Behrooz Kamgar-Parsi

Clustering with neural networks

Partitioning a set ofN patterns in ad-dimensional metric space intoK clusters — in a way that those in a given cluster are more similar to each other than the rest — is a problem of interest in many fields, such as, image analysis, taxonomy, astrophysics, etc. As there are approximatelyKN/K! possible ways of partitioning the patterns amongK clusters, finding the best solution is beyond exhaustive search whenN is large. We show that this problem, in spite of its exponential complexity, can be formulated as an optimization problem for which very good, but not necessarily optimal, solutions can be found by using a Hopfield model of neural networks. To obtain a very good solution, the network must start from many randomly selected initial states. The network is simulated on the MPP, a 128 × 128 SIMD array machine, where we use the massive parallelism not only in solving the differential equations that govern the evolution of the network, but also in starting the network from many initial states at once thus obtaining many solutions in one run. We achieve speedups of two to three orders of magnitude over serial implementations and the promise through Analog VLSI implementations of further speedups of three to six orders of magnitude.

Distribution and moments of the weighted sum of uniforms random variables, with applications in reducing monte carlo simulations

We derive analytical expressions for the distribution function and the moments of the weighted sum where Xi are independent random variables with non-identical uniform distributions, for an arbitrary number of variables N and arbitrary coefficient values ai These results are the generalizations of those for the regular sum of uniform random variables. Using the results, we examine the inadequacy of the central limit approximation for finite N We also discuss the savings in the cost of computing properties of the weighted sum using these results vs Monte Carlo simulations. We give an example of the application of the weighted sum to analyzing the effects of digitization error in computer vision.

Vehicle localization on gravity maps

Efforts are underway to develop the capability for small unmanned underwater vehicles to use the Earths gravitational field for autonomous navigation. A main aspect of navigation is vehicle localization on an existing gravity map. We have developed machine vision-like algorithms that match the onboard gravimeter measurements to the map values. In gravity maps there are typically a dearth of distinctive topographic features such as peaks, ridges, ravines, etc. Moreover, because the gravity field can only be measured in-place, probing for such features is infeasible as it would require extensive surveys. These factors, make the commonly used feature matching approach impractical. The localization algorithms we have developed are based on matching with contours of constant field value. These algorithms are tested on simulated data with encouraging results. Although these algorithms are developed for underwater navigation using gravity maps, they are equally applicable to other domains, for example vehicle localization on an existing terrain map.

Simultaneous fitting of several planes to point sets using neural networks

It is a simple problem to fit one line to a collection of points in the plane. But when the problem is generalized to two or more lines then the problem complexity becomes exponential in the number of points because we must decide on a partitioning of the points among the lines they are to fit. The same is true for fitting lines to points in three-dimensional space or hyperplanes to data points of high dimensions. We show that this problem despite its exponential complexity can be formulated as an optimization problem for which very good, but not necessarily optimal, solutions can be found by using an artificial neural network. Furthermore, we show that given a tolerance one can determine the number of lines (or planes) that should be fitted to a given point configuration. This problem is prototypical of a class of problems in computer vision, pattern recognition, and data fitting. For example, the method we propose can be used in reconstructing a planar world from range data or in recognizing point patterns in an image.

Optimally isotropic Laplacian operator

Laplacian operators used in the literature for digital image processing are not rotationally invariant. We examine the anisotropy of 3 x 3 Laplacian operators for images quantized in square pixels, and find the operator which has the minimum overall anisotropy.

Three-dimensional computer vision for micro air vehicles

Results are described of an ongoing project whose goal is to provide advanced Computer Vision for small low flying autonomous aircraft. The work consists of two parts; range-based vision for object recognition and pose estimation, and monocular vision for navigation and collision avoidance. A wide variety of range imaging methods were considered for the former, and it was found that a promising approach is multi-ocular stereo with a pseudo-random texture projected with a xenon flash. This provides high range resolution despite motion, and can be small and light. The resulting range images, taken at a few meters range, would support the use of Tripod Operators, an efficient and general method for recognizing and localizing surface shapes in 6 DOF. This would provide the ability to recognize immediately upon encounter many kinds of targets. The monocular navigation system is based on finding corresponding features in successive images, and deducing from these the relative pose of the aircraft. Two methods are under development, based on horizon registration and point correspondences, respectively. The first can serve as a preprocessor for the second. This approach aims to continuously and accurately estimate the net motion of the vehicle.

Improved image thresholding for object extraction in IR images

Object extraction from an IR image background is of great interest both to the military and the commercial sector. A convenient and popular approach to object extraction is image thresholding. In this paper, we describe a new and easy to implement approach for extracting object(s) in single frame IR images, which has many similarities to image thresholding. Both on the basis of theoretical considerations and experimental results, however, our approach appears to be noticeably more dependable than image thresholding for IR images.

Automatic aircraft recognition: toward using human similarity measure in a recognition system

The problem of screening images of the skies to determine whether they contain aircraft or not is both of theoretical and practical interest. After the most prominent visual signal in the infrared image of the sky is extracted, the question is whether the signal is a correct match of an aircraft. Common approaches calculate the degree of similarity of the shape of the signal with a model aircraft using a similarity measure such as Euclidean distance, and make a decision based on whether the degree of similarity exceeds a (pre-specified) threshold. Our approach avoids metric similarity measures and the use of thresholds as it attempts to employ similarity measures used by humans. In the absence of sufficient real data, the approach allows to specifically generate an arbitrarily large number of training exemplars projecting near classification boundary. Once trained on such a training set, the performance of the neural network was comparable to that of a human expert, and far better than a network trained only on the available real data. Furthermore, the results were considerably better than those obtained using a Euclidean discriminator.

Short Communication: Using shorelines for autonomous air vehicle guidance

We suggest the use of extended landmarks, such as shorelines, creeks, tree lines, and railroads, as well as roads for autonomous navigation of an unmanned air vehicle (UAV). In particular, we recommend the use of shorelines, because of their common availability, their ease of detection, and their significance in terms of events happening along them. Monitoring coastlines and waterways from low flying UAVs has many applications for military and civilian use. We report the development of a vision system that has enabled a prototype UAV to follow shorelines autonomously (without requiring maps or GPS). Using a near-infrared sensor the vision system distinguishes water from land (irrespective of waters color) and issues commands to the autopilot to follow the coastline or the riverbank. One insight of this problem is that the control algorithm could be integrated deeply with the vision system. This has the benefit of delaying smoothing/regularization so that it could occur in the context of the control coordinate system rather than the image or ground coordinate system. The algorithm itself is simple, but it possibly points the way to future algorithms which could more closely couple image processing and control. Furthermore, the experience gained in this work may be of value in the development of vision systems for following other types of paths.

Hopfield model and optimization problems

Publisher Summary This chapter discusses Hopfield model and optimization problems. Hopfield neural networks application are divided in two areas: (1) content addressable memory or information storage and retrieval and (2) solving optimization problems. The chapter discusses the optimization problems application. It focuses on the effectiveness of Hopfield nets in solving optimization problems and the performance scales with the size of the problem. The chapter presents the results of the simulations of Hopfield and Tank solution to the travelling salesman problem (TSP). TSP can be solved by a neural network. The success rate of the neural network in finding valid solutions to TSP can be improved by changing the neural net formulation of the problem. Although the quality of solutions that are found by the neural network are of good quality, finding valid solutions becomes difficult as the size of the problem increases. This suggests that neural nets might not be suitable for solving computationally hard problems.