communication and coordination tasks. In this paper, we investigate the ability of a group of robots, that communicate by leaving traces, to perform the task of cleaning the floor of an un-mapped building, or any task that requires the traversal of an unknown region. More specifically, we consider robots which leave chemical odor traces that evaporate with time, and are able to evaluate the strength of smell at every point they reach, with some measurement error. Our abstract model is a decentralized multiagent adaptive system with a shared memory, moving on a graph whose vertices are the floor-tiles. We describe three methods of covering a graph in a distributed fashion, using smell traces that gradually vanish with time, and show that they all result in eventual task completion, two of them in a time polynomial in the number of tiles. As opposed to existing traversal methods (e.g., depth first search), our algorithms are adaptive: they will complete the traversal of the graph even if some of the a(ge)nts die or the graph changes (edges/vertices added or deleted) during the execution, as long as the graph stays connected. Another advantage of our agent interaction processes is the ability of agents to use noisy information at the cost of longer cover time.

The Karhunen-Loeve (KL) transform is an optimal method for approximating a set of vectors or images, which was used in image processing and computer vision for several tasks such as face and object recognition. Its computational demands and its batch calculation nature have limited its application. Here we present a new, sequential algorithm for calculating the KL basis, which is faster in typical applications and is especially advantageous for image sequences: the KL basis calculation is done with much lower delay and allows for dynamic updating of image databases. Systematic tests of the implemented algorithm show that these advantages are indeed obtained with the same accuracy available from batch KL algorithms.

Most existing inductive learning algorithms work under the assumption that their training examples are already tagged. There are domains, however, where the tagging procedure requires significant computation resources or manual labor. In such cases, it may be beneficial for the learner to be active, intelligently selecting the examples for labeling with the goal of reducing the labeling cost. In this paper we present LSS-a lookahead algorithm for selective sampling of examples for nearest neighbor classifiers. The algorithm is looking for the example with the highest utility, taking its effect on the resulting classifier into account. Computing the expected utility of an example requires estimating the probability of its possible labels. We propose to use the random field model for this estimation. The LSS algorithm was evaluated empirically on seven real and artificial data sets, and its performance was compared to other selective sampling algorithms. The experiments show that the proposed algorithm outperforms other methods in terms of average error rate and stability.

A space-filling curve is a linear traversal of a discrete finite multidimensional space. In order for this traversal to be useful in many applications, the curve should preserve "locality". We quantify "locality" and bound the locality of multidimensional space-filling curves. Classic Hilbert space-filling curves come close to achieving optimal locality.

No abstract

Nonnegative matrix factorization (NMF) approximates a given data matrix as a product of two low-rank nonnegative matrices, usually by minimizing the L2 or the KL distance between the data matrix and the matrix product. This factorization was shown to be useful for several important computer vision applications. We propose here two new NMF algorithms that minimize the Earth mover's distance (EMD) error between the data and the matrix product. The algorithms (EMD NMF and bilateral EMD NMF) are iterative and based on linear programming methods. We prove their convergence, discuss their numerical difficulties, and propose efficient approximations. Naturally, the matrices obtained with EMD NMF are different from those obtained with L2-NMF. We discuss these differences in the context of two challenging computer vision tasks, texture classification and face recognition, perform actual NMF-based image segmentation for the first time, and demonstrate the advantages of the new methods with common benchmarks.

No abstract