Approximate Fitting of a Circular Arc When Two Points Are Known

The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of circular arcs fitting requires an efficient way of fitting circular arcs with complexity O(1). The elegant solution to this task based on an eigenvector problem for a square nonsymmetrical matrix is described in [1]. For the compression algorithm described in [2], it is necessary to solve this task when two points on the arc are known. This paper describes a different approach to efficiently fitting the arcs and solves the task when one or two points are known.Comment: 15 pages, 4 figures, extended abstract published at the conferenc

Hybrid model for vascular tree structures

This paper proposes a new representation scheme of the cerebral blood vessels. This model provides information on the semantics of the vascular structure: the topological relationships between vessels and the labeling of vascular accidents such as aneurysms and stenoses. In addition, the model keeps information of the inner surface geometry as well as of the vascular map volume properties, i.e. the tissue density, the blood flow velocity and the vessel wall elasticity. The model can be constructed automatically in a pre-process from a set of segmented MRA images. Its memory requirements are optimized on the basis of the sparseness of the vascular structure. It allows fast queries and efficient traversals and navigations. The visualizations of the vessel surface can be performed at different levels of detail. The direct rendering of the volume is fast because the model provides a natural way to skip over empty data. The paper analyzes the memory requirements of the model along with the costs of the most important operations on it.Postprint (published version

Implicit geological modelling : a new approach to 3D volumetric national-scale geological models

This report provides information on implicit geological modelling and a possible application in the construction of national-scale (in the UK context) volumetric geological models. The stratigraphy of the UK is reviewed in the context of unconformity-bound stratigraphic sequences and how these can be applied in the modelling process. A range of input datasets are outlined with discussion on how these can be used and where gaps exist in available information. Model outputs are discussed highlighting the new opportunities offered by 3D stratigraphic grids. Some of the advantages and disadvantages of implicit modelling are discussed

Numerical methods for polyline‐to‐point‐cloud registration with applications to patient‐specific stent reconstruction

We present novel numerical methods for polyline‐to‐point‐cloud registration and their application to patient‐specific modeling of deployed coronary artery stents from image data. Patient‐specific coronary stent reconstruction is an important challenge in computational hemodynamics and relevant to the design and improvement of the prostheses. It is an invaluable tool in large‐scale clinical trials that computationally investigate the effect of new generations of stents on hemodynamics and eventually tissue remodeling. Given a point cloud of strut positions, which can be extracted from images, our stent reconstruction method aims at finding a geometrical transformation that aligns a model of the undeployed stent to the point cloud. Mathematically, we describe the undeployed stent as a polyline, which is a piecewise linear object defined by its vertices and edges. We formulate the nonlinear registration as an optimization problem whose objective function consists of a similarity measure, quantifying the distance between the polyline and the point cloud, and a regularization functional, penalizing undesired transformations. Using projections of points onto the polyline structure, we derive novel distance measures. Our formulation supports most commonly used transformation models including very flexible nonlinear deformations. We also propose 2 regularization approaches ensuring the smoothness of the estimated nonlinear transformation. We demonstrate the potential of our methods using an academic 2D example and a real‐life 3D bioabsorbable stent reconstruction problem. Our results show that the registration problem can be solved to sufficient accuracy within seconds using only a few number of Gauss‐Newton iterations.We present novel numerical methods for nonlinear polyline‐to‐point‐cloud registration and their application to patient‐specific modeling of deployed coronary artery stents from image data. We design a general and mathematically sound framework that includes novel (almost everywhere) differentiable distance measures and 2 new regularization approaches to overcome the ill‐posedness and enable robust registration in the presence of outliers. We demonstrate that 3D registration problem arising in stent reconstruction can be solved within seconds using only a small number of Gauss‐Newton iterations.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142552/1/cnm2934.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142552/2/cnm2934_am.pd

Slope Stability Monitoring Using Remote Sensing Techniques

During the past six years the Arkansas State Highway and Transportation Department (AHTD) has spent over nine million dollars repairing slope failures that have occurred in the state of Arkansas. Specifically, higher than average precipitation in 2004 and 2008 led to large quantities of slides, all of which were repaired. Two highways, within the state of Arkansas, with known historical movements along or across the highways are being monitored using traditional surveying techniques and advanced remote sensing techniques. These slides, both of which are located in fill slopes. One a 500-foot long slide located north of Chester, Arkansas, within the median of Interstate I-540. The other site is a 1200-foot long slide located east of Malvern, Arkansas, cutting across all four-lanes of Interstate I-30, have visible evidence of movement (tension cracks, traverse cracks, head scarps, flank displacement, etc.) A ground portable RADAR interferometer (GPRI-II) constructed by Gamma Remote Sensing is the first device in the United States being used to remotely monitor slopes. Surveying monuments (2.5-inch diameter aluminum monuments placed on 24-inch long, ½-inch diameter rebar encased in 6-inches of concrete) were installed inside and outside of the sliding mass at each site (29 monuments at the calibration site in Chester, Arkansas site and 54 monuments at the validation site in Malvern, Arkansas), and are being monitored using traditional surveying techniques (using a Nikon DTM-520 total station) to identify the movement of each monument as detected from two observation points. The GPRI-II and a Leica C-10 LIDAR are also being used to identify the movement of the slopes. Inclinometers have been also installed at the validation site near Malvern, Arkansas to compare the displacements obtained by remote sensing techniques with standard borehole slope monitoring methods. The results of the movements observed using in-situ instrumentation, total station, RADAR, and LIDAR are discussed. A full geotechnical subsurface investigation was perform at the validation site in Malvern, Arkansas during the summer of 2011. The drilling and sampling investigation provided the necessary soil and rock samples for laboratory testing. The results from the laboratory tests permitted the displacement rates to be inspected in the light of the shear strength of the soil strata and the depth to the shear failure plane. Since December 2010, site visits have been conducted every two weeks for the Chester site and every month for the Malvern site. During each visit total station, RADAR, and LIDAR observations were conducted

3D-modelling of microfracture networks associated with faulting in the crystalline Wiborg rapakivi granite

The main purpose of this MSc thesis is to study the 3D geometry of secondary microfracture associated with faults by using grinding the tomography method. Information on the 3D geometry of microfractures can be used, for example, for predicting the hydraulic conductivity of rocks and for more accurate interpretation of generation mechanisms and kinematics of faults. A 3D model of a microfracture network of one oriented rock sample was constructed from data collected with grinding tomography methods. The interpretations made on the 3D model were compared with the field measurements and GIS fracture trace interpretations based on 2D orthophotography data collected with a drone and a digital SLR camera. The second purpose of this thesis was to compare these two scales of 2D fracture trace datasets and find out how the change of observation scale from meters to centimeters affects the 2D topology and orientation distribution of the fracture networks. The study area is located on the Island of Orrengrund, Loviisa, SW Finland. The fault studied in the thesis is a sinistral strike-slip fault with a vertical dip, and a N-S trend. In the grinding tomography method used in this thesis, a cylindrical 50*50*50 mm sample of rock is glued on a glass plate and grinded in slices with a 3D-grinder, so that after each slice the machine takes an image of the surface of the sample. When the images are combined by knowing the vertical position of each image, interpretations can be made on the observed fractures, and a 3D model can be constructed. In this thesis, a new GRN16 3D grinder of the University of Turku geology section was used. Grinding tomography images of the oriented rock sample were georeferenced on the orthophotos with QGIS software, so that the orientation data obtained from the 3D model of microfracture network was comparable with 2D fracture trace data and field measurements. The results of the thesis showed that the 3D model of microfracture network constructed using grinding tomography has almost perfect correlation with the orientation distribution and crosscut relationships of field measurements. The study also revealed that the new 3D grinder of the University of Turku geology Section solves numerous problems regarding the use of the grinding tomography method in geosciences. In addition, topological differences were observed between the two different-scale 2D fracture trace datasets, reflecting that the topological properties of the fault’s fracture systems could be scale-dependent

WOMD-LiDAR: Raw Sensor Dataset Benchmark for Motion Forecasting

Widely adopted motion forecasting datasets substitute the observed sensory inputs with higher-level abstractions such as 3D boxes and polylines. These sparse shapes are inferred through annotating the original scenes with perception systems' predictions. Such intermediate representations tie the quality of the motion forecasting models to the performance of computer vision models. Moreover, the human-designed explicit interfaces between perception and motion forecasting typically pass only a subset of the semantic information present in the original sensory input. To study the effect of these modular approaches, design new paradigms that mitigate these limitations, and accelerate the development of end-to-end motion forecasting models, we augment the Waymo Open Motion Dataset (WOMD) with large-scale, high-quality, diverse LiDAR data for the motion forecasting task. The new augmented dataset WOMD-LiDAR consists of over 100,000 scenes that each spans 20 seconds, consisting of well-synchronized and calibrated high quality LiDAR point clouds captured across a range of urban and suburban geographies (https://waymo.com/open/data/motion/). Compared to Waymo Open Dataset (WOD), WOMD-LiDAR dataset contains 100x more scenes. Furthermore, we integrate the LiDAR data into the motion forecasting model training and provide a strong baseline. Experiments show that the LiDAR data brings improvement in the motion forecasting task. We hope that WOMD-LiDAR will provide new opportunities for boosting end-to-end motion forecasting models.Comment: Dataset website: https://waymo.com/open/data/motion