Simultaneous drone localisation and wind turbine model fitting during autonomous surface inspection

We present a method for simultaneous localisation and wind turbine model fitting for a drone performing an automated surface inspection. We use a skeletal parameterisation of the turbine that can be easily integrated into a non-linear least squares optimiser, combined with a pose graph representation of the drone's 3-D trajectory, allowing us to optimise both sets of parameters simultaneously. Given images from an onboard camera, we use a CNN to infer projections of the skeletal model, enabling correspondence constraints to be established through a cost function. This is then coupled with GPS/IMU measurements taken at key frames in the graph to allow successive optimisation as the drone navigates around the turbine. We present two variants of the cost function, one based on traditional 2D point correspondences and the other on direct image interpolation within the inferred projections. Results from experiments on simulated and real-world data show that simultaneous optimisation provides improvements to localisation over only optimising the pose and that combined use of both cost functions proves most effective.Comment: Submitted to IROS201

3-D data handling and registration of multiple modality medical images

The many different clinical imaging modalities used in diagnosis and therapy deliver two different types of information: morphological and functional. Clinical interpretation can be assisted and enhanced by combining such information (e.g. superimposition or fusion). The handling of such data needs to be performed in 3-D. Various methods for registration developed by other authors are reviewed and compared. Many of these are based on registering external reference markers, and are cumbersome and present significant problems to both patients and operators. Internal markers have also been used, but these may be very difficult to identify. Alternatively, methods based on the external surface of an object have been developed which eliminate some of the problems associated with the other methods. Thus the methods which have been extended, developed, and described here, are based primarily on the fitting of surfaces, as determined from images obtained from the different modalities to be registered. Annex problems to that of the surface fitting are those of surface detection and display. Some segmentation and surface reconstruction algorithms have been developed to identify the surface to be registered. Surface and volume rendering algorithms have also been implemented to facilitate the display of clinical results. An iterative surface fitting algorithm has been developed based on the minimization of a least squares distance (LSD) function, using the Powell method and alternative minimization algorithms. These algorithms and the qualities of fit so obtained were intercompared. Some modifications were developed to enhance the speed of convergence, to improve the accuracy, and to enhance the display of results during the process of fitting. A common problem with all such methods was found to be the choice of the starting point (the initial transformation parameters) and the avoidance of local minima which often require manual operator intervention. The algorithm was modified to apply a global minimization by using a cumulative distance error in a sequentially terminated process in order to speed up the time of evaluating of each search location. An extension of the algorithm into multi-resolution (scale) space was also implemented. An initial global search is performed at coarse resolution for the 3-D surfaces of both modalities where an appropriate threshold is defined to reject likely mismatch transformations by testing of only a limited subset of surface points. This process is used to define the set of points in the transformation space to be used for the next level of resolution, again with appropriately chosen threshold levels, and continued down to the finest resolution level. All these processes were evaluated using sets of well defined image models. The assessment of this algorithm for 3-D surface registration of data from (3-D) MRI with MRI, MRI with PET, MRI with SPECT, and MRI with CT data is presented, and clinical examples are illustrated and assessed. In the current work, the data from multi-modality imaging of two different types phantom (e.g. Hoffman brain phantom, Jaszczak phantom), thirty routinely imaged patients and volunteer subjects, and ten patients with setting external markers on their head were used to assess and verify 3-D registration. The accuracy of the sequential multi-resolution method obtained by the distance values of 4-10 selected reference points on each data set gave an accuracy of 1.44±0.42 mm for MR-MR, 1.82±0.65 for MR-CT, 2.38±0.88 for MR-PET, and 3.17±1.12 for MR-SPECT registration. The cost of this process was determined to be of the order of 200 seconds (on a Micro-VAX II), although this is highly dependent on some adjustable parameters of the process (e.g. threshold and the size of the geometrical transformation space) by which the accuracy is aimed

Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed

Polynomial Meshes: Computation and Approximation

We present the software package WAM, written in Matlab, that generates Weakly Admissible Meshes and Discrete Extremal Sets of Fekete and Leja type, for 2d and 3d polynomial least squares and interpolation on compact sets with various geometries. Possible applications range from data fitting to high-order methods for PDEs

Interpolating point spread function anisotropy

Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). We also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics $\sigma_{sys}^2$ better than the $1\times10^{-7}$ upper bound expected by future space-based surveys, with the local interpolators performing better than the global ones

Parameter Estimation and Uncertainty Quantication for an Epidemic Model

We examine estimation of the parameters of Susceptible-Infective-Recovered (SIR) models in the context of least squares. We review the use of asymptotic statistical theory and sensitivity analysis to obtain measures of uncertainty for estimates of the model parameters and the basic reproductive number (R0 )—an epidemiologically significant parameter grouping. We find that estimates of different parameters, such as the transmission parameter and recovery rate, are correlated, with the magnitude and sign of this correlation depending on the value of R0. Situations are highlighted in which this correlation allows R0 to be estimated with greater ease than its constituent parameters. Implications of correlation for parameter identifiability are discussed. Uncertainty estimates and sensitivity analysis are used to investigate how the frequency at which data is sampled affects the estimation process and how the accuracy and uncertainty of estimates improves as data is collected over the course of an outbreak. We assess the informativeness of individual data points in a given time series to determine when more frequent sampling (if possible) would prove to be most beneficial to the estimation process. This technique can be used to design data sampling schemes in more general contexts

A new method for aspherical surface fitting with large-volume datasets

In the framework of form characterization of aspherical surfaces, European National Metrology Institutes (NMIs) have been developing ultra-high precision machines having the ability to measure aspherical lenses with an uncertainty of few tens of nanometers. The fitting of the acquired aspherical datasets onto their corresponding theoretical model should be achieved at the same level of precision. In this article, three fitting algorithms are investigated: the Limited memory-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), the Levenberg–Marquardt (LM) and one variant of the Iterative Closest Point (ICP). They are assessed based on their capacities to converge relatively fast to achieve a nanometric level of accuracy, to manage a large volume of data and to be robust to the position of the data with respect to the model. Nev-ertheless, the algorithms are first evaluated on simulated datasets and their performances are studied. The comparison of these algorithms is extended on measured datasets of an aspherical lens. The results validate the newly used method for the fitting of aspherical surfaces and reveal that it is well adapted, faster and less complex than the LM or ICP methods.EMR