Florian Bugarin

A speckle texture image generator

We propose a framework for obtaining synthetic speckle-pattern images based on successive transformations of Perlins coherent noise function. In addition we show how a given displacement function can be used to produce deformed images, making this framework suitable for performance analysis of speckle-based displacement/strain measurement techniques, such as Digital Image Correlation, widely used in experimental mechanics.

Minimizing the sum of many rational functions

We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of variables can be relatively large (10 to 100) provided some kind of sparsity is present. We describe a formulation of the rational optimization problem as a generalized moment problem and its hierarchy of convex semidefinite relaxations. Under some conditions we prove that the sequence of optimal values converges to the globally optimal value. We show how public-domain software can be used to model and solve such problems. Finally, we also compare with the epigraph approach and the BARON software.

Rank-Constrained Fundamental Matrix Estimation by Polynomial Global Optimization Versus the Eight-Point Algorithm

The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment. The eight-point algorithm first computes a simple linear least squares solution by minimizing an algebraic cost and then projects the result to the closest rank-deficient matrix. We propose a single-step method that solves both steps of the eight-point algorithm. Using recent results from polynomial global optimization, our method finds the rank-deficient matrix that exactly minimizes the algebraic cost. In this special case, the optimization method is reduced to the resolution of very short sequences of convex linear problems which are computationally efficient and numerically stable. The current gold standard is known to be extremely effective but is nonetheless outperformed by our rank-constrained method for bootstrapping bundle adjustment. This is here demonstrated on simulated and standard real datasets. With our initialization, bundle adjustment consistently finds a better local minimum (achieves a lower reprojection error) and takes less iterations to converge.

CAD-guided inspection of aeronautical mechanical parts using monocular vision

This paper focuses on quality control of mechanical parts in aeronautical context by using a single PTZ camera and the CAD model of the mechanical part. In our approach two attributed graphs are matched using a similarity function. The similarity scores are injected in the edges of a bipartite graph. A best-match-search procedure in bipartite graph guarantees the uniqueness of the match solution. The method achieves excellent performance in tests with synthetic data, including missing elements, displaced elements, size changes, and combination of these cases.

Cooling channel optimization for injection molding

In injection molding process, heat transfer during the cooling step plays an important role. This step has a great influence on the quality of the final parts that are produced, as well as on the molding cycle time. We introduce an optimization procedure in order to locate automatically the cooling channels in 3D injection molds. The temperature distribution is computed using the Boundary Elements Method (BEM) that allows reducing the computation space from 3D to 2D, (avoiding full 3D remeshing). In our study, BEM is used to solve the stationary heat conduction problem. The BEM heat transfer solver is coupled with the non‐linear optimization algorithm SQP (Sequential Quadratic Programming). The SQP algorithm permits to calculate the best set of cooling parameters, for a given cost function. For example, one such cost function involves minimizing the temperature variations at the interface between the mold cavity and the polymer. We present preliminary 3D computational results.

Optimization of structures under buckling constraints using frame elements

ABSTRACT Structural optimization is of increasing interest in a wide variety of application fields. In this article, structural optimization under stress and buckling constraints is investigated. A structure comprised of a set of frame elements is considered. The aim is to obtain the minimal mass structure, by optimizing the number of frame elements and their cross sectional dimensions. A formulation as a mixed-integer nonlinear optimization problem with a tailored objective function is introduced. This cost function is a combination of the structural mass and the sum of the second moments of inertia of each structural element. Moreover, a new algorithm, tailored to the considered problem, is proposed. Numerical results show that the proposed approach provides interesting structural mass savings.

Automated thermal 3D reconstruction based on a robot equipped with uncalibrated infrared stereovision cameras

Abstract In many industrial sectors, Non Destructive Testing (NDT) methods are used for the thermomechanical analysis of parts in assemblies of engines or reactors or for the control of metal forming processes. This article suggests an automated multi-view approach for the thermal 3 D reconstruction required in order to compute 3 D surface temperature models. This approach is based only on infrared cameras mounted on a Cartesian robot. The low resolution of these cameras associated to a lack of texture to infrared images require to use a global approach based first on an uncalibrated rectification and then on the simultaneous execution, in a single step, of the dense 3 D reconstruction and of an extended self-calibration. The uncalibrated rectification is based on an optimization process under constraints which calculates the homographies without prior calculation of the Fundamental Matrix and which minimizes the projective deformations between the initial images and the rectified ones. The extended self-calibration estimates both the parameters of virtual cameras that could provide the rectified images directly, and the parameters of the robot. It is based on two criteria evaluated according to the noise level of the infrared images. This global approach is validated through the reconstruction of a hot object against a reference reconstruction acquired by a 3 D scanner.

Structural Optimization Under Buckling Constraints Using Frame Elements with Anisotropic Cross Sections

Structural optimization is of increasing interest in a wide variety of application fields. In this paper, we focus on structural optimization under stress and buckling constraints. We use frame elements and investigate the impact of considering anisotropic cross sections, i.e. whose dimensions in the principal directions of the cross section are different (e.g. rectangles instead of squares, ellipses instead of circles). This allows us a better tailoring of the cross sections to the applied loading, thus having the potential to lead to lighter structures. We propose a formulation as a mixed-integer nonlinear optimization problem with a tailored objective function and decision variables involving cross sectional dimensions, considering more degrees of freedom than what is generally done. Moreover, a new algorithm tailored to the considered problem is proposed. Numerical results show that the proposed approach provides interesting structural weight savings.

Multiscale FE-Based DIC for Enhanced Measurements and Constitutive Parameter Identification

Since they provide a large amount of information, full-field measurement techniques like Digital Image Correlation (DIC) allow the identification of several material parameters from a single non-homogeneous test. However the level of uncertainty associated with the identified parameters depends on the displacement measurement uncertainties, which are related to the spatial resolution of the measurement. To overcome the well-known compromise between spatial resolution and uncertainty, a multiscale approach to Finite Element DIC (FE-DIC) is proposed by considering additional nearfield images to improve locally the resolution of the measurement. An accurate estimation of the nearfield/farfield transformation is obtained by a dedicated global DIC method to bridge precisely the measurements at both scales. This multiscale FE-DIC measurement is then associated to a multiscale Finite Element Model Updating (FEMU) identification technique. After being validated on synthetic test cases, the method is applied to a tensile test carried out on an open-hole specimen made of glass/epoxy laminate. The four in-plane orthotropic elastic parameters are identified. Results show that the multiscale approach greatly improves the uncertainties of both the measured displacements and the identified material parameters.

Inspection of aeronautical mechanical parts with a pan-tilt-zoom camera: an approach guided by the computer-aided design model

Abstract. We focus on quality control of mechanical parts in aeronautical context using a single pan-tilt-zoom (PTZ) camera and a computer-aided design (CAD) model of the mechanical part. We use the CAD model to create a theoretical image of the element to be checked, which is further matched with the sensed image of the element to be inspected, using a graph theory–based approach. The matching is carried out in two stages. First, the two images are used to create two attributed graphs representing the primitives (ellipses and line segments) in the images. In the second stage, the graphs are matched using a similarity function built from the primitive parameters. The similarity scores of the matching are injected in the edges of a bipartite graph. A best-match-search procedure in the bipartite graph guarantees the uniqueness of the match solution. The method achieves promising performance in tests with synthetic data including missing elements, displaced elements, size changes, and combinations of these cases. The results open good prospects for using the method with realistic data.