Dissertations / Theses on the topic 'Geometric fitting'

This thesis concerns detection and recognition of ground object using data from laser radar systems. Typical ground objects are vehicles and land mines. For these objects, the orientation and articulation are unknown. The objects are placed in natural or urban areas where the background is unstructured and complex. The performance of laser radar systems is analyzed, to achieve models of the uncertainties in laser radar data. A ground object recognition method is presented. It handles general, noisy 3D point cloud data. The approach is based on the fact that man-made objects on a large scale can be considered be of rectangular shape or can be decomposed to a set of rectangles. Several approaches to rectangle fitting are presented and evaluated in Monte Carlo simulations. There are error-in-variables present and thus, geometric fitting is used. The objects can have parts that are subject to articulation. A modular least squares method with outlier rejection, that can handle articulated objects, is proposed. This method falls within the iterative closest point framework. Recognition when several similar models are available is discussed. The recognition method is applied in a query-based multi-sensor system. The system covers the process from sensor data to the user interface, i.e., from low level image processing to high level situation analysis. In object detection and recognition based on laser radar data, the range value’s accuracy is important. A general direct-detection laser radar system applicable for hard-target measurements is modeled. Three time-of-flight estimation algorithms are analyzed; peak detection, constant fraction detection, and matched filter. The statistical distribution of uncertainties in time-of-flight range estimations is determined. The detection performance for various shape conditions and signal-tonoise ratios are analyzed. Those results are used to model the properties of the range estimation error. The detector’s performances are compared with the Cramér-Rao lower bound. The performance of a tool for synthetic generation of scanning laser radar data is evaluated. In the measurement system model, it is possible to add several design parameters, which makes it possible to test an estimation scheme under different types of system design. A parametric method, based on measurement error regression, that estimates an object’s size and orientation is described. Validations of both the measurement system model and the measurement error model, with respect to the Cramér-Rao lower bound, are presented.

Surface fitting methods play an important role in many scientific fields as well as in computer aided geometric design. The problem treated here is that of constructing a smooth surface that interpolates data values associated with scattered nodes in the plane. The data is said to be convex if there exists a convex interpolant. The problem of convexity-preserving interpolation is to determine if the data is convex, and construct a convex interpolant if it exists.

The author developed a computational framework for the study of the correlation between airway morphology and aerosol deposition based on a population of human subjects. The major improvement on the previous framework, which consists of a geometric airway model, a computational fluid dynamics (CFD) model, and a particle tracking algorithm, lies in automatic geometry construction and mesh generation of airways, which is essential for a population-based study. The new geometric model overcomes the shortcomings of both centerline (CL)-based cylindrical models, which are based on the skeleton and average branch diameters of airways called one-dimensional (1-D) trees, and computed tomography (CT)-based models. CL-based models are efficient in terms of pre- and post-processing, but fail to represent trifurcations and local morphology. In contrast, in spite of the accuracy of CT-based models, it is time-consuming to build these models manually, and non-trivial to match 1-D trees and three-dimensional (3-D) geometry. The new model, also known as a hybrid CL-CT-based model, is able to construct a physiologically-consistent laryngeal geometry, represent trifurcations, fit cylindrical branches to CT data, and create the optimal CFD mesh in an automatic fashion. The hybrid airway geometries constructed for 8 healthy and 16 severe asthmatic (SA) subjects agreed well with their CT-based counterparts. Furthermore, the prediction of aerosol deposition in a healthy subject by the hybrid model agreed well with that by the CT-based model. To demonstrate the potential application of the hybrid model to investigating the correlation between skeleton structure and aerosol deposition, the author applied the large eddy simulation (LES)-based CFD model that accounts for the turbulent laryngeal jet to three hybrid models of SA subjects. The correlation between diseased branch and aerosol deposition was significant in one of the three SA subjects. However, whether skeleton structure contributes to airway abnormality requires further investigation.

This work presents a new extension for Uniform Marker Field, which is able to detect UMF on the cylinder. First part of the text deals with Augmented reality and focuses on systems using markers. It discusses the actual state-of-the-art systems and its possibilities. After that it focuses more deeply on the marker system Uniform marker field and its grayscale variants. Next part of the work describes properties of the cylinder projected in real space. Important properties for detecting are discussed in detail. Then the proposal and description of detection algorithm is presented. Implementation of algorithm is tested and evaluated on the very end of this thesis.

A estrutura de uma aeronave ée composta de muitas partes, que devem ser unidas para formar sub-partes. Entre muitas opções, "channel fittings" são amplamente utilizados na conexão da asa com a fuselagem do avião. Esse trabalho aplica o método de elementos finitos na modelagem de um "channel fitting", com o propósito principal de avaliação da distribuição de tensões de acordo com a alteração de alguns parâmetros geométricos. Quatro modelos são construídos e apresentados. Os resultados mostram uma sensibilidade importante dos níveis de tensão de acordo com a posição do furo de conexão com o parafuso. Este trabalho também propõe e descreve um procedimento iterativo que permite a aplicação mais precisa de condições de contorno na zona de contato do "fitting" com estrutura de ligação.

La numérisation est un procédé qui consiste à enregistrer un objet dans un ordinateur pour pouvoir ensuite le manipuler à l'aide d'outils informatiques. Nous nous intéressons dans ce manuscrit à la numérisation d'objets tridimensionnels. Il s'agit tout d'abord d'enregistrer leur forme. De nombreuses méthodes ont été développées pour répondre à ce problème, et nous nous concentrerons sur les objets représentés par des maillages. Sur ces objets, il est alors utile de pouvoir représenter des attributs tels que la couleur, la température ou la charge électrique, selon l'application. Nous proposons deux approches complémentaires pour aborder ce problème. La première est fondée sur le placage de textures. Cette technique consiste à déplier (paramétrer) le maillage à plat sur une image dans laquelle l'attribut est stocké. Une valeur récupérée dans l'image est ainsi associée à chaque point de l'objet. Nous proposerons une méthode permettant de masquer l'artéfact des coutures qui est inhérent à cette technique. Déplier le maillage nécessite qu'il soit de bonne qualité, ce qui n'est pas toujours le cas. Nous décrivons donc également dans un second temps une approche de l'échantillonnage d'une surface via un diagramme de Voronoï restreint. Nous expliquons en particulier comment calculer efficacement un tel objet et comment l'optimiser par rapport à un critère de qualité. Ces résultats sont ensuite appliqués au problème de l'ajustement de surfaces
Digitalisation is an operation which consists in storing an object in a computer for further manipulation using data processing tools. In this document, we are interested in the digitalisation of three-dimensional objects. It is first a matter of recording the shape of the object. Many methods have been developed to address this problem, and we will focus on objects described as meshes. On such objects the storage of attributes like colour, temperature or electrical charge is often useful, depending on the application. We will describe two complementary approaches to deal with this issue. The first one relies on texture mapping. This technique consists in unfolding ? parametrising ? the mesh on a flat image in which the attribute is stored. A value recovered from the image can therefore be associated with each point of the object. We will describe a method which hides the seam artifact, commonly encountered using this technique. Unfolding the mesh demands that its quality be good, which is not always the case. We thus secondly describe a surface sampling method based on a restricted Voronoï diagram. We especially detail how to efficiently compute such an object and how to optimise it with respect to some quality measure. These results are then applied to the surface fitting problem

碩士
國立成功大學
測量及空間資訊學系
103
SUMMARY Many building models have been created and shared in the website. These user- created models have high-quality appearances. However, the size of these building models would not be suitable for each case. Therefore, a model refinement approach had proposed in this paper to refine building models by using airborne LiDAR data. The proposed approach consists of three steps: data processing, geometric reconstruction, and model refinement. First step is point cloud segmentation to model surface. Second step is to establish the geometric relations and constraints of building models. And the last step is to refine building models with the constraints built in second step. By using the proposed method, the building models can be refined more efficiently and accurately, and the original geometric relations can be also maintained. Keywords: point cloud reconstruction, building modeling, model refinement. INTRODUCTION Point cloud reconstruction is a fundamental step for building and city modeling with a variety of applications, such as urban planning, virtual tourism, real-time emergency response, and navigation. An increasing number of 3D building models have been available in the Internet with the developments of Web 2.0 techniques and scanning equipment. For example, Trimble 3D Warehouse and MakerBot Thingiverse allow users to upload and share their models in their web-based data-sharing platforms. Generally, models from these web platforms are built up manually or processed by semi-automated and complicated procedures. By using model retrieval techniques with an airborne LiDAR point cloud, several models similar to an input point cloud can be extracted from these databases. However, the extracted building models may not well fit the point cloud. Thus, a model refinement method is proposed in this study to fit and refine a building model with its corresponding point cloud. In addition, geometric relationships and geometric constraints of the building models are maintained with the proposed iterative refinement approaches. A set of airborne LiDAR point cloud data is tested to evaluate the proposed method. The experimental results demonstrate that the proposed method can refine building models efficiently and accurately without nontrivial modeling processes in related model reconstruction methods. MATERIALS AND METHODS In this study, a model refinement scheme is proposed to reduce the differences between point clouds and building models. Most of the roofs in building models are constructed by planes. Therefore, our refinement scheme is based on plane fitting, which refine a plane by using its corresponding points. The goal of our refinement scheme is to minimize the sum of the squared Euclidean distances between a point cloud and a plane. Figure 1 illustrates the workflow of the proposed approach which consists of three main procedures: geometric analysis, point cloud segmentation, and model refinement. In previous studies, the process of plane fitting is to find a fitting plane that minimizes the sum of the squared Euclidean distances to given point cloud. However, the geometric relationships of planes do not fully considered in the fitting process. In this study, the geometric relationships are taken to construct building models, including plane normal and angle. These geometric relationships are regarded as geometric constraints in the model fitting and refinement. Besides, these relationships are also used to reconstruct the surfaces of building model after the model refinement. The proposed refinement approach is based on plane fitting that fits planes by their corresponding points. Region growing is a standard approach to segment the point cloud by using features, e.g., normal and curvature. However, these features are sensitive to noise. In this study, the point cloud is segmented by the surface of the input model. This approach assigns each point to the nearest surface. The nearest surface is determined by using Euclidean distance. Our refinement procedure combines the geometric relationships and the corresponding points to refine the building model. This procedure is inspired by plane fitting which minimizes the sum of the squared Euclidean distances to the given point cloud. In this part, we used least square fitting to minimize the distance from point to their own plane. When updating the parameters of these plane equations that we can use these updating plane equations to do another least square procedure. The second time least square procedure used to calculate the coordinate of every corner for the candidate model. Therefore, we can get the updating coordinate in this procedure. For more details, please refer to the references [3]. Finally, the solved coordinate are used to reconstruct the surfaces of building model by geometric relationships. Each point of point cloud data is assigned to the nearest surface. However, some points near the corners of a building model may be assigned to incorrect surface. In order to avoid fail assignment, an iterative optimization procedure is adopted to segment the point cloud and refine the model. After each refinement step, the surface is more close to the point cloud data, the point of point cloud would be re-assigned to the nearest and more correct surface. RESULTS AND DISCUSSION To demonstrate the robustness and feasibility of the proposed approach, we use LiDAR point cloud and building model from Trimble 3D Warehouse to verify the geometric constraints. Figure 2 show the refinement result of Technology Building in National Cheng Kung University. Figure 3 show the relation between iterations and root mean-square error (RMSE). CONCLUSION A model refinement method is presented to refine building models by using the newest point cloud data. The experimental results show that our approach can deal with multi-plane fitting by geometric constraints. In addition, the building models can be refined efficiently and accurately, and the original geometric relationships can also be maintained.

Parameter estimation plays an important role in computer vision. Many computer vision problems can be reduced to estimating the parameters of a mathematical model of interest from the observed data. Parameter estimation in computer vision is challenging, since vision data unavoidably have small-scale measurement noise and large-scale measurement errors (outliers) due to imperfect data acquisition and preprocessing. Traditional parameter estimation methods developed in the statistics literature mainly deal with noise and are very sensitive to outliers. Robust parameter estimation techniques are thus crucial for effectively removing outliers and accurately estimating the model parameters with vision data. The research conducted in this thesis focuses on single structure parameter estimation and makes a direct contribution to two specific branches under that topic: geometric fitting and deformable registration. In geometric fitting problems, a geometric model is used to represent the information of interest, such as a homography matrix in image stitching, or a fundamental matrix in three-dimensional reconstruction. Many robust techniques for geometric fitting involve sampling and testing a number of model hypotheses, where each hypothesis consists of a minimal subset of data for yielding a model estimate. It is commonly known that, due to the noise added to the true data (inliers), drawing a single all-inlier minimal subset is not sufficient to guarantee a good model estimate that fits the data well; the inliers therein should also have a large spatial extent. This thesis investigates a theoretical reasoning behind this long-standing principle, and shows a clear correlation between the span of data points used for estimation and the quality of model estimate. Based on this finding, the thesis explains why naive distance-based sampling fails as a strategy to maximise the span of all-inlier minimal subsets produced, and develops a novel sampling algorithm which, unlike previous approaches, consciously targets all-inlier minimal subsets with large span for robust geometric fitting. The second major contribution of this thesis relates to another computer vision problem which also requires the knowledge of robust parameter estimation: deformable registration. The goal of deformable registration is to align regions in two or more images corresponding to a common object that can deform nonrigidly such as a bending piece of paper or a waving flag. The information of interest is the nonlinear transformation that maps points from one image to another, and is represented by a deformable model, for example, a thin plate spline warp. Most of the previous approaches to outlier rejection in deformable registration rely on optimising fully deformable models in the presence of outliers due to the assumption of the highly nonlinear correspondence manifold which contains the inliers. This thesis makes an interesting observation that, for many realistic physical deformations, the scale of errors of the outliers usually dwarfs the nonlinear effects of the correspondence manifold on which the inliers lie. The finding suggests that standard robust techniques for geometric fitting are applicable to model the approximately linear correspondence manifold for outlier rejection. Moreover, the thesis develops two novel outlier rejection methods for deformable registration, which are based entirely on fitting simple linear models and shown to be considerably faster but at least as accurate as previous approaches.
Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 2014

Robust model fitting is a crucial task in numerous computer vision applications, where the information of interest is often expressed as a mathematical model. The goal of model fitting is to estimate the model parameters that “best” explain the observed data. However, robust model fitting is a challenging problem in computer vision, since vision data are (1) unavoidably contaminated by outliers due to imperfections in data acquisition and preprocessing, and (2) often contain multiple instances (or structures) of a model. Many robust fitting methods involve generating hypotheses using random sampling, and then (1) score the hypotheses using a robust criterion or (2) use a mode seeking or clustering method to elicit the potential structures in the data. Obtaining a good set of hypotheses is crucial for success, however this is often timeconsuming, especially for heavily contaminated data. In addition, many irrelevant hypotheses are unavoidably generated during sampling process. This frequently becomes an obstacle for accurate estimation, and has been ignored in previous methods. In particular, mode seeking-based fitting methods are very sensitive to the proportion of good/bad hypotheses. This thesis proposes several sampling methods for rapid and effective generation of good hypotheses, and hypothesis filtering methods to remove bad hypotheses for accurate estimation. The techniques developed here can be easily integrated into existing fitting methods to significantly improve fitting accuracy. We also propose a hierarchical fitting method, which recognizes that details in real-life data are organized hierarchically (i.e., large structures cascading down to finer structures). This can avoid excessive parameter tuning to obtain a particular fitting result, whereas existing fitting methods often fit data with a single number of structures and permit only one interpretation of the data. The algorithms in this thesis are motivated by preference (or ranking) analysis, which has been widely used in areas such as information retrieval, artificial intelligence and marketing. Preference analysis provides a sophisticated non-parametric approach to analyzing the data and hypotheses in model fitting problems. The algorithms developed here are shown to be more reliable than previous methods, and to perform well in various vision tasks.
Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 2013

碩士
正修科技大學
機電工程研究所
94
Scroll type compressors have been becoming increasingly popular in refrigeration and air conditioning applications due to their high efficiency, low noise, fewer components, low vibration and small size compared with other types of compressors. To design and manufacture scroll compressors is not easy as their key parts have complex shapes with involute curves. In order to comprehensive the concepts of design and improve the flexibility of the machining, the aims of the thesis are the regeneration of scroll profile and the study of the curve fitting and the interpolators. The geometry of example’s profile is unrecognized, so it is compared with the scroll configuration based on the reverse engineering firstly. The design parameters are retrieved and confirmed by the analysis of the obtained surface data. Then, the geometry of the scroll is derived in accordance with the conjugate surface theory. The error analysis between the theoretical curve and the actual curve is implemented to modify the design parameters. In order to generate a continuous smooth toolpath, a circular biarcs-fitting method is adopted to approximate the profile of the scroll. The developed biarcs-fitting method eliminates the problem in conventional straight-line approximation toolpath where it leaves ridges on the finished surface of the workpiece. The geometric model and the assembly of the components are constructed using the CAD/CAM software. The interference check between the built components can be performed to provide the exactness in the design stage. The cutting simulations with solid model are performed to verify the proposed toolpath generation method. The method and technique established in this thesis will confirm the design concepts of the scroll configuration.

碩士
國立臺灣大學
土木工程學研究所
106
This thesis continues the experimental and theoretical researches on yield surface conducted in the MSV lab of the NTU. The present emphasis was on the observation of the whole evolution process of initial and several subsequent yield surfaces in three dimensional axial-torsional-hoop stress space for alloy Al 6061. Combined with the fitting method developed in the lab, we studied the evolution behavior of yield surfaces. In the experiments, the tubes at annealed state were tested along multiple pre-strain paths to produce successive plastic behavior, combined with automated experimental method, improved procedure and appropriate yield point determination method. By probing yield points on different planes of constant hoop stress, the yield surfaces in three-dimensional stress space were built up using cubic polynomial fitting method, while the fitting method for a single yield surface proposed by Liu & Hong and modified by Huang was researched and further modified. In so doing we have reduced the complexity of the fitting process yet ensured better results, improving the applicability of the fitting method and making each parameter acquiring a specific geometric/physical meaning, such as the internal time of plasticity, translation, rotation, linear transformation, and projective transformation. We endeavored to connect these parameters so as to reveal what underlie the evolution behavior of yield surface. It is expected these would provide helpful clues in establishing an evolution rule.

abstract: The essence of this research is the reconciliation and standardization of feature fitting algorithms used in Coordinate Measuring Machine (CMM) software and the development of Inspection Maps (i-Maps) for representing geometric tolerances in the inspection stage based on these standardized algorithms. The i-Map is a hypothetical point-space that represents the substitute feature evaluated for an actual part in the inspection stage. The first step in this research is to investigate the algorithms used for evaluating substitute features in current CMM software. For this, a survey of feature fitting algorithms available in the literature was performed and then a case study was done to reverse engineer the feature fitting algorithms used in commercial CMM software. The experiments proved that algorithms based on least squares technique are mostly used for GD&T; inspection and this wrong choice of fitting algorithm results in errors and deficiency in the inspection process. Based on the results, a standardization of fitting algorithms is proposed in light of the definition provided in the ASME Y14.5 standard and an interpretation of manual inspection practices. Standardized algorithms for evaluating substitute features from CMM data, consistent with the ASME Y14.5 standard and manual inspection practices for each tolerance type applicable to planar features are developed. Second, these standardized algorithms developed for substitute feature fitting are then used to develop i-Maps for size, orientation and flatness tolerances that apply to their respective feature types. Third, a methodology for Statistical Process Control (SPC) using the I-Maps is proposed by direct fitting of i-Maps into the parent T-Maps. Different methods of computing i-Maps, namely, finding mean, computing the convex hull and principal component analysis are explored. The control limits for the process are derived from inspection samples and a framework for statistical control of the process is developed. This also includes computation of basic SPC and process capability metrics.
Dissertation/Thesis
M.S. Mechanical Engineering 2011

The present dissertation develops an invariant framework for 3D gesture comparison studies. 3D gesture comparison without Lagrangian models is challenging not only because of the lack of prediction provided by physics, but also because of a dual geometry representation, spatial dimensionality and non-linearity associated to 3D-kinematics. In 3D spaces, it is difficult to compare curves without an alignment operator since it is likely that discrete curves are not synchronized and do not share a common point in space. One has to assume that each and every single trajectory in the space is unique. The common answer is to assert the similitude between two or more trajectories as estimating an average distance error from the aligned curves, provided that the alignment operator is found. In order to avoid the alignment problem, the method uses differential geometry for position and orientation curves. Differential geometry not only reduces the spatial dimensionality but also achieves view invariance. However, the nonlinear signatures may be unbounded or singular. Yet, it is shown that pattern recognition between intrinsic signatures using correlations is robust for position and orientation alike. A new mapping for orientation sequences is introduced in order to treat quaternion and Euclidean intrinsic signatures alike. The new mapping projects a 4D-hyper-sphere for orientations onto a 3D-Euclidean volume. The projection uses the quaternion invariant distance to map rotation sequences into 3D-Euclidean curves. However, quaternion spaces are sectional discrete spaces. The significance is that continuous rotation functions can be only approximated for small angles. Rotation sequences with large angle variations can only be interpolated in discrete sections. The current dissertation introduces two multi-scale approaches that improve numerical stability and bound the signal energy content of the intrinsic signatures. The first is a multilevel least squares curve fitting method similar to Haar wavelet. The second is a geodesic distance anisotropic kernel filter. The methodology testing is carried out on 3D-gestures for obstetrics training. The study quantitatively assess the process of skill acquisition and transfer of manipulating obstetric forceps gestures. The results show that the multi-scale correlations with intrinsic signatures track and evaluate gesture differences between experts and trainees.

碩士
國立中央大學
光電科學與工程學系
105
In the thesis, according to the lighting condition of several international sport fields and the badminton lighting standard by SportAccord, we used LED as the light source and proposed a lighting design with a specific lens for beam shaping. The optical efficiency of the specific lens was 77.6%. Besides, we introduced the designed luminaire and general commercial lamps to international sport fields with three different geometry arrangements, such as at two sides, at four-corner, and along ring structure. The lighting performance in these sport fields were analyzed. Finally, with use of the designed luminaire, the average illuminance and the uniformity on the ground of sport field were higher than 1000 lx and 0.9, respectively. The optical utilization factor at the region of 36 m × 21 m was higher than 60%. Therefore, the proposed luminaire with beam shaping effect not only fits the lighting standard of international sport field but also achieves anti-glare property. Also, the illuminance and contrast across the sports field were enhanced, so that the design perform high-quality lighting and energy saving.

La scoliose idiopathique de l’adolescent (SIA) est une déformation tridimensionnelle (3D) de la colonne vertébrale. Pour la plupart des patients atteints de SIA, aucun traitement chirurgical n’est nécessaire. Lorsque la déformation devient sévère, un traitement chirurgical visant à réduire la déformation est recommandé. Pour déterminer la sévérité de la SIA, l’imagerie la plus utilisée est une radiographie postéroantérieure (PA) ou antéro-postérieure (AP) du rachis. Plusieurs indices sont disponibles à partir de cette modalité d’imagerie afin de quantifier la déformation de la SIA, dont l’angle de Cobb. La conduite thérapeutique est généralement basée sur cet indice. Cependant, les indices disponibles à cette modalité d’imagerie sont de nature bidimensionnelle (2D). Celles-ci ne décrivent donc pas entièrement la déformation dans la SIA dû à sa nature tridimensionnelle (3D). Conséquemment, les classifications basées sur les indices 2D souffrent des mêmes limitations. Dans le but décrire la SIA en 3D, la torsion géométrique a été étudiée et proposée par Poncet et al. Celle-ci mesure la tendance d’une courbe tridimensionnelle à changer de direction. Cependant, la méthode proposée est susceptible aux erreurs de reconstructions 3D et elle est calculée localement au niveau vertébral. L’objectif de cette étude est d’évaluer une nouvelle méthode d’estimation de la torsion géométrique par l’approximation de longueurs d’arcs locaux et par paramétrisation de courbes dans la SIA. Une première étude visera à étudier la sensibilité de la nouvelle méthode présentée face aux erreurs de reconstructions 3D du rachis. Par la suite, deux études cliniques vont présenter la iv torsion géométrique comme indice global et viseront à démontrer l’existence de sous-groupes non-identifiés dans les classifications actuelles et que ceux-ci ont une pertinence clinique. La première étude a évalué la robustesse de la nouvelle méthode d’estimation de la torsion géométrique chez un groupe de patient atteint de la SIA. Elle a démontré que la nouvelle technique est robuste face aux erreurs de reconstructions 3D du rachis. La deuxième étude a évalué la torsion géométrique utilisant cette nouvelle méthode dans une cohorte de patient avec des déformations de type Lenke 1. Elle a démontré qu’il existe deux sous-groupes, une avec des valeurs de torsion élevées et l’autre avec des valeurs basses. Ces deux sous-groupes possèdent des différences statistiquement significatives, notamment au niveau du rachis lombaire avec le groupe de torsion élevée ayant des valeurs d’orientation des plans de déformation maximales (PMC) en thoraco-lombaire (TLL) plus élevées. La dernière étude a évalué les résultats chirurgicaux de patients ayant une déformation Lenke 1 sous-classifiées selon les valeurs de torsion préalablement. Cette étude a pu démontrer des différences au niveau du PMC au niveau thoraco-lombaire avec des valeurs plus élevées en postopératoire chez les patients ayant une haute torsion. Ces études présentent une nouvelle méthode d’estimation de la torsion géométrique et présentent cet indice quantitativement. Elles ont démontré l’existence de sous-groupes 3D basés sur cet indice ayant une pertinence clinique dans la SIA, qui n’étaient pas identifiés auparavant. Ce projet contribue dans la tendance actuelle vers le développement d’indices 3D et de classifications 3D pour la scoliose idiopathique de l’adolescent.
Adolescent idiopathic scoliosis (AIS) is a three dimensional (3D) deformity of the spine. For most patients, no surgical intervention is required. However, for patients with severe deformities, surgery is often recommended. Postero-anterior (PA) and antero-posterior (AP) x-rays are the most common modality for viewing and evaluating this deformity. From this imaging modality, clinical indices such as the Cobb angle can quantify and evaluate the severity of AIS. Clinical decision making is often based on this descriptor. However, the descriptors based on spinal radiographies are two- dimensional (2D) by nature. Therefore, they do not fully describe the deformity in AIS due to its three-dimensional (3D) nature. Poncet et al. have studied and presented geometric torsion as a 3D descriptor of AIS. This index measures a curve’s tendency to twist out of a plane. However, the method presented in their study is susceptible to errors from an imperfect 3D spinal reconstruction due to the local approach taken and is presented in a qualitative fashion. Hence, the objective of this study is to evaluate a new method of estimating geometric torsion in AIS employing parametric curve fitting techniques based on local arc-length approximations. The first study attempts to evaluate the sensitivity of the presented method of estimating geometric torsion against noisy data or 3D reconstruction errors. Two clinical studies will then present this descriptor as a quantitative measurement of AIS and will attempt to identify potential new sub-groups and demonstrate the clinical relevance of these new sub-groups. vi The first study evaluated the robustness of the new method in estimating geometric torsion in the presence of reconstruction errors. This study demonstrated that the new method is robust to 3D spinal reconstruction errors and achieves quantitative measures in a global fashion. The second study evaluated this new method of estimating geometric torsion in patients with Lenke type 1 deformities. This study identified two sub-groups based on torsion values, a high torsion and a low torsion group. These two sub-groups showed differences in the orientation of the planes of maximum deformity (PMC) in the thoraco-lumbar segment of the spine with the high torsion group having greater values. The last study evaluated the surgical results of patients with Lenke type 1 deformities having been sub-classified in high and low torsion groups. This study showed differences in TLL PMC with the high torsion group of patients having higher values pre and post-operatively, These studies present a novel method of estimating geometric torsion in AIS and present this 3D descriptor quantitatively. They have demonstrated the existence of new sub-groups within current classification systems that were previously undetected and have shown the clinical relevance of this new method of estimating geometric torsion in AIS. This project contributes towards the development of new 3D indices for AIS and opens the door to potential new 3D classifications.