Of the wide variety of existing optical techniques for non-contact 3D surface mapping, Fourier Transform Interferometry (FTI) is the method that most elegantly combines simplicity with high speed and high resolution. FTI generates continuous-phase surface maps from a projected optical interference pattern, which is generated with a simple double-pinhole source and collected in a single snapshot using conventional digital camera technology. For enhanced stability and reduced system size, the fringe source can be made from a fiber optic coupler. Unfortunately, many applications require mapping of surfaces that contain challenging features not ideally suited for reconstruction using FTI. Rough and discontinuous surfaces, commonly seen in applications requiring imaging of rock particles, present a unique set of obstacles that cannot be overcome using existing FTI techniques. This work is based on an original analysis of the limitations of FTI and the means in which errors are generated by the particular features encountered in the aggregate mapping application. Several innovative solutions have been developed to enable the use of FTI on rough and discontinuous surfaces. Through filter optimization and development of a novel phase unwrapping and referencing technique, the Method of Multiple References (MoMR), this work has enabled surface error correction and simultaneous imaging of multiple particles using FTI. A complete aggregate profilometry system has been constructed, including a MoMR-FTI software package and graphical user interface, to implement these concepts. The system achieves better than 22µm z-axis resolution, and comprehensive testing has proven it capable to handle a wide variety of particle surfaces. A range of additional features have been developed, such as error correction, particle boundary mapping, and automatic data quality windowing, to enhance the usefulness of the system in its intended application. Because of its high accuracy, high speed and ability to map varied particles, the developed system is ideally suited for large-scale aggregate characterization in highway research laboratories. Additionally, the techniques developed in this work are potentially useful in a large number of applications in which surface roughness or discontinuities pose a challenge. / Ph. D.

De nombreux scanners laser permettent d'obtenir la surface 3D a partir d'un objet. Néanmoins, la surface reconstruite est souvent lisse, ce qui est du au débruitage interne du scanner et aux décalages entre les scans. Cette these utilise des scans haute precision et choisit de ne pas perdre ni alterer les echantillons initiaux au cours du traitement afin de les visualiser. C'est en effet la seule façon de decouvrir les imperfections (trous, decalages de scans). De plus, comme les donnees haute precision capturent meme le plus leger detail, tout debruitage ou sous-echantillonnage peut amener a perdre ces details.La these s'attache a prouver que l'on peut trianguler le nuage de point initial en ne perdant presque aucun echantillon. Le probleme de la visualisation exacte sur des donnees de plus de 35 millions de points et de 300 scans differents est ainsi resolu. Deux problemes majeurs sont traites: le premier est l'orientation du nuage de point brut complet et la creation d'un maillage. Le second est la correction des petits decalages entre les scans qui peuvent creer un tres fort aliasing et compromettre la visualisation de la surface. Le second developpement de la these est une decomposition des nuages de points en hautes/basses frequences. Ainsi, des methodes classiques pour l'analyse d'image, l'arbre des ensembles de niveau et la representation MSER, sont etendues aux maillages, ce qui donne une methode intrinseque de segmentation de maillages. Une analyse mathematiques d'operateurs differentiels discrets, proposes dans la litterature et operant sur des nuages de points est realisee. En considerant les developpements asymptotiques de ces operateurs sur une surface reguliere, ces operateurs peuvent etre classifies. Cette analyse amene au developpement d'un operateur discret consistant avec Ie mouvement par courbure moyenne (l'equation de la chaleur intrinseque) definissant ainsi un espace-echelle numerique simple et remarquablement robuste. Cet espace-echelle permet de resoudre de maniere unifiee tous les problemes mentionnes auparavant (orientation et triangulation du nuage de points, fusion de scans, segmentation de maillages) qui sont ordinairement traites avec des techniques distinctes. / Many laser devices acquire directly 3D objects and reconstruct their surface. Nevertheless, the final reconstructed surface is usually smoothed out as a result of the scanner internal de-noising process and the offsets between different scans. This thesis, working on results from high precision scans, adopts the somewhat extreme conservative position, not to loose or alter any raw sample throughout the whole processing pipeline, and to attempt to visualize them. Indeed, it is the only way to discover all surface imperfections (holes, offsets). Furthermore, since high precision data can capture the slightest surface variation, any smoothing and any sub-sampling can incur in the loss of textural detail.The thesis attempts to prove that one can triangulate the raw point cloud with almost no sample loss. It solves the exact visualization problem on large data sets of up to 35 million points made of 300 different scan sweeps and more. Two major problems are addressed. The first one is the orientation of the complete raw point set, an the building of a high precision mesh. The second one is the correction of the tiny scan misalignments which can cause strong high frequency aliasing and hamper completely a direct visualization.The second development of the thesis is a general low-high frequency decomposition algorithm for any point cloud. Thus classic image analysis tools, the level set tree and the MSER representations, are extended to meshes, yielding an intrinsic mesh segmentation method.The underlying mathematical development focuses on an analysis of a half dozen discrete differential operators acting on raw point clouds which have been proposed in the literature. By considering the asymptotic behavior of these operators on a smooth surface, a classification by their underlying curvature operators is obtained.This analysis leads to the development of a discrete operator consistent with the mean curvature motion (the intrinsic heat equation) defining a remarkably simple and robust numerical scale space. By this scale space all of the above mentioned problems (point set orientation, raw point set triangulation, scan merging, segmentation), usually addressed by separated techniques, are solved in a unified framework.

Fundação de Amparo a Pesquisa do Estado de Minas Gerais / The aim of this work is to develop a non-contact 3D scanning robot to measure surfaces from objects of small sizes. The 3D scanner is shaped for a mechanical structure and an optic lecture system. The mechanical structure has 5 degrees of freedom. Such system is composed by two kinematic chains used to move the laser sensor and the workpiece respectively. The lecture system is derived from a laser sensor, based on 3D active triangulation technique that acquires the surface workpiece data. This technique assurance the scanning of the workpiece surface with reduced dimensional errors and consequently it makes possible the use less data points. Therefore it is achievable the fast data processing to reverse engineering method. In order to analyze its kinematics and dynamic model, its workspace, error analysis, and efforts at the joints, methods for reading the surface coordinates were proposed. For the analysis were considered the resolution and mechanical characteristics of the components used for the construction of a prototype. / O objetivo deste trabalho consiste no estudo e desenvolvimento de um digitalizador tridimensional robótico que será empregado para adquirir as dimensões superficiais de objetos de tamanho reduzido. O digitalizador é composto por uma estrutura mecânica e um sistema de leitura ótico. A estrutura mecânica do digitalizador possui 5 graus de liberdade e é composta por duas cadeias cinemáticas acopladas cinematicamente, onde uma delas é utilizada para movimentar o sensor laser e a outra para movimentar o objeto. O sistema de leitura é composto por um sensor laser que é baseado no método da triangulação ativa espacial para adquirir as medidas superficiais do objeto. Neste trabalho é utilizado o método da triangulação espacial porque ele garante o acompanhamento superficial do objeto para diminuir os erros nas medições, facilita a redução da quantidade de dados, facilitando o processamento de dados nas tarefas de engenharia reversa. Para permitir analisar os modelos cinemático e dinâmico, com o conseqüente estudo de seu espaço de trabalho de leitura, análise de erros, e dos esforços nas articulações, foram propostas metodologias de leitura da superfície do objeto. Para as análises foram consideradas as características mecânicas e de resolução dos componentes utilizados para a construção de um protótipo. / Doutor em Engenharia Mecânica

Measuring 3D surface geometry with precision and accuracy is an important part of many engineering and scientific tasks. 3D Scanning techniques measure surface geometry by estimating the locations of sampled surface points. In recent years, Structured-Light 3D scanners have gained significant popularity owing to their ability to produce highly accurate scans in real-time at a low cost. In this thesis we describe an approach for Structured-Light 3D scanning using a digital camera and a digital projector. We utilise the projective geometric relationships between the projector and the camera to carry out both an implicit calibration of the system and to solve for 3D structure. Our approach to geometric calibration is flexible, reliable and amenable to robust estimation. In addition, we model and account for the radiometric non-linearities in the projector such as gamma distortion. Finally, we apply a post-processing step to efficiently smooth out high-frequency surface noise while retaining the structural details. Consequently, the proposed work reduces the computational load and set-up time of a Structured-Light 3D scanner; thereby speeding up the whole scanning process while retaining the ability to generate highly accurate results. We demonstrate the accuracy of our scanning results on real-world objects of varying degrees of surface complexity. Introduction The projective geometry for a pair of pin-hole viewing devices is completely defined by their intrinsic calibration and their relative motion or extrinsic calibration in the form of matrices. For a Euclidean reconstruction, the geometry elements represented by the calibration matrices must be parameterised and estimated in some form. The use of a projector as the ‘second viewing’ device has led to numerous approaches to model and estimate its intrinsic parameters and relative motion with respect to the camera's 3D co-ordinate system. Proposed thesis work assimilates the benefits of projective geometry constructs such as Homography and the invariance of the cross-ratios to simplify the system calibration and the 3D estimation processes by an implicit modeling of the projector's intrinsic parameters and its relative motion. Though linear modeling of the projective geometry between a camera-projector view-pair captures the most essential aspects of the underlying geometry, it does not accommodate system non-linearities due to radiometric distortions of a projector device. We propose an approach that uses parametric splines to model the systematic errors introduced by radiometric non-linearities and thus correct for them. For 3D surfaces reconstructed as point-clouds, noise manifests itself as some high-frequency variations for the resulting mesh. Various pre and/or post processing techniques are proposed in the literature to model and minimize the effects of noise. We use simple bilateral filtering of the depth-map for the reconstructed surface to smoothen the surface while retaining its structural details. Modeling Projective Relations In our approach for calibrating the projective-geometric structure of a projector-camera view-pair, the frame of reference for measurements is attached to the camera. The camera is calibrated using a commonly used method. To calibrate the scanner system, one common approach is to project sinusoidal patterns onto the reference planes to generate reference phase maps. By relating the phase-information between the projector and image pixels, a dense mapping is obtained. However, this is an over-parameterisation of the calibration information. Since the reference object is a plane, we can use the projective relationships induced by a plane to implicitly calibrate the projector geometry. For the estimation of the three-dimensional structure of the imaged object, we utilise the invariance of cross-ratios along with the calibration information of two reference planes. Our formulation is also extensible to utilise more than two reference plane to compute more than one estimate of the location of an unknown surface point. Such estimates are amenable to statistical analysis which allows us to derive both the shape of an object and associate reliability scores to each estimated point location. Radiometric Correction Structured-light based 3D scanners commonly employ phase-shifted sinusoidal patterns to solve for the correspondence problem. For scanners using projective geometry between a camera and a projector, the projector's radiometric non-linearities introduce systematic errors in establishing correspondences. Such errors manifest as visual artifacts which become pronounced when fewer phase-shifted sinusoidal patterns are used. While these artifacts can be avoided by using a large number of phase-shifts, doing so also increases the acquisition time. We propose to model and rectify such systematic errors using parametric representations. Consequently, while some existing methods retain the complete reference phase maps to account for such distortions, our approach describes the deviations using a few model parameters. The proposed approach can be used to reduce the number of phase-shifted sinusoidal patterns required for codification while suppressing systematic artifacts. Additionally, our method avoids the 1D search steps that are needed when a complete reference phase map is used, thus reducing the computational load for 3D estimation. The effectiveness of our method is demonstrated with reconstruction of some geometric surfaces and a cultural figurine. Filtering Noise For a structured-light 3D scanner, various sources of noise in the environment and the devices lead to inaccuracies in estimating the codewords (phase map) for an unknown surface, during reconstruction. We examine the effects of such noise factors on our proposed methods for geometric and radiometric estimation. We present a quantitative evaluation for our proposed method by scanning the objects of known geometric properties or measures and then computing the deviations from the expected results. In addition, we evaluate the errors introduced due to inaccuracies in system calibration by computing the variance statistics from multiple estimates for the reconstructed 3D points, where each estimate is computed using a different pair of reference planes. Finally, we discuss the efficacy of certain filtering techniques in reducing the high-frequency surface noise when applied to: (a) the images of the unknown surface at a pre-processing stage, or (b) the respective phase (or depth) map at a post-processing stage. Conclusion In this thesis, we motivate the need for a procedurally simple and computationally less demanding approach for projector calibration. We present a method that uses homographies induced by a pair of reference planes to calibrate a structured-light scanner. By using the projective invariance of the cross-ratio, we solved for the 3D geometry of a scanned surface. We demonstrate the fact that 3D geometric information can be derived using our approach with accuracy on the order of 0.1 mm. Proposed method reduces the image acquisition time for calibration and the computational needs for 3D estimation. We demonstrate an approach to effectively model radiometric distortions for the projector using cubic splines. Our approach is shown to give significant improvement over the use of complete reference phase maps and its performance is comparable to that of a sate-of-the-art method, both quantitatively as well as qualitatively. In contrast with that method, proposed method is computationally less expensive, procedurally simpler and exhibits consistent performance even at relatively higher levels of noise in phase estimation. Finally, we use a simple bilateral filtering on the depth-map for the region-of-interest. Bilateral filtering provides the best trade-off between surface smoothing and the preservation of its structural details. Our filtering approach avoids computationally expensive surface normal estimation algorithms completely while improving surface fidelity.

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Vergleichende Untersuchungen zur Wiedergabegenauigkeit optoelektronischer berührungsloser und plastischer Abformungen weicher Gesichtsstrukturen Universität Leipzig, Dissertation Problemstellung: Deformation der fazialen Weichgewebe bei liegenden Patienten, hervorgerufen durch schwerkraft- und materialgewichtabhängige Einflüsse der bei konventionellen Abformmethoden verwendeten Materialien Hydrokolloiden und Elas- tomere. Ziel: Vergleich der Wiedergabegenauigkeit weicher Gesichtsstrukturen bei konven- tionellen plastischen Abformmethoden und einem optischen, mechanischen berüh- rungsfreien dreidimensionalen fotorealistischen Modell. Material und Methode: Konventionelle Abformung bei 20 Probanden mit Hydrokolloid und Elastomer sowie ein optischer Gesichtsscan vom Mittelgesicht. Studienaufbau: Digitali- sieren der Gipsmodelle und Auswertung aller STL-Datensätze zum Vergleich zwischen plastischen und optoelektronischen Abformungen sowie die Evaluation der vorhandenen Abweichungen in 34 konstruierten Punkten. Statistik: Testen auf Normalverteilung und Varianzengleichheit zum Prüfen der Signifikanz mittels Zweistichproben-t-Test und Wilcoxon-Rangsummen-Test. Ergebnisse: Der allgemeiner Abformfehler zwischen optischem Scan und konven- tionellen Abformungen liegt bei 1,19 mm ± 0,32 mm mit Variationen bei den Ma- terialien Alginat 1,02 mm ± 0,24 mm und Silikon 1,36 mm ± 0,31 mm. Signifikante Unterschiede zwischen den Abformmaterialien zeigen sich in 6 von 34 Messpunkten (p < 0,05). Alginat weist tendentiell die besseren Ergebnisse auf und ruft weniger Weichgewebsveränderung hervor. Die beschriebenen Differenzen entstehen durch die Deformation der Weichgewebe bei der Gesichtsabformung. Bei den Punkten ohne statistische Signifikanz ist die Abformtechnik als sehr präzise zu betrachten. In gut skelettal-unterstützten Regionen zeigt Silikon in einigen Messpunkten geringere Abweichungen. Schlussfolgerung: Die Auswahl des Abformmaterials sollte in Abhängigkeit von der Ausgangssituation gewählt werden. Trotz der modifizierten Abformtechnik zeigen die Ergebnisse einen deutlichen Unterschied zwischen digital erfasstem dreidimensionalem Gesichtsscan und konventionellen Abformmethoden. Den optischen Systemen ist derzeit der Vorzug zu geben. Die Vorteile sind hinsichtlich noninvasiver, iterierender Aufnahmen, genauerer und effektiverer Analyse sowie CAD/CAM-Herstellung von Epithesen aus biokompatiblen Werkstoffen beachtlich.:1. Einleitung und Zielstellung 2. Literatur 2.1 Geschichtliches 2.2 Konventionelle Methoden zur Erfassung der dreidimensionalen Gesichtsmorphologie 2.2.1 Abformwerkstoffe 2.2.2 Modellmaterial Gips 2.2.3 Einflussfaktoren auf konventionelle Gesichtsabformungen 2.3 Kontaktfreie Verfahren der Tiefenbilderzeugung zur Erfassung der dreidimensionalen Gesichtsmorphologie 2.3.1 Reflektive Verfahren 2.3.2 Transmissive Verfahren 2.4 Einführung in die praktische Herstellung von Epithesen mittels Computer Aided Design/Computer Aided Manufacturing (CAD/CAM-Techniken) und Rapid Prototyping 2.5 Synopsis der Vor- und Nachteile konventioneller Abformmethoden und optischer Methoden zur dreidimensionalen Oberflächenerfassung 3. Material und Methode 3.1 Versuchsaufbau und Prinzipübersicht 3.2 Konventionelle Abformmethodik 3.2.1 Herstellung eines individuellen Löffels 3.2.2 Gesichtsabformung mit Alginat 3.2.3 Gesichtsabformung mit Silikon 3.2.4 Modellherstellung aus Gips 3.3 Optische Methoden 3.3.1 Dreidimensionale Erfassung der Modelle mit Atos 3.3.2 Dreidimensionale Erfassung des Gesichtes mit Canfield 3.4 Auswertung der STL-Datensätze 3.4.1 Erstellen von überlagerten Bildern 3.4.2 Auswertung der Modelle mit Hilfe von festgelegten Bezugspunkten 3.5 Statistik 4. Ergebnisse 4.1 Deskriptive Darstellung der Ergebnisse der Norm zwischen dem opto- elektronischen berührungslosen dreidimensionalen Gesichtsscan und der plastischen Abformmethode mit dem Material Alginat 4.2 Deskriptive Darstellung der Ergebnisse der Norm zwischen dem opto- elektronischen berührungslosen dreidimensionalen Gesichtsscan und der plastischen Abformmethode mit dem Material Silikon 4.3 Synopsis der Abweichungen konventioneller Abformmethoden gegen- über optoelektronischen Gesichtsscans 4.4 Alters- und geschlechtsspezifische Einflüsse auf die Weichgewebs- schichtstärken bei konventionellen Abformungen 4.5 Statistische Verfahren zum Testen von Hypothesen 5. Diskussion 5.1 Diskussion der Problemstellung 5.2 Diskussion der Zielsetzung 5.3 Diskussion von Material und Methode 5.3.1 Festlegen des Studiendesigns 5.3.2 Herstellung des Löffels 5.3.3 Verwendete Abformmaterialien 5.3.4 Methodik 5.4 Diskussion der Ergebnisse 6. Zusammenfassung der Arbeit 7. Glossar 8. Literaturverzeichnis 9. Verzeichnis der Abbildungen und Tabellen 10. Anhang

L'utilisation de franges d'interférence en lumière blanche comme une sonde optique en microscopie interférométrique est d'une importance croissante dans la caractérisation des matériaux, la métrologie de surface et de l'imagerie médicale. L'Interférométrie en lumière blanche est une technique basée sur la détection de l'enveloppe de franges d'interférence. Il a été démontré antérieurement, la capacité des approches 2D à rivaliser avec certaines méthodes classiques utilisées dans le domaine de l'interférométrie, en termes de robustesse et de temps de calcul. En outre, alors que la plupart des méthodes tiennent compte seulement des données 1 D, il semblerait avantageux de prendre en compte le voisinage spatial utilisant des approches multidimensionnelles (2D/3D), y compris le paramètre de temps afin d'améliorer les mesures. Le but de ce projet de thèse est de développer de nouvelles approches n-D qui sont appropriées pour une meilleure caractérisation des surfaces plus complexes et des couches transparentes. / The use of white light interference fringes as an optical probe in microscopy is of growing importance in materials characterization, surface metrology and medical imaging. Coherence Scanning Interferometry (CSI, also known as White Light Scanning Interferometry, WSLI) is well known for surface roughness and topology measurement [1]. Full-Field Optical Coherence Tomography (FF-OCT) is the version used for the tomographic analysis of complex transparent layers. Both techniques generally make use of some sort of fringe scanning along the optical axis and the acquisition of a stack of xyz images. Image processing is then used to identify the fringe envelopes along z at each pixel in order to measure the positions of either a single surface or of multiple scattering objects within a layer.In CSI, the measurement of surface shape generally requires peak or phase extraction of the mono dimensional fringe signal. Most of the methods are based on an AM-FM signal model, which represents the variation in light intensity measured along the optical axis of an interference microscope [2]. We have demonstrated earlier [3, 4] the ability of 2D approaches to compete with some classical methods used in the field of interferometry, in terms of robustness and computing time. In addition, whereas most methods only take into account the 1D data, it would seem advantageous to take into account the spatial neighborhood using multidimensional approaches (2D, 3D, 4D), including the time parameter in order to improve the measurements.The purpose of this PhD project is to develop new n-D approaches that are suitable for improved characterization of more complex surfaces and transparent layers. In addition, we will enrich the field of study by means of heterogeneous image processing from multiple sensor sources (heterogeneous data fusion). Applications considered will be in the fields of materials metrology, biomaterials and medical imaging.

This thesis addresses the problem of constructing 3D CAD models from 2D engineering drawings of the object. Procedures for each step in the popular bottom-up approach are described. In each of the steps in this approach, the capability is extended to handle classes of parts not handled by present art. These include auxiliary views, parts with curved entities that are inclined to all viewing directions, and views that result in non-manifold edges in the surface model. In addition this thesis also presents procedures to extract features from the solid model constructed so that the 3D model can be manipulated and modified within current CAD systems. In order to enable extracting the construction history, detecting symmetry in the part is essential. This thesis presents an algorithm to detect symmetry (both global and partial) in the part given the solid model of the part. Working of the procedures is illustrated using benchmark parts from the literature. The thesis concludes with a discussion on scope for further work.

Abstract The use of 3D imaging of craniofacial soft tissue has increased in medical science, and imaging technology has been developed greatly in recent years. 3D models are quite accurate and with imaging devices based on stereophotogrammetry, capturing the data is a quick and easy operation for the subject. However, analyzing 3D models of the face or head can be challenging and there is a growing need for efficient quantitative methods. In this thesis, new mathematical methods and tools for measuring craniofacial structures are developed. The thesis is divided into three parts. In the first part, facial 3D data of Lithuanian twins are used for the determination of zygosity. Statistical pattern recognition methodology is used for classification and the results are compared with DNA testing. In the second part of the thesis, the distribution of surface normal vector directions of a 3D infant head model is used to analyze skull deformation. The level of flatness and asymmetry are quantified by functionals of the kernel density estimate of the normal vector directions. Using 3D models from infants at the age of three months and clinical ratings made by experts, this novel method is compared with some previously suggested approaches. The method is also applied to clinical longitudinal research in which 3D images from three different time points are analyzed to find the course of positional cranial deformation and associated risk factors. The final part of the thesis introduces a novel statistical scale space method, SphereSiZer, for exploring the structures of a probability density function defined on the unit sphere. The tools developed in the second part are used for the implementation of SphereSiZer. In SphereSiZer, the scale-dependent features of the density are visualized by projecting the statistically significant gradients onto a planar contour plot of the density function. The method is tested by analyzing samples of surface unit normal vector data of an infant head as well as data from generated simulated spherical densities. The results and examples of the study show that the proposed novel methods perform well. The methods can be extended and developed in further studies. Cranial and facial 3D models will offer many opportunities for the development of new and sophisticated analytical methods in the future. / Tiivistelmä Pään ja kasvojen pehmytkudoksen 3D-kuvantaminen on yleistynyt lääketieteessä, ja siihen tarvittava teknologia on kehittynyt huomattavasti viime vuosina. 3D-mallit ovat melko tarkkoja, ja kuvaus stereofotogrammetriaan perustuvalla laitteella on nopea ja helppo tilanne kuvattavalle. Kasvojen ja pään 3D-mallien analysointi voi kuitenkin olla haastavaa, ja tarve tehokkaille kvantitatiivisille menetelmille on kasvanut. Tässä väitöskirjassa kehitetään uusia matemaattisia kraniofakiaalisten rakenteiden mittausmenetelmiä ja -työkaluja. Työ on jaettu kolmeen osaan. Ensimmäisessä osassa pyritään määrittämään liettualaisten kaksosten tsygositeetti kasvojen 3D-datan perusteella. Luokituksessa hyödynnetään tilastollista hahmontunnistusta, ja tuloksia verrataan DNA-testituloksiin. Toisessa osassa analysoidaan pään epämuodostumia imeväisikäisten päiden 3D-kuvista laskettujen pintanormaalivektorien suuntiin perustuvan jakauman avulla. Tasaisuuden ja epäsymmetrian määrää mitataan normaalivektorien suuntakulmien ydinestimaatin funktionaalien avulla. Kehitettyä menetelmää verrataan joihinkin aiemmin ehdotettuihin lähestymistapoihin mittaamalla kolmen kuukauden ikäisten imeväisten 3D-malleja ja tarkastelemalla asiantuntijoiden tekemiä kliinisiä pisteytyksiä. Menetelmää sovelletaan myös kliiniseen pitkittäistutkimukseen, jossa tutkitaan pään epämuodostumien ja niihin liittyvien riskitekijöiden kehitystä kolmena eri ajankohtana otettujen 3D-kuvien perusteella. Viimeisessä osassa esitellään uusi tilastollinen skaala-avaruusmenetelmä SphereSiZer, jolla tutkitaan yksikköpallon tiheysfunktion rakenteita. Toisessa osassa kehitettyjä työkaluja sovelletaan SphereSiZerin toteutukseen. SphereSiZer-menetelmässä tiheysfunktion eri skaalojen piirteet visualisoidaan projisoimalla tilastollisesti merkitsevät gradientit tiheysfunktiota kuvaavalle isoviivakartalle. Menetelmää sovelletaan imeväisikäisen pään pintanormaalivektoridataan ja simuloituihin, pallotiheysfunktioihin perustuviin otoksiin. Tulosten ja esimerkkien perusteella väitöskirjassa esitetyt uudet menetelmät toimivat hyvin. Menetelmiä voidaan myös kehittää edelleen ja laajentaa jatkotutkimuksissa. Pään ja kasvojen 3D-mallit tarjoavat paljon mahdollisuuksia uusien ja laadukkaiden analyysityökalujen kehitykseen myöhemmissä tutkimuksissa.

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