Surface Reconstruction from Multiple Views using Rational B-Splines

A method for reconstructing 3D rational B-spline surfaces from multiple views is proposed. The method takes advantage of the projective invariance properties of rational B-splines. Given feature correspondences in multiple views, the 3D surface is reconstructed via a four step framework. First, corresponding features in each view are given an initial surface parameter value (s; t), and a 2D B-spline is fitted in each view. After this initialization, an iterative minimization procedure alternates between updating the 2D B-spline control points and re-estimating each feature's (s; t). Next, a non-linear minimization method is used to upgrade the 2D B-splines to 2D rational B-splines, and obtain a better fit. Finally, a factorization method is used to reconstruct the 3D B-spline surface given 2D B-splines in each view. This surface recovery method can be applied in both the perspective and orthographic case. The orthographic case allows the use of additional constraints in the recovery. Experiments with real and synthetic imagery demonstrate the efficacy of the approach for the orthographic case.

Surface Reconstruction from Multiple Views using Rational B-Splines and Knot Insertion

A method for reconstruction of 3D rational B-spline surfaces from multiple views is proposed. Given corresponding features in multiple views, though not necessarily visible in all views, the surface is reconstructed. First 2D B-spline patches are fitted to each view. The 3D B-splines and projection matricies can then be extracted from the 2D B-splines using factorization methods. The surface fit is then further refined via an iterative procedure. Finally, a hierarchal fitting scheme is proposed to allow modeling of complex surfaces by means of knot insertion. Experiments with real imagery demonstrate the efficacy of the approach.

B-splines neural network assisted PID autotuning

This papers describes an extantion of previous works on the subject of neural network proportional, integral and derivative (PID) autotuning. Basically, neural networks are employed to supply the three PID parameters, according to the integral of time multiplied by the absolute error (ITAE) criterion, to a standard PID controller.

B-splines neural networks assisted PID autotuning

This paper describes previous works (1), (2), on neural network pid autotuning. Basically, neural networks are employed to supply PID parameters, according to the ITAE criterion, to a standard PID controller.

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Otimização de forma aplicando B-splines sob critério integral de tensões

This work proposes a computational methodology to solve problems of optimization in structural design. The application develops, implements and integrates methods for structural analysis, geometric modeling, design sensitivity analysis and optimization. So, the optimum design problem is particularized for plane stress case, with the objective to minimize the structural mass subject to a stress criterion. Notice that, these constraints must be evaluated at a series of discrete points, whose distribution should be dense enough in order to minimize the chance of any significant constraint violation between specified points. Therefore, the local stress constraints are transformed into a global stress measure reducing the computational cost in deriving the optimal shape design. The problem is approximated by Finite Element Method using Lagrangian triangular elements with six nodes, and use a automatic mesh generation with a mesh quality criterion of geometric element. The geometric modeling, i.e., the contour is defined by parametric curves of type B-splines, these curves hold suitable characteristics to implement the Shape Optimization Method, that uses the key points like design variables to determine the solution of minimum problem. A reliable tool for design sensitivity analysis is a prerequisite for performing interactive structural design, synthesis and optimization. General expressions for design sensitivity analysis are derived with respect to key points of B-splines. The method of design sensitivity analysis used is the adjoin approach and the analytical method. The formulation of the optimization problem applies the Augmented Lagrangian Method, which convert an optimization problem constrained problem in an unconstrained. The solution of the Augmented Lagrangian function is achieved by determining the analysis of sensitivity. Therefore, the optimization problem reduces to the solution of a sequence of problems with lateral limits constraints, which is solved by the Memoryless Quasi-Newton Method It is demonstrated by several examples that this new approach of analytical design sensitivity analysis of integrated shape design optimization with a global stress criterion purpose is computationally efficient

Modelagem das trajetórias médias do peso vivo e do rendimento de carcaça de tilápias do Nilo (Oreochromis niloticus) por meio de funções B-spline

Employing the method of least squares and quadratic B-spline polynomials, different statistical models were tested to identify the most appropriate to model the mean trajectories of live weight and carcass yield of Nile tilapia (Oreochromis niloticus). Data of live weight (8,758) and carcass yield (2,042) of tilapias with ages between 106 and 245 days were obtained from 72 families derived from 36 males and 72 females. The sex and tank variables were considered as classificatory and the coefficients of quadratic polynomials B-spline of two to five intervals of the same size were used as covariables. According to most fit criteria used, the models with quadratic B-spline polynomial with five intervals of the same size presented the best adjustments. The increase in number of intervals of B-spline polynomial improved the fit of the polynomials to the data. The inclusion of classificatory effects from sex, tank, the interaction of these effects and the quadratic polynomial B-spline nested in this interaction indicated that, over time, each sex, grown in different tank, presented different mean trajectory, necessitating the inclusion of nesting time in the interaction sex x tank in order to avoid the under or overestimation of breeding values of the selection candidates in breeding programs of this species.

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

The objective of this paper is to model variations in test-day milk yields of first lactations of Holstein cows by RR using B-spline functions and Bayesian inference in order to fit adequate and parsimonious models for the estimation of genetic parameters. They used 152,145 test day milk yield records from 7317 first lactations of Holstein cows. The model established in this study was additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. Authors modeled the average lactation curve of the population with a fourth-order orthogonal Legendre polynomial. They concluded that a cubic B-spline with seven random regression coefficients for both the additive genetic and permanent environment effects was to be the best according to residual mean square and residual variance estimates. Moreover they urged a lower order model (quadratic B-spline with seven random regression coefficients for both random effects) could be adopted because it yielded practically the same genetic parameter estimates with parsimony. (C) 2012 Elsevier B.V. All rights reserved.

Estudo genético quantitativo do fluxo lácteo em bovinos da raça Holandesa

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estimação de parâmetros genéticos para características de crescimento em bovinos da raça Canchim com modelos de dimensão finita e infinita

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Smooth Finite Element Method Based on Reproducing Kernel DMS-Splines

The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper

B-Spline potential function for maximum a-posteriori image reconstruction in fluorescence microscopy

An iterative image reconstruction technique employing B-Spline potential function in a Bayesian framework is proposed for fluorescence microscopy images. B-splines are piecewise polynomials with smooth transition, compact support and are the shortest polynomial splines. Incorporation of the B-spline potential function in the maximum-a-posteriori reconstruction technique resulted in improved contrast, enhanced resolution and substantial background reduction. The proposed technique is validated on simulated data as well as on the images acquired from fluorescence microscopes (widefield, confocal laser scanning fluorescence and super-resolution 4Pi microscopy). A comparative study of the proposed technique with the state-of-art maximum likelihood (ML) and maximum-a-posteriori (MAP) with quadratic potential function shows its superiority over the others. B-Spline MAP technique can find applications in several imaging modalities of fluorescence microscopy like selective plane illumination microscopy, localization microscopy and STED. (C) 2015 Author(s).