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21
Path planning using Laplace’s equation
, 1990
"... A method for planning smooth robot paths is presented. The method relies on the use of Laplace’s Equation to constrain the generation of a potential function over regions of the configuration space of an effector. Once the function is computed, paths may be found very quickly. These functions do not ..."
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Cited by 96 (8 self)
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A method for planning smooth robot paths is presented. The method relies on the use of Laplace’s Equation to constrain the generation of a potential function over regions of the configuration space of an effector. Once the function is computed, paths may be found very quickly. These functions do not exhibit the local minima which plague the potential field method. Unlike decompositional and algebraic techniques, Laplace’s Equation is very well suited to computation on massively parallel architectures. 1
Harmonic functions and collision probabilities
 In Proc. IEEE Int. Conf. Robot. Automat
, 1994
"... There is a close relationship between harmonic functions { which have recently been proposed forpath planning { and hitting probabilities for random processes. The hitting probabilities for random walks can be cast as a Dirichlet problem for harmonic functions, in much the same way as in path planni ..."
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Cited by 17 (2 self)
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There is a close relationship between harmonic functions { which have recently been proposed forpath planning { and hitting probabilities for random processes. The hitting probabilities for random walks can be cast as a Dirichlet problem for harmonic functions, in much the same way as in path planning. This equivalence has implications both for uncertainty in motion planning and in the application of machine learning techniques to some robot problems. In particular, Erdmann's method can directly incorporate such hitting probabilities. In addition, the value functions obtained byreinforcement learning algorithms can be rapidly reconstructed byrelaxation or resistive networks, once the extrema for such functions are known.
Maximizing network lifetime of broadcasting over wireless stationary ad hoc networks
 MOBILE NETWORKS AND APPLICATIONS
, 2005
"... We investigate the problem of extending the network lifetime of a single broadcast session over wireless stationary ad hoc networks where the hosts are not mobile. We define the network lifetime as the time from network initialization to the first node failure due to battery depletion. We provide t ..."
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Cited by 16 (0 self)
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We investigate the problem of extending the network lifetime of a single broadcast session over wireless stationary ad hoc networks where the hosts are not mobile. We define the network lifetime as the time from network initialization to the first node failure due to battery depletion. We provide through graph theoretic approaches a polynomialtime globally optimal solution, a variant of the minimum spanning tree (MST), to the problem of maximizing the static network lifetime. We make use of this solution to develop a periodic tree update strategy for effective load balancing and show that a significant gain in network lifetime over the optimal static network lifetime can be achieved. We provide extensive comparative simulation studies on parameters such as update interval and control overhead and investigate their impact on the network lifetime. The simulation results are also compared with an upper bound to the network lifetime.
Population Markov Chain Monte Carlo
 Machine Learning
, 2003
"... Stochastic search algorithms inspired by physical and biological systems are applied to the problem of learning directed graphical probability models in the presence of missing observations and hidden variables. For this class of problems, deterministic search algorithms tend to halt at local optima ..."
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Cited by 12 (2 self)
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Stochastic search algorithms inspired by physical and biological systems are applied to the problem of learning directed graphical probability models in the presence of missing observations and hidden variables. For this class of problems, deterministic search algorithms tend to halt at local optima, requiring random restarts to obtain solutions of acceptable quality. We compare three stochastic search algorithms: a MetropolisHastings Sampler (MHS), an Evolutionary Algorithm (EA), and a new hybrid algorithm called Population Markov Chain Monte Carlo, or popMCMC. PopMCMC uses statistical information from a population of MHSs to inform the proposal distributions for individual samplers in the population. Experimental results show that popMCMC and EAs learn more efficiently than the MHS with no information exchange. Populations of MCMC samplers exhibit more diversity than populations evolving according to EAs not satisfying physicsinspired local reversibility conditions. KEY WORDS: Markov Chain Monte Carlo, MetropolisHastings Algorithm, Graphical Probabilistic Models, Bayesian Networks, Bayesian Learning, Evolutionary Algorithms Machine Learning MCMC Issue 1 5/16/01 1.
2007): “Nonparametric matching and efficient estimators of homothetically separable functions
 Econometrica
"... For vectors x and w, letr(x, w) be a function that can be nonparametrically estimated consistently and asymptotically normally. We provide consistent, asymptotically normal estimators for the functions g and h, where r(x, w) =h[g(x),w], g is linearly homogeneous and h is monotonic in g. This framewo ..."
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Cited by 8 (4 self)
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For vectors x and w, letr(x, w) be a function that can be nonparametrically estimated consistently and asymptotically normally. We provide consistent, asymptotically normal estimators for the functions g and h, where r(x, w) =h[g(x),w], g is linearly homogeneous and h is monotonic in g. This framework encompasses homothetic and homothetically separable functions. Such models reduce the curse of dimensionality, provide a natural generalization of linear index models, and are widely used in utility, production, and cost function applications. One of our estimator’s of g is oracle efficient, achieving the same performance as an estimator based on local least squares knowing h. We provide simulation evidence on the small sample performance of our estimators, and an empirical production function application.
Segmentation of coarse and fine scale features using multiscale diffusion and mumfordshah
 in Scale Space Methods in Computer Vision, 4th International Conference, ScaleSpace 2003, Isle of Skye, UK, June 1012, 2003, Proceedings
, 2003
"... Abstract. Here we present a segmentation algorithm that uses multiscale diffusion with the MumfordShah model. The image data inside and outside a surface is smoothed by minimizing an energy functional using a partial differential equation that results in a tradeoff between smoothing and data fidel ..."
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Cited by 3 (1 self)
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Abstract. Here we present a segmentation algorithm that uses multiscale diffusion with the MumfordShah model. The image data inside and outside a surface is smoothed by minimizing an energy functional using a partial differential equation that results in a tradeoff between smoothing and data fidelity. We propose a scalespace approach that uses a good deal of diffusion as its coarse scale space and that gradually reduces the diffusion to get a fine scale space. So our algorithm continually moves to a particular diffusion level rather than just using a set diffusion coefficient with the MumfordShah model. Each time the smoothing is decreased, the data fidelity term increases and the surface is moved to a steady state. This method is useful in segmenting biomedical images acquired using highresolution confocal fluorescence microscopy. Here we tested the method on images of individual dendrites of neurons in rat visual cortex. These dendrites are studded with dendritic spines, which have very small heads and faint necks. The coarse scale segments out the dendrite and the brighter spine heads, while avoiding noise. Backing off the diffusion to a medium scale fills in more of the structure, which gets some of the brighter spine necks. The finest scale fills in the small and detailed features of the spines that are missed in the initial segmentation. Because of the thin, faint structure of the spine necks, we incorporate into our level set framework a topology preservation method for the surface which aids in segmentation and keeps a simple topology. 1
A New Method for Performance Evaluation of TurboCodes Using . . .
 IEEE Transactions on Communications
, 2004
"... In this paper , we present a new method for the performance evaluation of TurboCodes. ..."
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Cited by 2 (2 self)
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In this paper , we present a new method for the performance evaluation of TurboCodes.
Image simplification and vectorization
 In Proceedings of the 9th International Symposium on NonPhotorealistic Animation and Rendering (NPAR
"... We present an unsupervised system which takes digital photographs as input, and generates simplified, stylized vector data as output. The three component parts of our system are imagespace stylization, edge tracing, and edgebased image reconstruction. The design of each of these components is spec ..."
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Cited by 2 (0 self)
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We present an unsupervised system which takes digital photographs as input, and generates simplified, stylized vector data as output. The three component parts of our system are imagespace stylization, edge tracing, and edgebased image reconstruction. The design of each of these components is specialized, relative to their state of the art equivalents, in order to improve their effectiveness when used in such a combined stylization / vectorization pipeline. We demonstrate that the vector data generated by our system is often both an effective visual simplification of the input photographs, and an effective simplification in the sense of memory efficiency, as judged relative to state of the art lossy image compression formats.
A Variational Approach to MR Bias Correction
, 2003
"... Magnetic resonance (MR) imaging has opened up new avenues of diagnosis and treatment that were not previously available. There are a number of artifacts which can arise in the MR imaging process and make subsequent analysis more challenging. Probably the most drastic visual e#ect is the intensity in ..."
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Cited by 2 (0 self)
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Magnetic resonance (MR) imaging has opened up new avenues of diagnosis and treatment that were not previously available. There are a number of artifacts which can arise in the MR imaging process and make subsequent analysis more challenging. Probably the most drastic visual e#ect is the intensity inhomogeneity caused by spatiallyvarying signal response in the electrical coil that receives the MR signal. This coil inhomogeneity results in a multiplicative gain field that biases the observed signal from the true underlying signal. A number of techniques exist that attempt to correct this bias field, but none are wholly satisfying. We present an algorithm derived from statistical principles that is based on our knowledge of the physical imaging model. Our algorithm is a variational method that produces nonlinear estimates of the bias field and true image. We regularize our solutions using # 2 norms to ensure smoothness in the bias field and # p norms to enforce piecewise smoothness in the true image. The latter has an e#ect similar to an anisotropic filter that reduces the noise and preserves edges. We deal with the nonlinearity in our equations by first using coordinate descent to convert the di#cult overall problem into simpler subproblems, and then using fixedpoint iterative methods to linearize our equations. This allows us to employ the large body of existing work on fast iterative linear solvers. We also use multiresolution techniques to increase our solver speed. This results in an algorithm that is nonparametric, fast, and robust. We show how to extend our algorithm into a more general framework which allows us to seamlessly handle multiple receiving coils and multiple image pulse sequences. We demonstrate the utility of our algorithm on real prostate, heart, an...