O multiplicador de Schur parcial de um grupo G é um semigrupo inverso comutativo pM(G) que, no estudo de representações parciais projetivas de grupos, desempenha um papel análogo ao do multiplicador de Schur clássico M(G). Há uma descrição de pM(G) como uma união de grupos abelianos, em que cada componente pM_D(G) é formada por classes de equivalência de certas funções parciais (chamadas de conjuntos fatores parciais), as quais assumem valores em um corpo e têm como domínio um subconjunto D de G × G. Os domínios D formam um reticulado e foram caracterizados como os subconjuntos T-invariantes de G × G, em que T é um monoide específico atuando em G × G. A componente total pM_(G), que corresponde aos conjuntos fatores totalmente definidos, é particularmente interessante pois contém M(G) como um de seus subgrupos e, além disso, qualquer outra componente é uma imagem epimorfa da componente total. Um dos objetivos deste trabalho é determinar a componente total do multiplicador de Schur parcial para algumas classes importantes de grupos, como os grupos diedrais, os grupos dicíclicos e os produtos de grupos cíclicos. Outro tópico que será abordado é a estrutura do reticulado dos domínios dos conjuntos fatores parciais, destacando-se propriedades daqueles que correspondem às representações parciais ditas elementares, as quais possuem um papel relevante na teoria. Provaremos que todo domínio pode ser representado em uma forma única como uma reunião de certos domínios indecomponíveis, que consistem de peças estruturais chamadas de blocos e domínios minimais. Também será determinada a estrutura dos domínios elementares e serão obtidos alguns invariantes numéricos do conjunto parcialmente ordenado dos domínios elementares. Como uma consequência dos resultados obtidos, serão caracterizados os grupos para os quais todos os domínios elementares são indecomponíveis. Além disso será feita uma aplicação da teoria de álgebras de semigrupos à álgebra parcial de grupo, que é uma álgebra responsável pelas representações parciais de grupos. / The partial Schur multiplier of a group G is a commutative inverse semigroup pM(G) which, in the study of partial projective representations, plays a role analogous to the classical Schur multiplier M(G). There is a description of pM(G) as a union of abelian groups, in which each component pM_D(G) is formed by the equivalence classes of certain partial functions (called partial factor sets), taking values in a field and having as its domain a subset D of G × G. The domains D form a lattice and were characterized as the T-invariant subsets of G × G, where T is a specific monoid acting on G × G. The total component pM_(G), which corresponds to the totally defined factor sets, is particularly interesting because it contains M(G) as one of its subgroups and, moreover, any other component is an epimorphic image of the total component. One of the objectives of this work is to determine the total component of the partial Schur multiplier for some important classes of groups, such as the dihedral groups, the dicyclic groups and the products of cyclic groups. Another topic which will be considered is the structure of the lattice of domains of partial factor sets, emphasizing properties of those domains that correspond to the so-called elementary partial representations, which play a relevant role in the theory. We shall prove that each domain can be represented in a unique way as a union of certain indecomposable domains, where the latter consists of the so-called blocks and minimal domains. The structure of the elementary domains also will be determined, and some numerical invariants of the partially ordered set of the elementary domains will be given. As a consequence of the obtained facts, the groups whose elementary domains are indecomposable will be characterized. We will also give an application of the theory of semigroup algebras to the partial group algebra, an algebra which is responsible for partial group representations.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-05-17T13:38:00Z No. of bitstreams: 1 marcelocunhafigueiredo.pdf: 942741 bytes, checksum: 463b01a7fb542d3aa4a0d2f5867445e7 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-05-22T13:54:17Z (GMT) No. of bitstreams: 1 marcelocunhafigueiredo.pdf: 942741 bytes, checksum: 463b01a7fb542d3aa4a0d2f5867445e7 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-05-22T13:55:00Z (GMT) No. of bitstreams: 1 marcelocunhafigueiredo.pdf: 942741 bytes, checksum: 463b01a7fb542d3aa4a0d2f5867445e7 (MD5) / Made available in DSpace on 2018-05-22T13:55:00Z (GMT). No. of bitstreams: 1 marcelocunhafigueiredo.pdf: 942741 bytes, checksum: 463b01a7fb542d3aa4a0d2f5867445e7 (MD5) Previous issue date: 2018-02-28 / As geometrias denominadas não-euclidianas fazem parte da história da Matemática e nossas leituras mostram que elas não têm tido muito espaço nas licenciaturas da matéria no Brasil. Contrapondo esse panorama, buscamos estruturar um material para atuais e futuros professores de matemática, vislumbrando um outro olhar para a Geometria. Nosso estudo tem como objetivo buscar nas literaturas sobre o tema formas de apresentação da Geometria Projetiva, para confecção de um produto educacional que mostre uma das possibilidades de axiomatização desta teoria. O curso proposto foi aplicado na prática junto a um grupo de licenciandos de uma universidade pública que já tinham estudado Geometria Euclidiana Plana, oportunizando uma pesquisa de campo. As atividades propostas no produto são de cunho investigativo, e buscam solucionar problemas de Geometria Euclidiana de forma alternativa, com auxílio de software de geometria dinâmica e após a apresentação de uma concepção geométrica projetiva. Nossa investigação teve como foco a questão: ‘Como um curso básico e introdutório de Geometria Projetiva pode contribuir para licenciandos repensarem a geometria estruturalmente, de modo ampliado em seus fundamentos?’ Da pesquisa empreendida resultaram dados, analisados com base na metodologia fenomenológica, através da qual se procede com as reduções a partir das manifestações genuínas dos sujeitos de pesquisa, obtendo-se categorizações em forma de convergências de significações. / The so named non-Euclidean geometries are a part of the History of Mathematics, but our readings indicate an absence of space for this subject in Brazilian Mathematics teaching degree courses. Opposing this scenario, we aimed to devise materials for both current and future Mathematics teachers under a different perspective for Geometry. Our goal was to search the literature for ways of presenting projective geometry in order to make up an educational product that shows a possibility of axiomatizing such theory. The proposed course was applied to a group of Mathematics teaching undergraduate students who had already gone through a Plane Euclidean Geometry class at a public University, which created the opportunity for a field study. The activities we propose in our product are of investigative nature, aiming to solve Euclidean Geometry problems in alternative ways with the help of a Dynamic Geometry software after the presentation of a Projective Geometry conception. Our investigation was focused on the question “In which ways can a basic and introductory class on Projective Geometry contribute for teaching degree students to structurally rethink Geometry by widening its foundations?”. The data we generated in our research was analyzed according to the phenomenological approach, in which reductions are made based from genuine manifestations of the study subjects and categorizations are obtained in the form of signification convergences.

A partir d’une clinique constituée de 15 sujets bourreaux et victimes, cette étude porte sur « Les logiques de survie des réfugiés de guerre », en se servant du Rorschach et du TAT comme «dispositifs à symboliser» (Roussillon, 2003 ; Roman, 2005 ; Dérivois, 2004). Comment les réfugiés se reconstruisent-ils dans un pays d’asile ? A quel niveau topique les traumatismes vécus se seraient-ils enkystés ? A quelles stratégies de survie recourent-ils ? Quels mécanismes de défense mettent-ils en œuvre ? Comment les traumatismes subis, les éventuels (ré) aménagements s’expriment-ils au Rorschach et au TAT ? Enfin, l’établissement des indices d’une « personnalité traumatique » est-elle possible au Rorschach et au TAT ?Il existerait un lien entre les traumatismes subis, les troubles référés à l’identité dans le pays d’asile et les différentes modalités de reconstruction psychiques. Les logiques de survie se déclinent en victimisation et logiques victimaires ; bourreaux et boucs-émissaires ; triomphalismes et engagements ; honte et culpabilité ; errance ; silence ; recherche et création. La somatisation constitue une autre déclinaison.Les effets du traumatique sont souvent pensés sous le primat de la négativité. L’hypothèse du traumatisme-moteur a été envisagée. Enfin, un appareil psychique des liens inter-institutionnels a été modélisé. / From a clinical subjects consisting of 15 executioners and victims, this study focuses on "survival strategies of refugees from war, "using the Rorschach and the TAT as "devices to symbolize" (Roussillon, 2003; Roman 2005; Dérivois, 2004).How do they rebuild refugees in asylum countries? At what level topical traumas would they encysted? Which coping strategies do they use? What defenses are they implemented? How trauma, the possible (re) development they are expressed on the Rorschach and the TAT? Finally, Compiling a "personality disorder" is it possible the Rorschach and the TAT? There is a link between trauma, disorders referred to identity in the country of asylum and the various methods of psychological reconstruction. The logic of survival and victimization are divided into logical victimizers; executioners and scapegoats; triumphalism and commitments; shame and guilt, wander; silence, research and creation. Somatization is another variation. The effects of trauma are often designed under the primacy of negativity. The hypothesis of trauma-engine was considered. Finally, a psychic apparatus of inter-institutional linkages have been modeled.

Cette thèse a pour première vocation d’être un état de l’art sur le calcul quantique, sinon exhaustif, simple d’accès (chapitres 1, 2 et 3). La partie originale de cet essai consiste en deux approches mathématiques du calcul quantique concernant quelques systèmes quantiques : la première est de nature algébrique et fait intervenir des structures particulières : les corps et les anneaux de Galois (chapitre 4), la deuxième fait appel à la géométrie dite projective (chapitre 5). Cette étude a été motivée par le théorème de Kochen et Specker et par les travaux de Peres et Mermin qui en ont découlé / The first vocation of this thesis would be a state of the art on the field of quantum computation, if not exhaustive, simple access (chapters 1, 2 and 3). The original (interesting) part of this treatise consists of two mathematical approaches of quantum computation concerning some quantum systems : the first one is an algebraic nature and utilizes some particular structures : Galois fields and rings (chapter 4), the second one calls to a peculiar geometry, known as projective one (chapter 5). These two approaches were motivated by the theorem of Kochen and Specker and by work of Peres and Mermin which rose from it

The main goal of this thesis is a contribution to the classification of all incidence geometries<p>of rank two on which some group PSL(2,q), q a prime power, acts flag-transitively.<p>Actually we require that the action be RWPRI (residually weakly primitive) and (2T)1<p>(doubly transitive on every residue of rank one). In fact our definition of RWPRI requires<p>the geometry to be firm (each residue of rank one has at least two elements) and RC<p>(residually connected).<p><p>The main goal is achieved in this thesis.<p>It is stated in our "Main Theorem". The proof of this theorem requires more than 60pages.<p><p>Quite surprisingly, our proof in the direction of the main goal uses essentially the classification<p>of all subgroups of PSL(2,q), a famous result provided in Dickson’s book "Linear groups: With an exposition of the Galois field theory", section 260, in which the group is called Linear Fractional Group LF(n, pn).<p><p>Our proof requires to work with all ordered pairs of subgroups up to conjugacy.<p><p>The restrictions such as RWPRI and (2T)1 allow for a complete analysis.<p><p>The geometries obtained in our "Main Theorem" are bipartite graphs; and also locally 2-arc-transitive<p>graphs in the sense of Giudici, Li and Cheryl Praeger. These graphs are interesting in their own right because of<p>the numerous connections they have with other fields of mathematics. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Projecting Urban Natures is a compilation thesis in critical studies in architecture. It comprises three journal articles and four design proposals in which I have taken an active part. The point of departure for this thesis is the renewed emphasis on social-ecological interaction and resilience that is currently taking place within ecological systems science, and the opportunities that these paradigmatic insights in turn have opened up within urbanism and design. The thesis argues that although they are promising, these emerging integrative frameworks are seldom brought into mainstream planning and urban design practice. Instead, the structuring of “nature” and “city” into a dualistic balance relationship still permeates not only the general planning discourse, but also makes its way into planning documents, notably influencing distinctions between professions. In response, this thesis sets out to rethink and explore more integrated approaches to human/nature relationships, through the utilization of design-based and transdisciplinary research methods. While this core aim of the thesis remains the same throughout the work, the task is approached from different perspectives: through different constellations of collaborative work as well as through parallel case-based explorations that emphasize the relational, anti-essentialist and situated articulation of values of urban natures and how these forces come into play. The work has been propelled through workshop-based, site-specific, and experimental design processes with professionals and researchers from the fields of e.g. systems ecology, natural resource management, political ecology, urban design, architecture, and landscape design, as well as planners, developers, local interest groups, and NGOs. Specifically, projects performed within this thesis include: Nature as an Infrastructural Potential – An Urban Strategy for Järvafältet; Kymlinge UrbanNatur together with NOD, Wingårdhs, MUST and Storylab; Årsta Urban Natures with James Corner Field Operations and Buro Happold; and Albano Resilient Campus — a collaboration between Stockholm Resilience Centre, KTH and KIT. / <p>QC 20171102</p>

Abstract A psychological test may be defined as an objective and standardized measure of a sample of behaviour. The interpretation of test results is usually based on comparing an individual’s performance to norms based on a representative sample of the population. The present study examined the norms of popular adult tests. The validity of the Wartegg drawing test (WZT) was studied using two rating scales, the Toronto Alexithymia Scale and the Beck Depression Inventory as criterion tests. Weak to moderate correlations were found. It is concluded that the WZT has some validity in the assessment of Alexithymia. Efforts to develop a psychometrically valid and reliable method of interpreting the WZT should be continued. Cross-national and historical analyses of the norms of Wechsler’s adult intelligence scale (WAIS) were performed. The results show that the Finnish WAIS III test norms are distorted in the younger age groups. Significant cross-national and cross-generational differences in relative subtest scores, test profiles were also observed. Differences in general intelligence cannot explain such variations, and educational and cultural factors probably underlie the observed differences. It is suggested that the concept of a national IQ profile is useful for cross-national test validation studies. The validity of a validity scale, the Chapman Infrequency Scale, was studied in the context of a survey study. Results showed that careless responding is significantly more frequent among psychiatric patients relative to healthy respondents. The common procedure of excluding careless responders from final samples may affect the results of survey studies targeting individuals with psychiatric symptoms. Cut-off scores for exclusion should be flexible and chosen according to the demographic and health characteristics of the sample. In conclusion, the results of this study underscore the need for up-to-date and representative test norms for valid test interpretation. / Tiivistelmä Psykologiset testit voidaan ymmärtää otoksiksi tutkittavan käyttäytymisestä. Mittauksen tulosta tulkitaan yleensä vertaamalla sitä tavalliseen tai keskimääräiseen tulokseen eli testinormeihin. Väitöskirjatutkimus tarkastelee suosittujen aikuistestien normien pätevyyttä. Warteggin piirrostestin validiteettia aleksitymian ja depression mittarina tutkittiin käyttämällä vertailukriteerinä kahta lomaketestiä, Toronton aleksitymia-asteikkoa ja Beckin depressioasteikkoa. Mitatut korrelaatiot olivat melko matalia. Tutkimuksen johtopäätöksenä oli, että Wartegg-testi saattaa olla hyödyllinen menetelmä aleksitymian toteamisessa ja että empiiriseen tutkimukseen perustuvaa tulkintamenetelmien kehittämistä pitäisi jatkaa. Tutkimuksessa selvitettiin myös Wechslerin aikuisten älykkyystestien (WAIS) eri versioiden osatestien kansallisten normien välisiä eroja ja eroja ikäkohorttien välillä. Tulokset osoittivat, että suomalaiset WAIS III testinormit ovat vinoutuneet nuorempien ikäryhmien osalta. Tutkimuksessa havaittiin merkitseviä eroja osatestien keskiarvojen suhteissa eli testiprofiileissa eri maiden ja ikäkohorttien välillä. Kyseisiä eroja ei voida selittää älykkyyden yleisellä faktorilla, vaan niiden taustalla on luultavasti koulutukseen ja kulttuuriin liittyviä tekijöitä. Osa eroista kansallisissa testiprofiileissa näyttää olevan luonteeltaan pysyviä, ja tätä tietoa voidaan käyttää hyväksi testinormien pätevyyttä arvioitaessa. Chapmanin vastaustapa-asteikon (CIS) validiteettia tutkittiin Pohjois-Suomen vuoden 1966 syntymäkohortin kyselytutkimusaineistolla. Psykiatrisista oireista kärsivät henkilöt saivat korkeampia pistemääriä kuin terveet vastaajat. Johtopäätöksenä oli, että vastaustapamittarit voivat karsia psykiatrisia potilaita liian herkästi ulos tutkimusjoukosta, mikä voi vääristää tutkimusten tuloksia. Kriteeripistemäärän pitäisi olla joustava ja sen määrityksessä pitäisi ottaa huomioon tutkimusjoukon ominaisuudet. Tutkimukset osoittavat, että testituloksen luotettava tulkinta vaatii ajanmukaiset ja edustavaan otokseen perustuvat testinormit.

Bereavement of a miscarriage is complex because of factors that are unique to this loss. There is no visible child to mourn for, no memories or shared life experiences. The death is sudden and there usually a lack of recognition of the significance of such a loss by society. In addition, women who miscarry are often in need of the absent social and emotional support that is provided with other types of bereavement. The suppression of appropriate mourning due to society’s inhibitions may cause further stress and long-term emotional consequences. Prenatal loss is unique in the sense that the parents do not know the object of loss as it would be with the death of a loved one who has been part of their lives and social structure. The anticipated child is both a fantasy child and an internal entity within a woman’s body. The loss of a baby is also the loss of part of a women’s self. The researcher is of the opinion that a miscarriage is a traumatic experience which, if not thoroughly dealt with, can cause great damage to a sufferer’s life. According to her, projective techniques in the form of play therapy can encourage women to talk about their miscarriage in order to deal with suppressed emotions. The purpose of this research was to determine to what extent projective techniques could be used in respect of a mother’s emotional experience of a miscarriage. For this study the qualitative research approach was used. The participants were selected by making use of purposive sampling as a form of non-probability sampling. During the empiric research two respondents attended eight in-depth interviewes with a therapeutic component. The first interview comprised a semi-structured interview schedule. Six interviews followed where projective play therapeutic techniques were used. The empirical data was obtained from the interview schedule and the researcher was the primer instrument of gathering information. The value of meaning that the participants attached to the subject was of great importance. The empirical data showed that the two participants were better enabled to deal with their miscarriages after the interviews. Thus, regarding the experience of the two paricipants, it was possible to answer the research question positively. It seems as if projective techniques can indeed be used in respect of a mother’s emotional experience of a miscarriage. / Dissertation (MA (Play Therapy))--University of Pretoria, 2005. / Social Work / unrestricted

L’approche de la problématique des agirs via les tests projectifs en se penchant sur l’expression des défaillances narcissiques du sujet, propose, le plus souvent, une vision unitaire basée sur le mécanisme du recours à l’acte tel que définit par Balier. Nous proposerons de traiter cette question à partir d’une dimension plurielle différenciant deux types d’agirs : le recours à l’acte (Balier) et l’acting-out (Lacan). Nous présenterons une étude mixte, quantitative et qualitative, à partir de la comparaison de Rorschach et TAT administrés à 24 sujets. Notre analyse de ces deux formes d’agir portera principalement sur la capacité du sujet à pouvoir ou non se différencier de l’environnement. Le groupe recours à l’acte se caractérise par une continuité intérieur / extérieur et un transitivisme morbide expression d’une absence de constitution d’un soi différencié. Le groupe acting-out présente une problématique narcissique spécifique dans la validation du spéculaire par le symbolique. Les prises en charges thérapeutiques peuvent ainsi s’aider de ces résultats pour proposer des approches différentielles au sein desquelles les tests projectifs pourraient avoir une fonction pré-thérapeutique. / In the modern societies, the answer to the criminal act is a prison sentence. Due to the nature of certain acts, with this prison sentence, some court-ordered treatments (COT) (obligations and injunctions of treatments) have been added. Ethically, this law request and its social asking don’t exempt to think about the prisoner ‘asking, which is the trigger of psychotherapies. There is any retroactivity of the law and of pronounced sentence. For this research, the prisoners were selected on their own asking of care (the court-ordered treatments couldn’t applicate). The asking of the prisoners is therefore a criterion common to them (these prisoners). In this context, the acts have distinguished according to the mechanisms which have governed the nature of the act: recourse of act or acting out. Many experts agree on the existence of premature narcissistic failures. However, discussions persist on the nature of the act and on its aspect, either single dimension or multiple and complex dimensions (objective behavior, social consequences and underlying mechanisms ...). Yet all these theoretical models on narcissistic failures lean on the “recourse to act” as if there was only a simple nature to act.

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.