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Device characterization
Published in Sharma Gaurav, Digital Color Imaging Handbook, 2017
Several researchers have explored other refinements of the model. Arney et al.64 showed that the colors of both the paper and the dots are functions of the relative dot area coverages, and they extended the Neugebauer model to account for this. Lee et al.65 departed from the Demichel model and used a sequential quadratic programming method to estimate these parameters. Iino and Berns66 accounted for optical interactions among the colorants by introducing a correction to the dot gain of a given colorant that depends on the area coverages of the other colorants. Hua and Huang67 and Iino and Berns68,69 explored the use of a wavelengthdependent Yule–Nielsen factor. Agar and Allebach70 developed an iterative technique of selectively increasing the resolution of a cellular model in those regions where prediction errors are high. Xia et al.71 used a generalization of least squares, known as total least-squares (TLS) regression to optimize model parameters. Unlike least-squares regression, which assumes uncertainty only in the output space of the function being approximated, total least-squares assumes uncertainty in both the input and output spaces and can provide more robust and realistic estimates. In this regard, TLS has wide applicability in device characterization.
Neural-Based Orthogonal Regression
Published in Maurizio Cirrincione, Marcello Pucci, Vitale Gianpaolo, Power Converters and AC Electrical Drives with Linear Neural Networks, 2017
Generally, A ∈ ℜmxn is called data matrix, and b ∈ ℜm is called observation vector. According to the classical ordinary least squares (OLS) approach, errors are implicitly assumed to be confined to the observation vector. This assumption is however unrealistic. Actually, also the data matrix is affected by noise, like sampling errors, human errors, modeling errors, and measurement errors. In Refs [3,4], some methods are presented to estimate the influence of these errors on the OLS solution. The total least squares (TLS) method is a technique devised to make up for these errors. The TLS problem has been presented for the first time in Ref. [5], where it is solved by using the singular value decomposition (SVD), as proposed in Ref. [4] and more completely in Ref. [36]. This estimation method stems historically from statistics literature, where it is called orthogonal regression or errors-in-variables (EIV) regression.* As a matter of fact, the problem of the regression straight line has been considered since last century [6]. The main contributions are in Refs [6–10]. About 30 years ago, this technique has been extended to multivariable cases and later to multidimensional cases (where several observation vectors b are treated), as in Refs [11] and [12]. A complete analysis of the TLS problem can be found in Ref. [13], where the algorithm of Ref. [5] is generalized to the nongeneric case (no, generic TLS), where the initial algorithm failed to find a solution. According to the data least squares (DLS) approach, errors are assumed to be confined only to the data matrix [14]. The DLS case is particularly suitable for certain deconvolution problems, like in system identification or channel equalization [14].
Direct 3D coordinate transformation based on the affine invariance of barycentric coordinates
Published in Journal of Spatial Science, 2021
The most appropriate transformation model can be determined by multiple hypothesis testing methods, as reported in Lehmann (2014). In fact, the 12-parameter, 9-parameter and 8-parameter affine transformation models are extensions of the 7-parameter 3D similarity transformation model that have been successfully applied to LiDAR point cloud registration (Wu et al. 2013), medical image registration (Mondal et al. 2016), and coordinate transformation in geodesy (Awange et al. 2008, Paláncz et al. 2010) . The linear 12-parameter affine transformation model is a universal model of 3D affine transformation model and 3D similarity transformation model. The conversion between transformation models can be realised through various combinations of unknowns which can be adjusted by explicitly imposing different constraints. And then, the optimal parameters can be iteratively obtained based on the least-squares criterion or the total least-squares criterion (Amiri-Simkooei 2018).
Unmanned aerial vehicle inspection of the Placer River Trail Bridge through image-based 3D modelling
Published in Structure and Infrastructure Engineering, 2018
Ali Khaloo, David Lattanzi, Keith Cunningham, Rodney Dell’Andrea, Mark Riley
Throughout this study a value of k = 50 points was assigned in order to achieve a sufficiently large and robust neighbourhood to quantify noise while still reflecting local surface properties. Using Singular Value Decomposition (SVD) (Golub & Reinsch, 1970), the covariance matrix is then decomposed into eigenvalues and eigenvectors. Since C is symmetric and positive semi-definite, all eigenvalues λ are real-valued and the eigenvectors V form an orthogonal frame, corresponding to the principal components of the point set defined by the k-Nearest Neighbours (k-NN) of the 3D point pi. Within this approach, v0 approximates the point’s pi normal, while v2 and v1 span the local tangent plane. The utilised method gives an equivalent solution to the total least squares formalisation of the plane-fitting problem.
Recent Development on Photovoltaic Parameters Estimation: Total Least Squares Approach and Metaheuristic Algorithms
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2022
Oumaima Mesbahi, Mouhaydine Tlemçani, Fernando M. Janeiro, Abdeloawahed Hajjaji, Khalid Kandoussi
To enhance the optimization for photovoltaic parameters estimation, this work suggests an RMSE function that also considers the voltage measurement uncertainties. Figure 3b) shows the I–V characteristic along with the orthogonal distances between the measured data and the estimated curve. These distances form the core of the total least squares (TLS) concept and are calculated by the square root of the mean of the square deviations of both current and voltage. The total least squares cost function is