Decomposing the Laplacian

A correction is made and an elementary derivation is given of Clark's (ibid., vol.11, p.43-57, 1989) decomposition of the Laplacian Δ²f(x,y) into a second directional derivative in the gradient direction of f, and a product of gradient magnitude by curvature of the level curve through f(x,y)     

Fabrication of submicron high-aspect-ratio GaAs actuators

Submicron, single-crystal gallium arsenide (SC-GaAs) actuators have been designed, fabricated, and operated. The fabrication process, called SCREAM-II (single crystal reactive etching and metallization II), uses chemically assisted ion beam etching (CAIBE) and reactive ion etching (RIE) to produce suspended and movable SC-GaAs structures with up to a 25:1 aspect ratio of vertical depth (10 μm) to lateral width (400 nm). Integrated actuators with predominantly vertical sidewall (PVS) aluminum electrodes are used to move the structures. Silicon nitride is used as an etch mask, structural stiffener, and electrical insulator. An x-y stage with integrated actuators produces controllable x-y displacements of ±1.8 μm when a voltage of 54.5 V is applied to either or both of the x and y actuators. The x-y stage resonates for an applied sinewave of 20 V (peak to peak) with f=10.5 kHz and a DC offset of 10 V. The structural vibration amplitude is 0.6 μm     

A tracking algorithm for implicitly defined curves

A tracking algorithm is given for curves that have equations of the form f(x,y)=0. It produces the next approximating pixel by looking for a sign difference in function evaluations at midpoints between the eight nearest neighboring pixels. The search proceeds in order of decreasing likelihood, examining the most probable candidates first     

Estimation of planar curves, surfaces, and nonplanar space curvesdefined by implicit equations with applications to edge and range imagesegmentation

The author addresses the problem of parametric representation and estimation of complex planar curves in 2-D surfaces in 3-D, and nonplanar space curves in 3-D. Curves and surfaces can be defined either parametrically or implicitly, with the latter representation used here. A planar curve is the set of zeros of a smooth function of two variables x-y, a surface is the set of zeros of a smooth function of three variables x-y-z, and a space curve is the intersection of two surfaces, which are the set of zeros of two linearly independent smooth functions of three variables x-y-z For example, the surface of a complex object in 3-D can be represented as a subset of a single implicit surface, with similar results for planar and space curves. It is shown how this unified representation can be used for object recognition, object position estimation, and segmentation of objects into meaningful subobjects, that is, the detection of `interest regions' that are more complex than high curvature regions and, hence, more useful as features for object recognition     

An improved synthesis method for multilayered neural networks usingqualitative knowledge

An improved synthesis method for the multilayered neural network (NN) as function approximator is proposed. The method offers a translation mechanism that maps the qualitative knowledge into a multilayered NN structure. Qualitative knowledge is expressed in the form of representative points, which can be linguistically described as, `when x is around x_i, then y_i is around y'. Synthesis equations for the translation mechanism are provided. After the direct synthesis of the initial NN, the NN is tuned by backpropagation (BP), using the training data. The direct synthesis decreases the burden on BP and contributes to improved learning efficiency, accuracy, and stability. It is demonstrated that the translation mechanism is also useful for incremental modeling, i.e., increasing the number of neurons, or representative points, based on the results of BP     

Further remarks on potentially global stabilizability

Given a control system with a nonlinear drift term, it is proved that a linear-like criterion for almost-global stabilizability can be stated, at least for control systems of the form x'=f( x)+Bu, where f is a polynomial but not necessarily homogeneous vector field. These stability criteria also allow for the control of the size of the region of attraction     

Splitting-shooting methods for nonlinear transformations ofdigitized patterns

New splitting-shooting methods are presented for nonlinear transformations T: (ξ,η)→(x,y) where x=x(ξ,η), y=y(ξ,η). These transformations are important in computer vision, image processing, pattern recognition, and shape transformations in computer graphics. The methods can eliminate superfluous holes or blanks, leading to better images while requiring only modest computer storage and CPU time. The implementation of the proposed algorithms is simple and straightforward. Moreover, these methods can be extended to images with gray levels, to color images, and to three dimensions. They can also be implemented on parallel computers or VLSI circuits. A theoretical analysis proving the convergence of the algorithms and providing error bounds for the resulting images is presented. The complexity of the algorithms is linear. Graphical and numerical experiments are presented to verify the analytical results and to demonstrate the effectiveness of the methods     

A new realization theory

A realization theory that is based on the Kalman system theory and motivated by the Fuhrmann realization theory is presented. In the Fuhrmann realization theory, the realization state-space is defined by a natural polynomial module K_Q, which is related to a nonsingular polynomial matrix Q. The module K_Q is formed of all f where Q^-1f is strictly proper. In the realization theory proposed, the realization state-space is defined by a different module M_Q, which is formed of properly truncated, strictly proper formal power series of Q^-1f. The realization theory can be used to prove the dual-realization scheme induced by the Fuhrmann realization theory     

A note on a classical bound for the moduli of all zeros of apolynomial

Considers the monic polynomial f(z):=z ⁿ+a_n-1z^n-1+. . .+a₀ in the complex variable z with complex coefficients. Under the assumption that the nonleading coefficients of f lie in the disk |z|⩽A the authors give an estimate for the smallest disk |z|⩽R containing all zeros of f. The estimate has a guaranteed precision of a few percent. They proceed similarly to obtain a zero-free disk |z |⩽r     

Consensus with dual failure modes

The problem of achieving consensus in a distributed system is discussed. Systems are treated in which either or both of two types of faults may occur: dormant (essentially omission and timing faults) and arbitrary (exhibiting arbitrary behavior, commonly referred to as Byzantine). Previous results showed that are number of dormant faults may be tolerated when there are no arbitrary faults and that, at most, [n-1/3] arbitrary faults may be tolerated when there are no dormant faults (n is the number of processors). A continuum is established between the previous results: an algorithm exists iff n >f_max+2m_max and c >f_max+m_max (where c is the system connectivity), when faults are constrained so that there are at most f_max and at most m_max of these that are arbitrary. An algorithm is given and compared to known algorithms. A method is given to establish virtual links so that the communications graph appears completely connected     

Handling timing errors in distributed programs

The authors describe a tool called TAP, which is defined to aid the programmer in discovering the causes of timing errors in running programs. TAP is similar to a postmortem debugger, using the history of interprocess communication to construct a timing graph, a directed graph where an edge joins node x to node y if event x directly precedes event y in time. The programmer can then use TAP to look at the graph to find the events that occurred in an unacceptable order. Because of the nondeterministic nature of distributed programs, the authors feel a history-keeping mechanism but always be active so that bugs can be dealt with as they occur. The goal is to collect enough information at run time to construct the timing graph if needed. Since it is always active, this mechanism must be efficient. The authors also describe experiments run using TAP and report the impact that TAP's history-keeping mechanism has on the running time of various distributed programs     

On the number of digital straight line segments

A closed-form expression has been reported in the literature for L_N, the number of digital line segments of length N that correspond to lines of the form y=ax+β, O⩽α, β<1. The authors prove an asymptotic estimate for L_N that might prove useful for many applications, namely, L_N=N ³/π²+O(N² log N). An application to an image registration problem is given     

Using motion from orthographic views to verify 3-D point matches

The specific problem addressed by the authors is how to detect the true match of a fourth point from among candidate matches in a situation in which three points have already been matched. The two sets of points to be matched are both subject to measurement errors. The depth error is more dominant than errors in the other two coordinates; however, the exact statistical distribution of the measurement errors is not known. The authors present a new method for solving the problem. The method is based on the technique of motion analysis using orthographic views. It discards the noisy z (depth) coordinates and uses only the x and y coordinates of the points to verify the match. The effect of depth errors on the motion estimate is completely prevented. Results show that this method is substantially more effective than previous methods that use all three coordinates     

A unified task-based dependability model for hypercube computers

A unified analytical model for computing the task-based dependability (TDB) of hypercube architectures is presented. A hypercube is deemed operational as long as a task can be executed on the system. The technique can compute both reliability and availability for two types of task requirements-I-connected model and subcube model. The I-connected TBD assumes that a connected group of at least I working nodes is required for task execution. The subcube TBD needs at least an m-cube in an n-cube, m⩽ n, for task execution. The dependability is computed by multiplying the probability that x nodes (x⩾I or x⩾2^m) are working in an n-cube at time t by the conditional probability that the hypercube can satisfy any one of the two task requirements from x working nodes. Recursive models are proposed for the two types of task requirements to find the connection probability. The subcube requirement is extended to find multiple subcubes for analyzing multitask dependability. The analytical results are validated through extensive simulation     

Linear systems with state and control constraints: the theory andapplication of maximal output admissible sets

The initial state of an unforced linear system is output admissible with respect to a constraint set Y if the resulting output function satisfies the pointwise-in-time condition y(t)∈Y, t⩾0. The set of all possible such initial conditions is the maximal output admissible set O_∞. The properties of O_∞ and its characterization are investigated. In the discrete-time case, it is generally possible to represent O_∞ or a close approximation of it, by a finite number of functional inequalities. Practical algorithms for generating the functions are described. In the continuous-time case simple representations of the maximal output admissible set are not available, however, it is shown that the discrete-time results may be used to obtain approximate representations     

On the imaging of fractal surfaces

An analysis is presented of the imaging of surfaces modeled by fractal Brownian elevation functions of the sort used in computer graphics. It is shown that, if Lambertian reflectance modest surface slopes and the absence of occlusions and self shadowing are assumed, a fractal surface with Fourier power spectrum proportional to f ^β produces an image with power spectrum proportional to f^2-β; here, f is the spatial frequency and β is related to the fractional dimension value. This allows one to use the spectral falloff of the images to predict the fractal dimension of the surface     

Two new estimation algorithms for linear models with unknown butbounded measurement noise

Attention is given to linear systems described by y=A _&thetas;+e where the measurement error vector e is unknown but bounded. Two algorithms for sequential parameter identification are introduced. Their convergence properties are illustrated and compared with those of existing algorithms. A simulation study is carried out using simulated data to investigate the possible practical use of the algorithms. Their performances are compared with those of other offline algorithms as well as with those of the widely used least-squares estimates     

Optimal flow control allocation policies in communication networkswith multiple message classes

Flow control is considered for M(⩾2) transmitting stations sending packets to a single receiver over a slotted time-multiplexed link. The optimal allocation problem is generalized to the case of nonidentical holding costs at the M transmitters. Qualitative properties of optimal discounted and time-average policies that reduce the computational complexity of the M-dimensional optimal flow control algorithm are derived. For M=2, a simple relationship between optimal allocations for states x and x +e_i (i=1,2) that leads to significant computational savings in the optimal algorithm is established     

Least-squares output estimation with multirate sampling

A least-squares output estimation algorithm is presented for applications where the output is sampled at a slower rate than the input. Given the sequence {u(kT), y(kJT )k=1,2,...}, where J is a positive integer and T is the basic sampling period, it is proven that the output estimation error converges to zero for instants at or between the output measurement instants. The assumptions required are essentially the same as for the case with equal sampling rates, i.e., for J=1. Simulation examples show excellent output estimation, based on measured y(kJT) with J=8