Unconstrained Approach Research Articles

Spectral color management using interim connection spaces based on spectral decomposition

AbstractA feasible approach to spectral color management was previously defined to include lookups performed within an interim connection space (ICS). ICS is relatively low in dimensions and is situated between a high‐dimensional spectral profile connection space and output units. The definition of ICS axes and the minimum number of ICS dimensions are explored here by considering the LabPQR, an ICS described in earlier research. LabPQR has three colorimetric dimensions (CIE L*a*b*) and additional dimensions to describe a metameric black (PQR). Several versions of LabPQR are explored. One type defines PQR axes based on metameric blacks generated from Cohen and Kappauf's spectral decomposition. The second type is constructed in an unconstrained way where metameric blacks are statistically derived based on the spectral characteristics of the target output device. For a six‐dimensional LabPQR, one that uses three colorimetric and three metameric black dimensions, it was found that Cohen and Kappauf‐based LabPQR was inferior for estimating the spectra when compared with the unconstrained method. However, when the limited spectral gamut of an output device was introduced through printer simulation and necessary spectral gamut mapping, the disadvantage of the six‐dimensional Cohen and Kappauf‐based LabPQR dissipated. On the other hand, reducing LabPQR to only five‐dimensions (two metameric black dimensions) reintroduced the advantage of the unconstrained approach even after simulated printing including spectral gamut mapping. Importantly, it was found that the five‐dimensional unconstrained approach achieved equivalent levels of performance to a full 31‐dimensional approach within simulated printer spectral gamut limitations. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 282–299, 2008.

Unconstrained Structural Equation Models of Latent Interactions: Contrasting Residual- and Mean-Centered Approaches

Little, Bovaird and Widaman (2006) proposed an unconstrained approach with residual centering for estimating latent interaction effects as an alternative to the mean-centered approach proposed by Marsh, Wen, and Hau (2004, 2006). Little et al. also differed from Marsh et al. in the number of indicators used to infer the latent interaction factor and how they were represented, but this issue is separate from the mean versus residual centering distinction that was their primary focus. However, their implementation of the Marsh et al. mean-centered approach failed to incorporate the mean structure that Marsh et al. argued was necessary to obtain unbiased estimates. One might suppose that their new approach would suffer this same problem, an issue not addressed by Little et al. However, we demonstrate here why the Little et al. approach obviates this requirement that heretofore was thought to be necessary for all constrained, partially constrained, and unconstrained approaches. Both the Marsh et al. and Little et al. unconstrained approaches typically result in similar results and are much easier to implement than traditional constrained approaches. They differ primarily in that the Little et al. approach is a 2-step approach involving a potentially large number of separate analyses prior to estimating the structural equation model that apparently does not require the estimation of a mean structure, whereas the Marsh et al. approach is a 1-step approach that includes a mean structure.

Propagation of the hip joint centre location error to the estimate of femur vs pelvis orientation using a constrained or an unconstrained approach

To estimate hip joint angles during selected motor tasks using stereophotogrammetric data, it is necessary to determine the hip joint centre position. The question is whether the errors affecting that determination propagate less to the angles estimates when a three degrees of freedom (DOFs) constraint (spherical hinge) is used between femur and pelvis, rather than when the two bones are assumed to be unconstrained (six DOFs). An analytical relationship between the hip joint centre location error and the joint angle error was obtained limited to the planar case. In the 3-D case, a similar relationship was obtained using a simulation approach based on experimental data. The joint angle patterns resulted in a larger distortion using a constrained approach, especially when wider rotations occur. The range of motion of the hip flexion–extension, obtained simulating different location errors and without taking into account soft tissue artefacts, varied approximately 7 deg using a constrained approach and up to 1 deg when calculated with an unconstrained approach. Thus, the unconstrained approach should be preferred even though its estimated three linear DOFs most unlikely carry meaningful information.

V1 non-linear properties emerge from local-to-global non-linear ICA

It has been argued that the aim of non-linearities in different visual and auditory mechanisms may be to remove the relations between the coefficients of the signal after global linear ICA-like stages. Specifically, in , it was shown that masking effects are reproduced by fitting the parameters of a particular non-linearity in order to remove the dependencies between the energy of wavelet coefficients. In this work, we present a different result that supports the same efficient encoding hypothesis. However, this result is more general because, instead of assuming any specific functional form for the non-linearity, we show that by using an unconstrained approach, masking-like behavior emerges directly from natural images. This result is an additional indication that Barlow's efficient encoding hypothesis may explain not only the shape of receptive fields of V1 sensors but also their non-linear behavior.

Spatial Decision Support System for Low-Income Families Relocation Tool for the Chicago, Illinois, Region

Housing relocation or housing mobility is not uncommon in the United States, with the average family relocating once every 6 years. As part of this process, individuals and families take into account a variety of factors. One of the important factors is that of transportation and its availability. Various researchers have studied the impact of transportation information on relocation choice. However, the need for a structured methodology that incorporates various factors, such as transportation, has been highlighted from a study of the current practice of relocation counseling. The objectives of this paper are threefold: (a) to develop an analytical hierarchy process to rank census tracts for relocation purposes of individuals, (b) to present a prototype of the spatial decision support system (SDSS) with an example, and (c) to evaluate the impact of relocation choice of individuals by using a spatially unconstrained approach. With data from the six-county northeastern Illinois region, the SDSS is developed and showcased with the help of a sample application. Two scenarios are tested for each respondent. The first is based on only housing criteria, and the second compares all criteria in the analytical hierarchy process matrix with each other. The improvements in travel time determined from the results of the two scenarios are compared, and the results are discussed to highlight the salient features of the decision support system.

Spatial Decision Support System for Low-Income Families

Housing relocation or housing mobility is not uncommon in the United States, with the average family relocating once every 6 years. As part of this process, individuals and families take into account a variety of factors. One of the important factors is that of transportation and its availability. Various researchers have studied the impact of transportation information on relocation choice. However, the need for a structured methodology that incorporates various factors, such as transportation, has been highlighted from a study of the current practice of relocation counseling. The objectives of this paper are threefold: (a) to develop an analytical hierarchy process to rank census tracts for relocation purposes of individuals, (b) to present a prototype of the spatial decision support system (SDSS) with an example, and (c) to evaluate the impact of relocation choice of individuals by using a spatially unconstrained approach. With data from the six-county northeastern Illinois region, the SDSS is developed and showcased with the help of a sample application. Two scenarios are tested for each respondent. The first is based on only housing criteria, and the second compares all criteria in the analytical hierarchy process matrix with each other. The improvements in travel time determined from the results of the two scenarios are compared, and the results are discussed to highlight the salient features of the decision support system.

Fast QRD-lattice-based unconstrained optimal filtering for acoustic noise reduction

We derive a fast QRD-least-squares lattice (QRD-LSL) based unconstrained optimal filtering algorithm for multichannel acoustic noise reduction. As known from the literature, the unconstrained optimal filtering approach is an alternative to the popular GSC beamforming, which does not rely on a priori information and hence possesses improved robustness. The optimal filtering problem involved is special in that the desired response signal is not known explicitly. The derivation of the QRD-LSL algorithm is based on a significantly reorganized version of a QRD-RLS-based unconstrained optimal filtering scheme. Overall an order of magnitude complexity reduction is obtained without any performance penalty, which makes this new approach affordable for real time implementation.

Model-based reconstructive elasticity imaging of deep venous thrombosis

Deep venous thrombosis (DVT) and its sequela, pulmonary embolism, is a significant clinical problem. Once detected, DVT treatment is based on the age of the clot. There are no good noninvasive methods, however, to determine clot age. Previously, we demonstrated that imaging internal mechanical strains can identify and possibly age thrombus in a deep vein. In this study the deformation geometry for DVT elasticity imaging and its effect on Young's modulus estimates is addressed. A model-based reconstruction method is presented to estimate elasticity in which the clot-containing vessel is modeled as a layered cylinder. Compared to an unconstrained approach in reconstructive elasticity imaging, the proposed model-based approach has several advantages: only one component of the strain tensor is used; the minimization procedure is very fast; the method is highly efficient because an analytic solution of the forward elastic problem is used; and the method is not very sensitive to the details of the external load pattern--a characteristic that is important for free-hand, external, surface-applied deformation. The approach was tested theoretically using a numerical model, and experimentally on both tissue-like phantoms and an animal model of DVT. Results suggest that elasticity reconstruction may prove to be a practical adjunct to triplex scanning to detect, diagnose, and stage DVT.

Model-based reconstructive elasticity imaging of deep venous thrombosis

Deep venous thrombosis (DVT) and its sequela, pulmonary embolism, is a significant clinical problem. Once detected, DVT treatment is based on the age of the clot. There are no good noninvasive methods, however, to determine clot age. Previously, we demonstrated that imaging internal mechanical strains call identify and possibly age thrombus in a deep vein. In this study the deformation geometry for DVT elasticity imaging and its effect on Young's modulus estimates is addressed. A model-based reconstruction method is presented to estimate elasticity in which the clot-containing vessel is modeled as a layered cylinder. Compared to all unconstrained approach in reconstructive elasticity imaging, the proposed model-based approach has several advantages: only one component of the strain tensor is used; the minimization procedure is very fast; the method is highly efficient because an analytic solution of the forward elastic problem is used; and the method is not very sensitive to the details of the external load pattern-a characteristic that is important for free-hand, external, surface-applied deformation. The approach was tested theoretically using a numerical model, and experimentally on both tissue-like phantoms and all animal model of DVT. Results Suggest that elasticity reconstruction may prove to be a practical adjunct to triplex scanning to detect, diagnose, and stage DVT.

Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction.

Interactions between (multiple indicator) latent variables are rarely used because of implementation complexity and competing strategies. Based on 4 simulation studies, the traditional constrained approach performed more poorly than did 3 new approaches--unconstrained, generalized appended product indicator, and quasi-maximum-likelihood (QML). The authors' new unconstrained approach was easiest to apply. All 4 approaches were relatively unbiased for normally distributed indicators, but the constrained and QML approaches were more biased for nonnormal data; the size and direction of the bias varied with the distribution but not with the sample size. QML had more power, but this advantage was qualified by consistently higher Type I error rates. The authors also compared general strategies for defining product indicators to represent the latent interaction factor.

Two-incision technique for rotational acetabular osteotomy: good outcome in 35 hips.

We have developed a 2-incision technique for rotational acetabular osteotomy. This includes both an extraperitoneal and an anterolateral exposure of the pelvic bones allowing an unconstrained approach without dissection of the muscle insertion. 2 plates are used to stabilize the osteotomy and full range motion of the hip is permitted within 2 days of surgery, while weight bearing is restricted for 6 weeks after the operation. We reviewed the complications and technical results in 27 patients (28 hips) after a minimum follow-up of mean 3 (1-5) years. No major surgical complications occurred, but dysfunction of the lateral femoral cutaneous nerve occurred frequently (14 patients). The radiographical correction of the femoral head covering was similar to those in previous reports of rotational osteotomy. The range of hip motion was not affected by the operation. A significant increase in the mean Merle D'Aubigné and Harris Hip scores was observed in a subgroup of 20 patients with a minimum follow-up of 2 years. In conclusion, the method we have used is safe and the early results are satisfactory.

Fully unconstrained non-collinear magnetism in triangularCr and Mn monolayers and overlayers on Cu(111) substrates

A recently developed fully unconstrained approach to non-collinearmagnetism has been applied to the investigation of the magneticground state of triangular free-standing Cr and Mn monolayers andoverlayers on Cu(111) substrates. Such systems represent aphysical realization of a frustrated two-dimensionalantiferromagnet. We find that the ground state of the Cr monolayersis non-collinear; it shows (3)1/2×(3)1/2 periodicitywith ±120° angles between the directions of the magneticmoments on neighbouring sites. Mn monolayers on the other hand havea collinear ground state with antiferromagnetically coupled rows andc(2×2) periodicity. The fully unconstrained descriptionallows for a detailed investigation of the spin densities in theinterstitial regions.

The numerical solution of bilinear data reconciliation problems using unconstrained optimization methods

A new approach to solving steady-state data reconciliation problems with bilinear constraints is proposed. Previously it was shown by Crowe that these problems can be solved using the method of matrix projection. In this work the objective function and its constraints are put into unconstrained form using Lagrange multipliers. Unconstrained optimization methods based on analytical derivatives are then used to solve the unconstrained formulation. The unconstrained approach is tested on two different reconciliation problems from the literature using number of Newton-type unconstrained optimization methods. The unconstrained methods are compared in terms of robustness and efficiency in solving the example problems. The performance of the unconstrained approach is compared to that of the method of matrix projection and the projected Lagrangian algorithm implemented in GAMS/MINOS.

Efficient algorithms for simulating complex mechanical systems using constraint dynamics

The constrained Lagrangian and constrained Hamiltonian equations of motion for a general non-relativistic classical mechanical system subject to rheonomous holonomic constraints are derived in an easy and straightforward manner. The numerical integration of the constrained equations of motion are discussed. It is shown how constraint errors introduced by the numerical integration can be avoided by introducing simple constraint correction schemes. As an example, the developed constrained methods are applied to the periodically driven inverted n -linked pendulum. It is demonstrated how the constrained methods leads to very efficient numerical algorithms. In the case of the n -linked pendulum, the computational complexity using the constrained methods is O(n) compared to O ( n 3 ) using the conventional unconstrained approach.

The numerical solution of bilinear data reconciliation problems using unconstrained optimization methods

A new approach to solving steady state data reconciliation problems with bilinear constraints is proposed. Previously it was shown by Crowe that these problems can be solved using the method of matrix projection. In this work the objective function and its constraints are put into unconstrained form using Lagrange multipliers. Unconstrained optimization methods based on analytical derivatives are then used to solve the unconstrained formulation. The unconstrained approach is tested on two different reconciliation problems from the literature using a number of Newton-type unconstrained optimization methods. The unconstrained methods are compared in terms of robustness and efficiency in solving the example problems. The performance of the unconstrained approach is compared to that of the method of matrix projection and the projected Lagrangian algorithm implemented in GAMS/MINOS.

An unconstrained dual approach to solving Karmarkar-type linear programs using conventional barrier functions

This paper proposes an unconstrained dual approach and an efficient algorithm for solving Karmarkar-type linear programming problems. Conventional barrier functions are incorporated as a perturbation term in the derivation of the associated duality theory. An optimal solution of the original linear program can be obtained by solving a sequence of unconstrained concave programs, or be approximated by solving one such dual program with a sufficiently small perturbation parameter. A globally convergent curved-search algorithm with a quadratic rate of convergence is designed for this purpose. Based on our testing results, we find that the computational procedure is very efficient and can be a viable approach for solving linear programming problems.

Unconstrained convex programming approach to linear programming

Recently, Fang proposed approximating a linear program in the Karmarkar standard form by adding an entropic barrier function to the objective function and derived an unconstrained dual concave program. We present in this note a necessary and sufficient condition for the existence of a dual optimal solution to the perturbed problem. In addition, a sharp upper bound of error estimation in this approximation scheme is provided.

A constrained empirical bayes estimator for incidence rates in areas with small populations

Maps that show the geographic distribution of incidence rates can be useful tools for analysing spatial variation in mortality and morbidity. To attain the necessary geographic resolution, however, production of such maps often requires estimation of incidence in areas with small populations where the observed rates may be highly unstable. Manton et al. have presented an empirical Bayes stabilization procedure in which the observed rate is combined with an area-specific estimate of the underlying incidence. The approach allows for the mapping of outcomes with varied and possibly unknown etiologies without necessitating covariate dependent modelling of the expected rate. The empirical distribution of a collection of these estimates, however, may not provide an adequate description of the dispersion among the true rates. As a result, decisions based on the histogram of the empirical Bayes estimates may be suspect. We propose a modified version of the approach in which the mean and sample variance of the ensemble of estimates are constrained to equal the appropriate moments of the posterior distribution. The resulting collection of constrained empirical Bayes estimators has nearly the stability of the unconstrained approach and provides an improved estimator of the true rate distribution. We illustrate use of the estimator by producing stabilized county-level maps of U.S. fire- and burn-related mortality rates and validate the analytic results using a simulation analysis.

Deriving an unconstrained convex program for linear programming

Consider a linear programming problem in Karmarkar's standard form. By perturbing its linear objective function with an entropic barrier function and applying generalized geometric programming theory to it, Fang recently proposed an unconstrained convex programming approach to finding an epsilon-optimal solution. In this paper, we show that Fang's derivation of an unconstrained convex dual program can be greatly simplified by using only one simple geometric inequality. In addition, a system of nonlinear equations, which leads to a pair of primal and dual epsilon-optimal solutions, is proposed for further investigation.

Adaptive entropy-coded predictive vector quantization of images

The authors consider 2-D predictive vector quantization (PVQ) of images subject to an entropy constraint and demonstrate the substantial performance improvements over existing unconstrained approaches. They describe a simple adaptive buffer-instrumented implementation of this 2-D entropy-coded PVQ scheme which can accommodate the associated variable-length entropy coding while completely eliminating buffer overflow/underflow problems at the expense of only a slight degradation in performance. This scheme, called 2-D PVQ/AECQ (adaptive entropy-coded quantization), is shown to result in excellent rate-distortion performance and impressive quality reconstructions of real-world images. Indeed, the real-world coding results shown demonstrate little distortion at rates as low as 0.5 b/pixel.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>