Properties of Gauss digitized sets and digital surface integration

International audienceThis paper presents new topological and geometrical properties of Gauss digitizations of Euclidean shapes, most of them holding in arbitrary dimension $d$. We focus on $r$-regular shapes sampled by Gauss digitization at gridstep $h$. The digitized boundary is shown to be close to the Euclidean boundary in the Hausdorff sense, the minimum distance $\frac{\sqrt{d}}{2}h$ being achieved by the projection map $\xi$ induced by the Euclidean distance. Although it is known that Gauss digitized boundaries may not be manifold when $d \ge 3$, we show that non-manifoldness may only occur in places where the normal vector is almost aligned with some digitization axis, and the limit angle decreases with $h$. We then have a closer look at the projection of the digitized boundary onto the continuous boundary by $\xi$. We show that the size of its non-injective part tends to zero with $h$. This leads us to study the classical digital surface integration scheme, which allocates a measure to each surface element that is proportional to the cosine of the angle between an estimated normal vector and the trivial surface element normal vector. We show that digital integration is convergent whenever the normal estimator is multigrid convergent, and we explicit the convergence speed. Since convergent estimators are now available in the litterature, digital integration provides a convergent measure for digitized objects

Continuous Modeling of 3D Building Rooftops From Airborne LIDAR and Imagery

In recent years, a number of mega-cities have provided 3D photorealistic virtual models to support the decisions making process for maintaining the cities' infrastructure and environment more effectively. 3D virtual city models are static snap-shots of the environment and represent the status quo at the time of their data acquisition. However, cities are dynamic system that continuously change over time. Accordingly, their virtual representation need to be regularly updated in a timely manner to allow for accurate analysis and simulated results that decisions are based upon. The concept of "continuous city modeling" is to progressively reconstruct city models by accommodating their changes recognized in spatio-temporal domain, while preserving unchanged structures. However, developing a universal intelligent machine enabling continuous modeling still remains a challenging task. Therefore, this thesis proposes a novel research framework for continuously reconstructing 3D building rooftops using multi-sensor data. For achieving this goal, we first proposes a 3D building rooftop modeling method using airborne LiDAR data. The main focus is on the implementation of an implicit regularization method which impose a data-driven building regularity to noisy boundaries of roof planes for reconstructing 3D building rooftop models. The implicit regularization process is implemented in the framework of Minimum Description Length (MDL) combined with Hypothesize and Test (HAT). Secondly, we propose a context-based geometric hashing method to align newly acquired image data with existing building models. The novelty is the use of context features to achieve robust and accurate matching results. Thirdly, the existing building models are refined by newly proposed sequential fusion method. The main advantage of the proposed method is its ability to progressively refine modeling errors frequently observed in LiDAR-driven building models. The refinement process is conducted in the framework of MDL combined with HAT. Markov Chain Monte Carlo (MDMC) coupled with Simulated Annealing (SA) is employed to perform a global optimization. The results demonstrates that the proposed continuous rooftop modeling methods show a promising aspects to support various critical decisions by not only reconstructing 3D rooftop models accurately, but also by updating the models using multi-sensor data

Output-Adaptive Tetrahedral Cut-Cell Validation for Sonic Boom Prediction

A cut-cell approach to Computational Fluid Dynamics (CFD) that utilizes the median dual of a tetrahedral background grid is described. The discrete adjoint is also calculated, which permits adaptation based on improving the calculation of a specified output (off-body pressure signature) in supersonic inviscid flow. These predicted signatures are compared to wind tunnel measurements on and off the configuration centerline 10 body lengths below the model to validate the method for sonic boom prediction. Accurate mid-field sonic boom pressure signatures are calculated with the Euler equations without the use of hybrid grid or signature propagation methods. Highly-refined, shock-aligned anisotropic grids were produced by this method from coarse isotropic grids created without prior knowledge of shock locations. A heuristic reconstruction limiter provided stable flow and adjoint solution schemes while producing similar signatures to Barth-Jespersen and Venkatakrishnan limiters. The use of cut-cells with an output-based adaptive scheme completely automated this accurate prediction capability after a triangular mesh is generated for the cut surface. This automation drastically reduces the manual intervention required by existing methods

Statistical distributions in the folding of elastic structures

The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that leads to complex fold patterns. By studying the case of a rod confined isotropically into a disk, we show that the emergence of the complexity is associated with a well defined underlying statistical measure that determines the energy distribution of sub-elements,``branches'', of the rod. This result suggests that branches act as the ``microscopic'' degrees of freedom laying the foundations for a statistical mechanical theory of this athermal and amorphous system

Prostate Tumor Volume Measurement on Digital Histopathology and Magnetic Resonance Imaging

An accurate assessment of prostate tumour burden supports appropriate treatment selection, ranging from active surveillance through focal therapy, to radical whole-prostate therapies. For selected patients, knowledge of the three-dimensional locations and sizes of prostate tumours on pre-procedural imaging supports planning of effective focal therapies that preferentially target tumours, while sparing surrounding healthy tissue. In the post-prostatectomy context, pathologic measurement of tumour burden in the surgical specimen may be an independent prognostic factor determining the need for potentially life-saving adjuvant therapy. An accurate and repeatable method for tumour volume assessment based on histology sections taken from the surgical specimen would be supportive both to the clinical workflow in the post-prostatectomy setting and to imaging validation studies correlating tumour burden measurements on pre-prostatectomy imaging with reference standard histologic tumour volume measurements. Digital histopathology imaging is enabling a transition to a more objective quantification of some surgical pathology assessments, such as tumour volume, that are currently visually estimated by pathologists and subject to inter-observer variability. Histologic tumour volume measurement is challenged by the traditional 3–5 mm sparse spacing of images acquired from sections of radical prostatectomy specimens. Tumour volume estimates may benefit from a well-motivated approach to inter-slide tumour boundary interpolation that crosses these large gaps in a smooth fashion. This thesis describes a new level set-based shape interpolation method that reconstructs smooth 3D shapes based on arbitrary 2D tumour contours on digital histology slides. We measured the accuracy of this approach and used it as a reference standard against which to compare previous approaches in the literature that are simpler to implement in a clinical workflow, with the aim of determining a method for histologic tumour volume estimation that is both accurate and amenable to widespread implementation. We also measured the effect of decreasing inter-slide spacing on the repeatability of histologic tumour volume estimation. Furthermore, we used this histologic reference standard for tumour volume to measure the accuracy, inter-observer variability, and inter-sequence variability of prostate tumour volume estimation based on radiologists’ contouring of multi-parametric magnetic resonance imaging (MPMRI). Our key findings were that (1) simple approaches to histologic tumour volume estimation that are based on 2- or 3-dimensional linear tumour measurements are more accurate than those based on 1-dimensional measurements; (2) although tumour shapes produced by smooth through-slide interpolation are qualitatively substantially different from those obtained from a planimetric approach normally used as a reference standard for histologic tumour volume, the volumes obtained were similar; (3) decreasing inter-slide spacing increases repeatability of histologic tumour volume estimates, and this repeatability decreases rapidly for inter-slide spacing values greater than 5 mm; (4) on MPMRI, observers consistently overestimated tumour volume as compared to the histologic reference standard; and (5) inter-sequence variability in MPMRI-based tumour volume estimation exceeded inter-observer variability

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Feature-based hybrid inspection planning for complex mechanical parts

Globalization and emerging new powers in the manufacturing world are among many challenges, major manufacturing enterprises are facing. This resulted in increased alternatives to satisfy customers\u27 growing needs regarding products\u27 aesthetic and functional requirements. Complexity of part design and engineering specifications to satisfy such needs often require a better use of advanced and more accurate tools to achieve good quality. Inspection is a crucial manufacturing function that should be further improved to cope with such challenges. Intelligent planning for inspection of parts with complex geometric shapes and free form surfaces using contact or non-contact devices is still a major challenge. Research in segmentation and localization techniques should also enable inspection systems to utilize modern measurement technologies capable of collecting huge number of measured points. Advanced digitization tools can be classified as contact or non-contact sensors. The purpose of this thesis is to develop a hybrid inspection planning system that benefits from the advantages of both techniques. Moreover, the minimization of deviation of measured part from the original CAD model is not the only characteristic that should be considered when implementing the localization process in order to accept or reject the part; geometric tolerances must also be considered. A segmentation technique that deals directly with the individual points is a necessary step in the developed inspection system, where the output is the actual measured points, not a tessellated model as commonly implemented by current segmentation tools. The contribution of this work is three folds. First, a knowledge-based system was developed for selecting the most suitable sensor using an inspection-specific features taxonomy in form of a 3D Matrix where each cell includes the corresponding knowledge rules and generate inspection tasks. A Travel Salesperson Problem (TSP) has been applied for sequencing these hybrid inspection tasks. A novel region-based segmentation algorithm was developed which deals directly with the measured point cloud and generates sub-point clouds, each of which represents a feature to be inspected and includes the original measured points. Finally, a new tolerance-based localization algorithm was developed to verify the functional requirements and was applied and tested using form tolerance specifications. This research enhances the existing inspection planning systems for complex mechanical parts with a hybrid inspection planning model. The main benefits of the developed segmentation and tolerance-based localization algorithms are the improvement of inspection decisions in order not to reject good parts that would have otherwise been rejected due to misleading results from currently available localization techniques. The better and more accurate inspection decisions achieved will lead to less scrap, which, in turn, will reduce the product cost and improve the company potential in the market

Development of a Fluoroscopic Radiostereometric Analysis System With an Application to Glenohumeral Joint Kinematics

Ideally, joint kinematics should be measured with high accuracy, void of skin motion artefact, in three dimensions, and under dynamic conditions. Radiostereometric analysis (RSA) has the potential to fulfill all of these requirements. The objectives of this thesis were (1) to implement and validate a fluoroscopy-based RSA system, (2) to determine the effect of varying the calibration frame, (3) to correct image distortion, (4) to investigate errors in coordinate system creation for glenohumeral (shoulder) joint kinematics, (5) to introduce a new coordinate system definition for the scapula with limited radiation exposure, and (6) to use RSA to examine glenohumeral joint motions in- vivo. An RSA system consisting of two portable C-arm fluoroscopy units and two personal computers was assembled. Calibration was performed using a custom-made calibration frame. Images were digitized and RSA reconstruction was performed using custom-written software. Images taken using fluoroscopy under ideal conditions can produce reconstructions that are as accurate as those taken with digital radiography, with standard errors of measurement of 43pm and 0.23° and 36pm and 0.12°, respectively. RSA is more accurate than optical tracking for rigid body motion. The fluoroscopes may be positioned at angles less than 135° without affecting the accuracy of reconstruction. A global polynomial approach to distortion correction is appropriate for use with RSA; however, the polynomial degree must be determined for each system with an independent accuracy measure. m An alternative scapular coordinate system was introduced to decrease the required radiation exposure for coordinate system creation by approximately half. The kinematic angles obtained using the alternative coordinate system were different from those obtained using the International Society of Biomechanics standard; however, the differences are not clinically significant. As a first clinical application, glenohumeral joint translation was examined. The preliminary data suggests that humeral head position does not differ in active and static joint positioning. Fluoroscopy allows subjects to be examined while in motion and should enable substantial improvements to the study of even subtle in-vivo kinematics. It is likely that the RSA system will lead to an increased understanding of the effects of disease progression, surgical techniques and rehabilitation protocols on joint motion

Range images

This article gives an overview of range‐imaging techniques with an aim to let the reader better understand how the difficult issue, such as the registration of overlapping range images, can be approached and solved. It firstly introduces the characteristics of range images and highlights examples of 3D image visualizations, associated technical issues, applications, and the differences of range imaging with respect to the traditional digital broadband imaging. Subsequently, one of the most popular feature extraction and matching methods, the signature of histograms of orientations (SHOT) method, is then outlined. However, the “matched” points generated by SHOT usually generate high proportion of false positives due to various factors such as imaging noise, lack of features, and cluttered backgrounds. Thus, the article discusses more about image‐matching issues, particularly to emphasize how the widely employed range image alignment technique, the random sample consensus (RANSAC) method, is compared with a simple, yet effective, technique based on normalized error penalization (NEP). This simple NEP method utilizes a strategy to penalize point matches whose errors are far away from the majority. The capability of the method for the evaluation of point matches between overlapping range images is illustrated by experiments using real range image data sets. Interestingly enough, these range images appear to be easier to register than expected. Finally, some conclusions have been drawn and further readings for other fundamental techniques and concepts have been suggested