Modelling of Orthogonal Craniofacial Profiles

We present a fully-automatic image processing pipeline to build a set of 2D morphable models of three craniofacial profiles from orthogonal viewpoints, side view, front view and top view, using a set of 3D head surface images. Subjects in this dataset wear a close-fitting latex cap to reveal the overall skull shape. Texture-based 3D pose normalization and facial landmarking are applied to extract the profiles from 3D raw scans. Fully-automatic profile annotation, subdivision and registration methods are used to establish dense correspondence among sagittal profiles. The collection of sagittal profiles in dense correspondence are scaled and aligned using Generalised Procrustes Analysis (GPA), before applying principal component analysis to generate a morphable model. Additionally, we propose a new alternative alignment called the Ellipse Centre Nasion (ECN) method. Our model is used in a case study of craniosynostosis intervention outcome evaluation, and the evaluation reveals that the proposed model achieves state-of-the-art results. We make publicly available both the morphable models and the profile dataset used to construct it

An approach to construct a three-dimensional isogeometric model from µ-CT scan data with an application to the bridge of a violin

We present an algorithm to build a ready to use isogeometric model from scan data gained by a µ-CT scan. Based on a three-dimensional multi-patch reference geometry, which includes the major topological features, we fit the outline, then the cross-section and finally the three-dimensional geometry. The key step is to fit the outline, where a non-linear least squares problem is solved with a Gauss-Newton approach presented by Borges and Pastva (2002). We extend this approach by a regularisation and a precise interpolation of selected data points. The resulting NURBS geometry is ready for applying isogeometric analysis tools for efficient numerical simulations. As a particular example we examine the scan data of a violin bridge and present the complete workflow from the µ-CT scan up to the numerical simulation based on isogeometric mortar methods. We illustrate the relevance of the constructed geometry with a vibro-acoustical application

Testing a new analytic model for gravitational lensing probabilities

We study gravitational lensing with a multiple lens plane approach, proposing a simple analytical model for the probability distribution function (PDF) of the dark matter convergence, kappa, for the different lens planes in a given cosmology as a function of redshift and smoothing angle, theta. The model is fixed solely by the variance of kappa, which in turn is fixed by the amplitude of the power spectrum, sigma_8. We test the PDF against a high resolution Tree-Particle-Mesh simulation and find that it is far superior to the Gaussian or the lognormal, especially for small values of theta << 1 arcmin and at large values of kappa relevant to strong lensing. With this model, we predict the probabilities of strong lensing by a single plane or by multiple planes. We find that for theta ~ 10 arcsec, a single plane accounts for almost all (~ 98%) of the strong lensing cases for source redshift unity. However, for a more typical source redshift of 4, about 12% of the strong lensing cases will result from the contribution of a secondary clump of matter along the line of sight, introducing a systematic error in the determination of the surface density of clusters, typically overestimating it by about 2-5%. We also find that matter inhomogenieties introduce a dispersion in the value of the angular diameter distance about its cosmological mean. The probable error relative to the mean increases with redshift to a value of about 8% for z ~ 6 and theta ~ 10 arcsec.Comment: Accepted for publication in ApJ, 13 pages, 12 figures, revised version, references added, section 6 expande

A fully automated three-stage procedure for spatio-temporal leaf segmentation with regard to the B-spline-based phenotyping of cucumber plants

Plant phenotyping deals with the metrological acquisition of plants in order to investigate the impact of environmental factors and a plant’s genotype on its appearance. Phenotyping methods that are used as standard in crop science are often invasive or even destructive. Due to the increase of automation within geodetic measurement systems and with the development of quasi-continuous measurement techniques, geodetic techniques are perfectly suitable for performing automated and non-invasive phenotyping and, hence, are an alternative to standard phenotyping methods. In this contribution, sequentially acquired point clouds of cucumber plants are used to determine the plants’ phenotypes in terms of their leaf areas. The focus of this contribution is on the spatio-temporal segmentation of the acquired point clouds, which automatically groups and tracks those sub point clouds that describe the same leaf. The application on example data sets reveals a successful segmentation of 93% of the leafs. Afterwards, the segmented leaves are approximated by means of B-spline surfaces, which provide the basis for the subsequent determination of the leaf areas. In order to validate the results, the determined leaf areas are compared to results obtained by means of standard methods used in crop science. The investigations reveal consistency of the results with maximal deviations in the determined leaf areas of up to 5

Spline-based medial axis transform representation of binary images

Medial axes are well-known descriptors used for representing, manipulating, and compressing binary images. In this paper, we present a full pipeline for computing a stable and accurate piece-wise B-spline representation of Medial Axis Transforms (MATs) of binary images. A comprehensive evaluation on a benchmark shows that our method, called Spline-based Medial Axis Transform (SMAT), achieves very high compression ratios while keeping quality high. Compared with the regular MAT representation, the SMAT yields a much higher compression ratio at the cost of a slightly lower image quality. We illustrate our approach on a multi-scale SMAT representation, generating super-resolution images, and free-form binary image deformation

Microdrone-Based Indoor Mapping with Graph SLAM

Unmanned aerial vehicles offer a safe and fast approach to the production of three-dimensional spatial data on the surrounding space. In this article, we present a low-cost SLAM-based drone for creating exploration maps of building interiors. The focus is on emergency response mapping in inaccessible or potentially dangerous places. For this purpose, we used a quadcopter microdrone equipped with six laser rangefinders (1D scanners) and an optical sensor for mapping and positioning. The employed SLAM is designed to map indoor spaces with planar structures through graph optimization. It performs loop-closure detection and correction to recognize previously visited places, and to correct the accumulated drift over time. The proposed methodology was validated for several indoor environments. We investigated the performance of our drone against a multilayer LiDAR-carrying macrodrone, a vision-aided navigation helmet, and ground truth obtained with a terrestrial laser scanner. The experimental results indicate that our SLAM system is capable of creating quality exploration maps of small indoor spaces, and handling the loop-closure problem. The accumulated drift without loop closure was on average 1.1% (0.35 m) over a 31-m-long acquisition trajectory. Moreover, the comparison results demonstrated that our flying microdrone provided a comparable performance to the multilayer LiDAR-based macrodrone, given the low deviation between the point clouds built by both drones. Approximately 85 % of the cloud-to-cloud distances were less than 10 cm

Continuous fusion of motion data using an axis-angle rotation representation with uniform B-spline

The fusion of motion data is key in the fields of robotic and automated driving. Most existing approaches are filter-based or pose-graph-based. By using filter-based approaches, parameters should be set very carefully and the motion data can usually only be fused in a time forward direction. Pose-graph-based approaches can fuse data in time forward and backward directions. However, pre-integration is needed by applying measurements from inertial measurement units. Additionally, both approaches only provide discrete fusion results. In this work, we address this problem and present a uniform B-spline-based continuous fusion approach, which can fuse motion measurements from an inertial measurement unit and pose data from other localization systems robustly, accurately and efficiently. In our continuous fusion approach, an axis-angle is applied as our rotation representation method and uniform B-spline as the back-end optimization base. Evaluation results performed on the real world data show that our approach provides accurate, robust and continuous fusion results, which again supports our continuous fusion concept

Feasible Form Parameter Design of Complex Ship Hull Form Geometry

This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design. In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry