We present a variational method for unfolding of the cortex based on a user-chosen point of view as an alternative to more traditional global flattening methods, which incur more distortion around the region of interest. Our approach involves three novel contributions. The first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface from a given viewpoint. The second is an additional energy function and flow designed to preserve the 3D topology of the evolving surface. This latter contribution receives significant focus in this thesis as it is crucial to obtain the desired unfolding effect derived from the first energy functional and flow. Without it, the resulting topology changes render the unconstrained evolution uninteresting for the purpose of cortical visualization, exploration, and inspection. The third is a method that dramatically improves the computational speed of the 3D topology-preservation approach by creating a tree structure of the triangulated surface and using a recursion technique.

Thesis (MSc)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: The United Nations Convention on the Law of the Sea (UNCLOS) provides an opportunity for qualifying coastal signatory states to claim extended maritime estate. The opportunity to claim rests on the precept that in certain cases a continental shelf extends beyond the traditionally demarcated two hundred nautical mile (200M) Exclusive Economic Zone (EEZ) mark. In these cases a successful claim results in states having sovereign rights to the living and non-living resources of the seabed and subsoil, as well as the sedentary species, of the area claimed. Where the continental shelf extends beyond the 200M mark, the Foot of the Continental Slope (FoS) has to be determined as one of the qualifying criteria. Article 76 of UNCLOS de nes the FoS as ". . . the point of maximum change in the gradient at its base." Currently Caris Lots is the most widely used software which incorporates public domain data to determine the FoS as a step towards defining the offshore extent of an extended continental shelf. In this software, existing methods to compute the FoS are often subjective, typically involving an operator choosing the best perceived foot point during consideration of a two dimensional profile of the continental slope. These foot points are then joined by straight lines to form the foot line to be used in the desk top study (feasibility study). The purpose of this thesis is to establish a semi-automated and mathematically based three dimensional method for determination of the FoS using South African data as a case study. Firstly, a general background of UNCLOS is given (with emphasis on Article 76), including a brief discussion of the geological factors that influence the characteristics of a continental shelf and thus factors that could influence the determination of the FoS. Secondly, a mathematical method for determination of the surfaces of extremal curvature (on three dimensional data), originally proposed by Vanicek and Ou in 1994, is detailed and applied to two smooth, hypothetical sample surfaces. A discussion of the bathymetric data to be used for application introduces the factors to be taken into account when using extensive survey data as well as methods to process the raw data for use. The method is then applied to two sets of gridded bathymetric data of differing resolution for four separate regions around the South African coast. The ridges formed on the resulting surfaces of maximum curvature are then traced in order to obtain a foot line definition for each region and each resolution. The results obtained from application of the method are compared with example foot points provided by the subjective two dimensional method of computation within the Caris Lots software suite. A comparison of the results for the different resolutions of data is included to provide insight as to the effectiveness of the method with differing spatial coarseness of data. Finally, an indication of further work is provided in the conclusion to this thesis, in the form of a number of recommendations for possible adaptations of the mathematical and tracing methods, and improvements thereof. / AFRIKAANSE OPSOMMING: Die Verenigde Nasies se Konvensie oor die Wet van die See (UNCLOS) bied 'n geleentheid aan kwalifiserende state wat ondertekenaars van die Konvensie is om aanspraak te maak op uitgebreide maritieme gebied. Die geleentheid om op uitgebreide gebied aanspraak te maak berus op die veronderstelling dat 'n kontinentale tafel in sekere gevalle tot buite die tradisioneel afgebakende 200 seemyl eksklusiewe ekonomiese zone (EEZ) strek. In sulke gevalle het 'n suksesvolle aanspraak die gevolg dat die staat soewereine reg oor die lewende en nie-lewende bronne van die seevloer en ondergrond verkry, sowel as die inwonende spesies van die gebied buite die EEZ waarop aanspraak gemaak word. Die voet van die kontinentale tafel (FoS) moet vasgestel word as een van die bepalende kriteria vir afbakening van die aanspraak waar die kontinentale tafel tot buite die EEZ strek. Artikel 76 van UNCLOS defineer die FoS as ". . . die punt van maksimale verandering in die helling by sy basis." Die mees algemeen gebruikte rekenaar sagteware wat openbare domein data aanwend om die voet van die helling te bepaal, is tans "Caris Lots." Die metodes wat in die program gebruik word om die voet van die helling te bepaal, is dikwels subjektief en berus tipies op 'n operateur se keuse van die beste afgeskatte punt van die voet van die helling uit 'n oorweging van 'n twee dimensionele profiel van die kontinentale tafel. Die berekende voet-punte word dan deur middel van reguit lyne verbind om 'n hellingsvoetlyn te vorm. Hierdie voetlyn kan dan in die Suid-Afrikaanse lessenaarstudie (doenlikheidstudie) oor die bepaling van die voet van die kontinentale tafel gebruik word. Die doel van hierdie verhandeling is om 'n semi-outomatiese en wiskundig gebaseerde drie-dimensionele metode te beskryf vir die vasstelling van die FoS, deur as 'n gevallestudie van Suid-Afrikaanse data gebruik te maak. 'n Algemene agtergrond van UNCLOS, met beklemtoning van Artikel 76, word eerstens gegee. 'n Kort bespreking van die geologiese faktore wat die kontinentale tafel beïnvloed en wat gevolglik 'n invloed kan hê op die vasstelling van die voet van die helling, is ingesluit. Tweedens word 'n wiskundige metode, wat oorspronklik in 1994 deur Vanicek en Ou voorgestel is, vir bepaling van die oppervlaktes van maksimale kromming (gebaseer op drie-dimensionele data) in detail bespreek en 'n voorbeeld van 'n toepassing op twee gladde, denkbeeldige oppervaktes word beskryf. Die faktore wat in ag geneem moet word wanneer omvattende dieptemeting data gebruik word, en die metodes wat gebruik word om die rou data te verwerk, word ingelei deur 'n bespreking van die aard van die dieptemeting data wat gebruik is. Die metode word dan toegepas op twee stelle geruite dieptemeting data van verskillende resolusies vir vier afsonderlike streke om die Suid-Afrikaanse kus. Die riwwe wat op die resulterende oppervlaktes van maksimale kromming gevorm word, word dan nagetrek ten einde 'n lyndefinisie van die voet van die kontinentale tafel vir elke streek teen elke resolusie te bepaal. Die resultate verkry uit toepassings van die metode word vergelyk met hellingsvoetpunte soos bepaal deur die subjektiewe twee dimensionele berekeningsmetode in die "Caris Lots" rekenaar-program. 'n Vergelyking van die resultate vir die verskillende data resolusies word ingesluit om die doeltreffendheid van die metode met betrekking tot die hantering van verskillende ruimtelike data resolusies te ondersoek. 'n Aanduiding van verdere werk, bestaande uit 'n aantal aanbevelings vir moontlike aanpassings en verbeterings van die wiskundige en natrek metodes, word ten slotte in die gevolgtrekking van die verhandeling verskaf.

Approved for public release, distribution is unlimited / An important capability that many modern 3D interactive training simulations lack is an After Action Review System (AARS) that helps both the trainer and trainee to conduct an After Action Review (AAR). Although AAR is not a new idea in the 3D simulation field, it is not widely used in training simulations. In real life training, AAR has been proven as one of the most important phases of the training procedure, sometimes taking the form of debriefing, or in other cases, by conducting a deeper analysis and discussion of the facts. In order to conduct an AAR, a well-designed system (AARS) must exist to keep track of the conditions and the actions during an exercise, so they can be available for review later. This thesis translates the idea of AAR for real training situations to the 3D interactive simulation domain and also develops an After Action Review System (AARS) using XML technology for capture, analysis, and interactive playback of an entire simulation training session. Users can change the point of view to any desired position and direction, something that is impossible in video streaming playbacks. / Lieutenant, Hellenic Navy

The Enigma of Appearances is an examination into the medium of three-dimensional photography, with particular focus on the technique of stereoscopy. Invented in the mid-Victorian era, stereoscopy was an attempt to simulate natural three-dimensional perception via a combination of optics, neurology, and a pair of dissimilar images. Whilst successful in producing a powerful illusion of spatial depth and tangibility, the illusion produced by stereoscopy is anything but ??natural??, when compared to three-dimensional perception observed with the naked eye. Rather, stereoscopic photography creates a strange and unnatural interpretation of three-dimensional reality, devoid of atmosphere, movement and sound, where figures appear frozen in mid-motion, like waxwork models, or embalmed creatures in a museum. However, it is precisely stereoscopic photography??s unique and enigmatic interpretation of three-dimensional reality, which gives it its strength, separating it from being a mere ??realistic?? recording of the natural world. This thesis examines the unique cultural position that stereoscopy has occupied since its invention in 1838, from its early role as a tool for the study of binocular vision, to its phenomenal popularity as a form of mass entertainment in the second half of the 19th century, to its emergence in contemporary fine art practice in the late 20th and 21stt centuries. Additionally, The Enigma of Appearances gives a detailed analysis of the theory of spatial depth perception; it discusses the dichotomy between naturalia versus artificialia in relation to stereoscopic vision; and finally, traces the development of experimental studio practice and research into stereoscopic photography, undertaken for this MFA between 2005 and 2007. The resulting work, Camera Mortuaria (Italian for ??Mortuary Room??), is a powerful and innovative series of anaglyptic portraits, based upon an experimental stereoscopic technique that enables the production of extreme close-up three-dimensional photography. Applying this technique to the reproduction of the human face in three-dimensional form, Camera Mortuaria presents a series of ??photo sculptures??, which hover between reality and illusion, pushing the boundaries of stills photography to the limit, and beyond.

A new depth-based method of seismic imaging is used to provide insights into the 3D structural geometry of faults, and to facilitate a detailed structural interpretation of the Penola Trough, Otway Basin, South Australia. The structural interpretation is used to assess fault kinematics through geological time and to evaluate across-fault juxtaposition, shale gouge and fault reactivation potential for three selected traps (Zema, Pyrus and Ladbroke Grove) thus providing a full and systematic assessment of fault seal risk for the area. Paper 1 demonstrates how a depth-conversion method was applied to two-way time seismic data in order to redisplay the seismic in a form more closely representative of true depth, here termed ‘pseudo-depth’. Some apparently listric faults in two-way time are demonstrated to be planar and easily distinguishable from genuine listric faults on pseudo-depth sections. The insights into fault geometry provided by pseudo-depth sections have had a significant impact on the new structural interpretation of the area. Paper 2 presents the new 3D structural interpretation of the area. The geometry of faulting is complex and reflects variable stress regimes throughout structural development and the strong influence of pre-existing basement fabrics. Some basement-rooted faults show evidence of continual reactivation throughout their structural history up to very recent times. Structural analysis of all the live and breached traps of the area demonstrate that traps associated with a basement rooted bounding fault host breached or partially breached accumulations, whereas non-basement rooted faults are associated with live hydrocarbon columns. Papers 3 and 4 demonstrate that for all the traps analysed (Zema, Pyrus and Ladbroke Grove), initial in-place seal integrity was good. The initial seal integrity was provided by a combination of both favourable across fault juxtaposition (Ladbroke Grove) and/or sufficiently well developed shale gouge over potential leaky sand on sand juxtaposition windows to retain significant hydrocarbon columns (Zema, Pyrus). The palaeocolumns observed at Zema and Pyrus indicate that there has been subsequent post-charge breach of seal integrity of these traps while Ladbroke Grove retains a live hydrocarbon column. Evidence of open, permeable fracture networks within the Zema Fault Zone suggest that it is likely to have recently reactivated, thus breaching the original hydrocarbon column. Analysis of the in-situ stress tensor and fault geometry demonstrates that most of the bounding faults to the selected traps are at or near optimal orientations for reactivation in the in-situ stress tensor. The main exception being the Ladbroke Grove Fault which has a NW-SE trending segment (associated with a relatively high risk of fault reactivation and possible leakage at the surface) and an E-W trending segment (associated with a relatively low risk of fault reactivation and a present day live column). The free water level of the Ladbroke Grove accumulation coincides with this change in fault orientation. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1339545 / Thesis (Ph.D.) - University of Adelaide, Australian School of Petroleum, 2008

<p>This project investigates a laser radar system. The system is based on the principles of time-correlated single photon counting, and by measuring the times-of-flight of reflected photons it can find range profiles and perform three-dimensional imaging of scenes. Because of the photon counting technique the resolution and precision that the system can achieve is very high compared to analog systems. These properties make the system interesting for many military applications. For example, the system can be used to interrogate non-cooperative targets at a safe distance in order to gather intelligence. However, signal processing is needed in order to extract the information from the data acquired by the system. This project focuses on the analysis of different signal processing methods.</p><p>The Wiener filter and the Richardson-Lucy algorithm are used to deconvolve the data acquired by the photon counting system. In order to find the positions of potential targets different approaches of non-linear least squares methods are tested, as well as a more unconventional method called ESPRIT. The methods are evaluated based on their ability to resolve two targets separated by some known distance and the accuracy with which they calculate the position of a single target, as well as their robustness to noise and their computational burden.</p><p>Results show that fitting a curve made of a linear combination of asymmetric super-Gaussians to the data by a method of non-linear least squares manages to accurately resolve targets separated by 1.75 cm, which is the best result of all the methods tested. The accuracy for finding the position of a single target is similar between the methods but ESPRIT has a much faster computation time.</p>

This project investigates a laser radar system. The system is based on the principles of time-correlated single photon counting, and by measuring the times-of-flight of reflected photons it can find range profiles and perform three-dimensional imaging of scenes. Because of the photon counting technique the resolution and precision that the system can achieve is very high compared to analog systems. These properties make the system interesting for many military applications. For example, the system can be used to interrogate non-cooperative targets at a safe distance in order to gather intelligence. However, signal processing is needed in order to extract the information from the data acquired by the system. This project focuses on the analysis of different signal processing methods. The Wiener filter and the Richardson-Lucy algorithm are used to deconvolve the data acquired by the photon counting system. In order to find the positions of potential targets different approaches of non-linear least squares methods are tested, as well as a more unconventional method called ESPRIT. The methods are evaluated based on their ability to resolve two targets separated by some known distance and the accuracy with which they calculate the position of a single target, as well as their robustness to noise and their computational burden. Results show that fitting a curve made of a linear combination of asymmetric super-Gaussians to the data by a method of non-linear least squares manages to accurately resolve targets separated by 1.75 cm, which is the best result of all the methods tested. The accuracy for finding the position of a single target is similar between the methods but ESPRIT has a much faster computation time.

The Enigma of Appearances is an examination into the medium of three-dimensional photography, with particular focus on the technique of stereoscopy. Invented in the mid-Victorian era, stereoscopy was an attempt to simulate natural three-dimensional perception via a combination of optics, neurology, and a pair of dissimilar images. Whilst successful in producing a powerful illusion of spatial depth and tangibility, the illusion produced by stereoscopy is anything but ??natural??, when compared to three-dimensional perception observed with the naked eye. Rather, stereoscopic photography creates a strange and unnatural interpretation of three-dimensional reality, devoid of atmosphere, movement and sound, where figures appear frozen in mid-motion, like waxwork models, or embalmed creatures in a museum. However, it is precisely stereoscopic photography??s unique and enigmatic interpretation of three-dimensional reality, which gives it its strength, separating it from being a mere ??realistic?? recording of the natural world. This thesis examines the unique cultural position that stereoscopy has occupied since its invention in 1838, from its early role as a tool for the study of binocular vision, to its phenomenal popularity as a form of mass entertainment in the second half of the 19th century, to its emergence in contemporary fine art practice in the late 20th and 21stt centuries. Additionally, The Enigma of Appearances gives a detailed analysis of the theory of spatial depth perception; it discusses the dichotomy between naturalia versus artificialia in relation to stereoscopic vision; and finally, traces the development of experimental studio practice and research into stereoscopic photography, undertaken for this MFA between 2005 and 2007. The resulting work, Camera Mortuaria (Italian for ??Mortuary Room??), is a powerful and innovative series of anaglyptic portraits, based upon an experimental stereoscopic technique that enables the production of extreme close-up three-dimensional photography. Applying this technique to the reproduction of the human face in three-dimensional form, Camera Mortuaria presents a series of ??photo sculptures??, which hover between reality and illusion, pushing the boundaries of stills photography to the limit, and beyond.

Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008. / In this thesis we consider the modelling of a particular layout optimisation problem, namely, the LEGO construction problem. The LEGO construction problem, in short, concerns the optimal layout of a set of LEGO bricks to represent a given object. Our goal is to develop a software package which LEGO enthusiasts can use to construct LEGO sculptures for any real-world object. We therefore not only consider the layout optimisation problem, but also the generation of the input data required by the LEGO construction problem. We show that by using 3D geometric models to represent the real-world object, our implemented voxelisation technique delivers accurate input data for the LEGO construction problem. The LEGO construction problem has previously been solved with optimisation techniques based on simulated annealing, evolutionary algorithms, and a beam search approach. These techniques all indicate that it is possible to generate LEGO building instructions for real-world objects, albeit not necessarily in reasonable time. We show that the LEGO construction problem can be modelled easily with cellular automata, provided that cells are considered as clusters which can merge or split during each time step of the evolution of the cellular automaton. We show that the use of cellular automata gives comparable layout results in general, and improves the results in many respects. The cellular automata method requires substantially less memory and generally uses fewer LEGO bricks to construct the LEGO sculpture when using comparable execution times.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A projeção de incisivos e expansão dos arcos dentários são uma alternativa valiosa à extração dentária, especialmente quando se considera a estética facial em pacientes adultos. O efeito da projeção ortodôntica dos incisivos inferiores sobre o periodonto é controverso devido às avaliações em exames bidimensionais e os aspectos multi-fatoriais que envolvem as recessões gengivais. O objetivo deste estudo foi comparar as modificações na altura da borda alveolar dos dentes ântero-inferiores de pacientes, que foram submetidos à projeção ortodôntica, com pacientes tratados sem projeção; e correlacionar estas modificações com o grau de inclinação dentária, com as alterações da distância bicanina e com o biotipo gengival. Pacientes adultos com mais de 3 mm de falta de espaço no arco inferior e curva de Spee moderada ou acentuada compuseram o grupo experimental (n=15). O grupo controle (n=7) consistiu de pacientes com bons arcos inferiores, que não necessitavam de grandes movimentos dentários. Estes pacientes foram submetidos a alinhamento e nivelamento dentário até o fio de aço .020". Tomografias computadorizadas de feixe cônico (TCFC) foram obtidas antes do tratamento e ao final da fase de alinhamento e nivelamento. As alturas das bordas alveolares (BA) de incisivos e caninos inferiores foram medidas nas TCFC em reconstruções 3D e comparadas entre os grupos e entre os tempos pelos testes-t de Student não pareado e pareado, respectivamente. As BA foram correlacionadas com o grau de inclinação dentária (IMPA), com a distância intercaninos (DIC) e com o biotipo gengival (BG) pelo teste de correlação de Pearson. Os resultados demonstraram que os caninos inferiores do grupo experimental apresentaram perda óssea significativa (p<0,005), quando comparados com o grupo controle, em média 2,5 mm. As BA dos dentes 43, 33 e 32 ao final do alinhamento e nivelamento eram significativamente maiores do que ao início do tratamento no grupo experimental (p<0,001). Não foram encontradas diferenças significativas entre as medidas iniciais e finais das BA de todos os dentes do grupo controle. Apesar destes resultados, não foram encontradas correlações entre a remodelação da BA e o IMPA, a DIC e o BG. Pode-se concluir que o aumento no comprimento do arco inferior com arcos ortodônticos contínuos aumenta a inclinação dos incisivos inferiores e a DIC. O aumento da DIC parece exercer maior efeito sobre a BA dos caninos inferiores do que a inclinação de incisivos sobre a BA dos incisivos inferiores. No entanto, as modificações da BA não estão associadas ao grau de inclinação dos incisivos, a quantidade de expansão do arco inferior e ao biotipo gengival. / Incisor proclination and dental arch expansion are a valuable choice of treatment instead of extraction, especially when considering facial aesthetics in adult patients. The effect of orthodontic projection of the lower incisors on the periodontium is controversial because of evaluation in two-dimensional exams and the multi factorial aspects of gingival recessions. The aim of this study was to compare alveolar height modifications in the lower arch of patients that were treated with orthodontic proclination, with patients treated without proclination, and correlate these modifications with the degree of dental projection, with the changes in the lower intercanine width and with gingival biotype. Adult patients with lower arch discrepancy of more than 3 mm and moderate or pronounced curve of Spee composed the experimental group (n=15). The control group (n=7) consisted of patients with good lower arches, that did not need large dental movements. These patients had their dental arches aligned and leveled up to a .020 wire. Cone beam computed tomography (CBCT) was taken before treatment and after leveling and alignment. The height of the alveolar border (AB) of the lower incisors and canines were measured on CBCT with 3D reconstruction, and compared between groups, and between times, by paired and independent Students t-test, respectively. The AB were correlated with the degree of dental inclination (IMPA), intercanine width (ICW) and gingival biotype (GB) by the Pearson correlation test. Results showed that the lower canines of the experimental group presented significant bone loss (p<0,005) when compared with the control group, with a mean of 2.5 mm. The AB of teeth 43, 33 and 32 at the end of alignment were significantly greater than at beginning of treatment for the experimental group (p<0,001). No significant differences were found between initial and final AB measurements for all control group teeth. Despite these results, no correlation was found between remodeling of AB and IMPA, ICW and GB. It can be concluded that the increase of lower arch length with continuous orthodontic archwires increases lower incisor inclination and ICW. The increase of the ICW seems to exert more effect over the AB of lower canines, than the incisor inclination over the AB of the incisors. However, AB modifications are not associated with the degree of incisors inclination, neither the amount of lower arch expansion, nor to the gingival biotype.