Institute for Systems Research
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Item Comparison of Run-to-Run Control Methods in Semiconductor Manufacturing Processes(2000) Zhang, Chang; Deng, Hao; Baras, John S.; Baras, John S.; ISRRun-to Run (RtR) control plays an important role in semiconductor manufacturing.In this paper, RtR control methods are generalized. The set-valued RtR controllers with ellipsoidapproximation are compared with other RtR controllers bysimulation according to the following criteria: A good RtR controller should be able to compensate for variousdisturbances, such as process drifts, process shifts (step disturbance)and model errors; moreover, it should beable to deal with limitations, bounds, cost requirement, multipletargets and time delays that are often encountered in realprocesses.
Preliminary results show the good performance of the set-valued RtRcontroller. Furthermore, this paper shows that it is insufficient to uselinear models to approximate nonlinear processes and it is necessary to developnonlinear model based RtR controllers.
Item Accurate Segmentation and Estimation of Parametric Motion Fields for Object-based Video Coding using Mean Field Theory(1997) Haridasan, Radhakrishan; Baras, John S.; ISR; CSHCNWe formulate the problem of decomposing a scene into its constituent objects as one of partitioning the current frame into objects comprising it. The motion parameter is modeled as a nonrandom but unknown quantity and the problem is posed as one of Maximum Likelihood (ML) estimation. The MRF potentials which characterize the underlying segmentation field are defined in a way that the spatio-temporal segmentation is constrained by the static image segmentation of the current frame. To compute the motion parameter vector and the segmentation simultaneously we use the Expectation Maximization (EM) algorithm. The E-step of the EM algorithm, which computes the conditional expectation of the segmentation field, now reflects interdependencies more accurately because of neighborhood interactions. We take recourse to Mean Field theory to compute the expected value of the conditional MRF. Robust M-estimation methods are used in the M- step. To allow for motions of large magnitudes image frames are represented at various scales and the EM procedure is embedded in a hierarchical coarse-to-fine framework. Our formulation results in a highly parallel algorithm that computes robust and accurate segmentations as well as motion vectors for use in low bit rate video coding.This report has been submitted as a paper to the SPIE conference on Visual Communications and Image Processing - VCIP98 to be held in San Jose, California on Jan 24- 30, 1998. Item Further Results on MAP Optimality and Strong Consistency of Certain Classes of Morphological Filters(1994) Sidiropoulos, N.D.; Baras, John S.; Berenstein, Carlos A.; ISRIn two recent papers [1], [2], Sidiropoulos et al. have obtained statistical proofs of Maximum A Posteriori} (MAP) optimality and strong consistency of certain popular classes of Morphological filters, namely, Morphological Openings, Closings, unions of Openings, and intersections of Closings, under i.i.d. (both pixel-wise, and sequence-wide) assumptions on the noise model. In this paper we revisit this classic filtering problem, and prove MAP optimality and strong consistency under a different, and, in a sense, more appealing set of assumptions, which allows the explicit incorporation of geometric and Morphological constraints into the noise model, i.e., the noise may now exhibit structure; Surprisingly, it turns out that this affects neither the optimality nor the consistency of these field-proven filters.Item Identification of Infinite Dimensional Systems Via Adaptive Wavelet Neural Networks(1993) Zhuang, Y.; Baras, John S.; ISRWe consider identification of distributed systems via adaptive wavelet neural networks (AWNNs). We take advantage of the multiresolution property of wavelet systems and the computational structure of neural networks to approximate the unknown plant successively. A systematic approach is developed in this paper to find the optimal discrete orthonormal wavelet basis with compact support for spanning the subspaces employed for system identification. We then apply backpropagation algorithm to train the network with supervision to emulate the unknown system. This work is applicable to signal representation and compression under the optimal orthonormal wavelet basis in addition to autoregressive system identification and modeling. We anticipate that this work be intuitive for practical applications in the areas of controls and signal processing.Item Optimal Filtering of Digital Binary Images Corrupted by Union/Intersection(1992) Sidiropoulos, N.D.; Baras, John S.; Berenstein, Carlos A.; ISRWe model digital binary image data as realizations of a bounded discrete random set, a mathematical object which can be directly defined on a finite lattice. We consider the problem of estimating realizations of discrete random sets distorted by a degradation process which can be described by a union/intersection model. First we present an important structural result concerning the probabilistic specification of discrete random sets defined on a finite lattice. Then we formulate the optimal filtering problem for the case of discrete random sets. Two distinct filtering approaches are pursued. For images which feature strong spatial statistical variations we propose a simple family of spatially varying filters, which we call mask filters, and, for each degradation model, derive explicit formulas for the optimal Mask filter. We also consider adaptive mask filters, which can be effective in a more general setting. For images which exhibit a stationary behavior, we consider the class of Morphological filters. First we provide some theoretical justification for the popularity of certain Morphological filtering schemes. In particular, we show that if the signal is smooth, then these schemes are optimal (in the sense of providing the MAP estimate of the signal) under a reasonable worst-case statistical scenario. Then we show that, by using an appropriate (under a given degradation model) expansion of the optimal filter, we can obtain universal characterizations of optimality which do not rely on strong assumptions regarding the spatial interaction of geometrical primitives of the signal and the noise. This approach corresponds to a somewhat counter- intuitive use of fundamental morphological operators; however it is exactly this mode of the use that enables us to arrive at characterizations of optimality in terms of the fundamental functionals of random set theory, namely the generating functionals of the signal and the noise.Item Structure of Divisible Discrete Random Sets and Their Randomized Superpositions(1991) Sidiropoulos, N.; Baras, John S.; Berenstein, Carlos A.; ISRIn this paper, we present an axiomatic formulation of Discrete Random Sets, and extend Choquet's uniqueness result to obtain a recursive procedure for the computation of the underlying event- space probability law, given a consistent Discrete Random Set specification via its generating functional. Based on this extension, we investigate the structure of Discrete Random Set models that enjoy the properties of independent decomposition/superposition, and present a design methodology for deriving models that are guaranteed to be consistent with some underlying event-space probability law. These results pave the way for the construction of various interesting models, and the solution of statistical inference problems for Discrete Random Sets.Item Bayesian Hypothesis Testing for Boolean Random Sets with Radial Convex Primary Grains Using Morphological Skeleton Transforms(1991) Sidiropoulos, N.; Baras, John S.; Berenstein, Carlos A.; ISRWe consider the problem of binary hypothesis testing for planar Boolean random sets with radial convex primary grains. We show that this problem is equivalent to the problem of binary hypothesis testing for Poisson points on a subset of R cube . The log-likelihood ratio for Poisson points can therefore be applied to observation points on this subset of R cube. Several interesting results pertaining to the asymptotic performance of the log-likelihood ratio for Poisson points are known. A major difficulty with this approach is that the test is based on observation points on a subset of R cube, and is not directly given in terms of the observation of a realization of a Boolean random set. An efficient means of mapping realizations of planar Boolean random sets to corresponding realizations of Poisson point processes on this subset of R cube is needed in order to implement the test. We show that this can be achieved via a class of morphological transformations known as morphological skeleton transforms. These transforms are flexible shape-size analysis tools based on elementary morphological and set-theoretic operations. This is the principal contribution of this paper.Item Exact, Recursive, Inference of Event Space Probability Law for Discrete Random Sets with Applications(1991) Sidiropoulos, N.; Baras, John S.; Berenstein, Carlos A.; ISRIn this paper we extend Choquet's result to obtain a recursive procedure for the computation of the underlying event-space probability law for Discrete Random Sets, based on Choquet's capacity functional. This is an important result, because it paves the way for the solution of statistical inference problems for Discrete Random Sets. As an example, we consider the Discrete Boolean Random Set with Radial Convex Primary Grains model, compute its capacity functional, and use our procedure to obtain a recursive solution to the problem of M-ary MAP hypothesis testing for the given model. The same procedure can be applied to the problem of ML model fitting. Various important probability functionals are computed in the process of obtaining the above results.