Nos anos recentes, suavização de superfícies é um assunto de intensa pesquisa em processamento geométrico. Muitas das abordagens para suavização de malhas usam um esquema de duas etapas: filtragem de normais seguido de um passo de atualização de vértices para corresponder com as normais filtradas. Neste trabalho, propomos uma adaptação de tais esquemas de duas etapas para superfícies representadas por nuvens de pontos. Para isso, exploramos esquemas de pesos para filtrar as normais. Além disso, investigamos três métodos para estimar normais, analisando o impacto de cada método para estimar normais em todo o processo de suavização da superfície. Para uma análise quantitativa, além da comparação visual convencional, avaliamos a eficácia de diferentes opções de implementação usando duas medidas, comparando nossos resultados com métodos de suavização de nuvens de pontos encontrados a literatura / In the last years, surface denoising is a subject of intensive research in geometry processing. Most of the recent approaches for mesh denoising use a twostep scheme: normal filtering followed by a point updating step to match the corrected normals. In this work, we propose an adaptation of such two-step approaches for point-based surfaces, exploring three different weight schemes for filtering normals. Moreover, we also investigate three techniques for normal estimation, analyzing the impact of each normal estimation method in the whole point-set smoothing process. Towards a quantitative analysis, in addition to conventional visual comparison, we evaluate the effectiveness of different choices of implementation using two measures, comparing our results against state-of-art point-based denoising techniques. Keywords: surface smoothing; point-based surface; normal estimation; normal filtering.

Point-based rendering methods have proven to be effective for the display of large point cloud surface models. For a realistic visualization of the models, transparency and shadows are essential features. We propose a method for point cloud rendering with transparency and shadows at interactive rates. Our approach does not require any global or local surface reconstruction method, but operates directly on the point cloud. All passes are executed in image space and no pre-computation steps are required. The underlying technique for our approach is a depth peeling method for point cloud surface representations. Having detected a sorted sequence of surface layers, they can be blended front to back with given opacity values to obtain renderings with transparency. These computation steps achieve interactive frame rates. For renderings with shadows, we determine a point cloud shadow texture that stores for each point of a point cloud whether it is lit by a given light source. The extraction of the layer of lit points is obtained using the depth peeling technique, again. For the shadow texture computation, we also apply a Monte-Carlo integration method to approximate light from an area light source, leading to soft shadows. Shadow computations for point light sources are executed at interactive frame rates. Shadow computations for area light sources are performed at interactive or near-interactive frame rates depending on the approximation quality.

Level-set methods have become a valuable and well-established field of visualization over the last decades. Different implementations addressing different design goals and different data types exist. In particular, level sets can be used to extract isosurfaces from scalar volume data that fulfill certain smoothness criteria. Recently, such an approach has been generalized to operate on unstructured point-based volume data, where data points are not arranged on a regular grid nor are they connected in form of a mesh. Utilizing this new development, one can avoid an interpolation to a regular grid which inevitably introduces interpolation errors. However, the global processing of the level-set function can be slow when dealing with unstructured point-based volume data sets containing several million data points. We propose an improved level-set approach that performs the process of the level-set function locally. As for isosurface extraction we are only interested in the zero level set, values are only updated in regions close to the zero level set. In each iteration of the level-set process, the zero level set is extracted using direct isosurface extraction from unstructured point-based volume data and a narrow band around the zero level set is constructed. The band consists of two parts: an inner and an outer band. The inner band contains all data points within a small area around the zero level set. These points are updated when executing the level set step. The outer band encloses the inner band providing all those neighbors of the points of the inner band that are necessary to approximate gradients and mean curvature. Neighborhood information is obtained using an efficient kd-tree scheme, gradients and mean curvature are estimated using a four-dimensional least-squares fitting approach. Comparing ourselves to the global approach, we demonstrate that this local level-set approach for unstructured point-based volume data achieves a significant speed-up of one order of magnitude for data sets in the range of several million data points with equivalent quality and robustness.

Det blir allt viktigare för dagens företag att diversifiera sig från konkurrenter och påvisa en god förmåga att tillfredsställa kundernas krav och önskemål. Detta kräver en hög intern effektivitet och en väl strukturerad organisation. Studiens syfte är uppbyggt utifrån detta och analyserar redan befintlig litteratur inom området produktutveckling för att visa på möjligheterna till en effektiv produktutvecklingsmetodik inom tillverkande företag i metallindustrin.  Den insamlade teorin utgör grunden för denna litteraturstudie som presenterar två olika strategier för att angripa ett produktutvecklingsprojekt. Strategierna som presenteras är PBE och SBCE, vilka båda är verksamma inom tillverkningsindustrin idag. Den stora skillnaden strategierna emellan är beslutsfattningen kring de genererade koncepten. PBE innefattar ett tidigt konceptval som sedan utvecklas via ett antal iterationer tills det att utvecklingsprojektets kravspecifikation är uppfylld. Inom SBCE utvecklas flera koncept parallellt med ambitionen att erhålla ny viktig kunskap samtidigt som koncepten optimeras innan ett slutgiltigt beslut fattas. Att etablera någon typ av strategi erbjuder verksamheten ett sätt att arbeta systematiskt och rationellt. Detta medför en medvetenhet i problemlösningen och att det slutgiltiga resultatet påverkas positivt. Vidare visar analysen av den ackumulerade teorin att flexibiliteten är viktig ur ett marknadsperspektiv samt att hanteringen av det mänskliga kapitalet är väsentligt för dagens företag, något som blir möjligt genom SBCE. SBCE är den mest effektiva strategin sett ur ett ledtidsperspektiv när graden av iteration är hög. Strategin tillgodoser också verksamhetens behov av flexibilitet samt hantering och utveckling av det mänskliga kapitalet, vilket gör den till det bästa sättet att angripa ett utvecklingsprojekt. / It is becoming increasingly important for today's companies to diversify themselves from competitors and demonstrate a good ability to satisfy customer requirements and requests. This requires high internal efficiency and a well-structured organization. The purpose of the study is based on this and analyzes already existing literature in the field of product development to demonstrate the possibilities for an effective product development methodology in manufacturing companies in the metal industry. The accumulated theory forms the foundation for this literature study, which presents two different strategies for lighting into a product development project. The strategies presented are PBE and SBCE, both of which are active in the manufacturing industry today. The big difference between the strategies is the decision-making around the generated concepts. PBE includes an early conceptual choice which then is developed through a number of iterations until requirements and requests in the specification sheet, for the specific development project, is met. Within SBCE, several concepts are developed simultaneously with the ambition to acquire new, important knowledge while optimizing the concepts before making a final decision. Establishing some kind of strategy offers the business a way to work systematically and rationally. This brings awareness to the problem solving and that the final result is positively affected. Furthermore, the analysis of the accumulated theory shows that a company’s flexibility is important from a market perspective and that the management of human capital is essential to today's business, which is possible through SBCE. SBCE is the most effective strategy seen from a lead time perspective when the rate of iteration is high. The strategy also meets the needs for flexibility in the organization, as well as the management and development of human capital, making it the best way to light into a development project.

This thesis enters on the development of a point-based statistical shape model relying on correspondence probabilities in a sound mathematical framework. Further focus lies on the integration of the model into a segmentation method where a novel approach is taken by combining an explicitly represented shape prior with an implicitly represented segmentation contour. In medical image analysis, the notion of shape is recognized as an important feature to distinguish and analyse anatomical structures. The modeling of shape realized by the concept of statistical shape models constitutes a powerful tool to facilitate the solutions to analysis, segmentation and reconstruction problems. A statistical shape model tries to optimally represent a set of segmented shape observations of any given organ via a mean shape and a variability model. A fundamental challenge in doing statistics on shapes lies in the determination of correspondences between the shape observations. The prevailing assumption of one-to-one point correspondences seems arguable due to uncertainties of the shape surface representations as well as the general di fficulty of pinpointing exact correspondences. In this thesis, the following solution to the point correspondence problem is derived: For all point pairs, a correspondence probability is computed which amounts to representing the shape surfaces by Mixtures of Gaussians. This approach allows to formulate the model computation in a generative framework where the shape observations are interpreted as randomly generated by the model. Based on that, the computation of the model is then treated as an optimization problem. An algorithm is proposed to optimize for model parameters and observation parameters through a single maximum a posteriori criterion which leads to a mathematically sound and unified framework. The method is evaluated and validated in a series of experiments on synthetic and real data. To do so, adequate performance measures and metrics are defined based on which the quality of the new model is compared to the qualities of a classical point-based model and of an established surface-based model that both rely on one-to-one correspondences. A segmentation algorithm is developed which employs the a priori shape knowledge inherent in the statistical shape model to constrain the segmentation contour to probable shapes. An implicit segmentation sheme is chosen instead of an explicit one, which is beneficial regarding topological exibility and implementational issues. The mathematically sound probabilistic shape model enables the challenging integration of an explicit shape prior into an implicit segmentation scheme in an elegant formulation. A maximum a posteriori estimation is developed of a level set function whose zero level set best separates the organ from the background under a shape constraint introduced by the model. This leads to an energy functional which is minimized with respect to the level set using an Euler-Lagrangian equation. Since both the model and the implicitly defined contour are well suited to represent multi-object shapes, an extension of the algorithm to multi-object segmentation is developed which is integrated into the same probabilistic framework. The novel method is evaluated on kidney and hip joint segmentation.

[pt] Operações booleanas em modelagem 3D são usadas para criar novos modelos ou para modificá-los. Na maioria dos tipos de representação de objetos 3D, estas operações são bastante complexas. Nos últimos anos tem sido muito explorado um novo tipo de modelagem, a modelagem por pontos, que apresenta muitas vantagens em relação às outras representações como maior simplicidade e eficiência. Dois trabalhos exploram as operações booleanas na modelagem por pontos, o trabalho de Adams e Dutré e o trabalho de Pauly et. al. Dada a grande importância deste novo tipo de modelagem e do uso de operações booleanas, esta dissertação apresenta uma introdução à modelagem por pontos, implementa o algoritmo proposto em Adams e Dutré com algumas melhorias e o compara com o método de Pauly et. al. / [en] Boolean operations are used to create or modify models. These operations in the majority of 3D object representations are very complex. In the last years a significant trend in computer graphics has been the shift towards point sampled 3D models due to their advantages over other representations, such as simplicity and efficiency. Two recent works present algorithms to perform interactive boolean operations on point-based models: the work by Adams and Dutré and the work by Pauly et. Al.. Due to great importance of this novel representation and of the use of boolean operations, the present work makes an introduction to point-based representation, implements the algorithm proposed by Adams and Dutré with some improvements, and compares this implementation with the work by Pauly et. al..

Introduction: Number of strata (NoS) is an informative descriptor of forest structure and is therefore useful in forest management. Collection of NoS as well as other forest properties is performed by fieldworkers and could benefit from automation. Objectives: This study investigates automated prediction of NoS from airborne laser scanned point clouds over Swedish forest plots.Methods: A previously suggested approach of using vertical gap probability is compared through experimentation against the geometric neural network PointNet++ configured for ordinal prediction. For both approaches, the mean accuracy is measured for three datasets: coniferous forest, deciduous forest, and a combination of all forests. Results: PointNet++ displayed a better point performance for two out of three datasets, attaining a top mean accuracy of 46.2%. However only the coniferous subset displayed a statistically significant superiority for PointNet++. Conclusion: This study demonstrates the potential of geometric neural networks for data mining of forest properties. The results show that impediments in the data may need to be addressed for further improvements.

Point-based rendering methods have proven to be effective for the display of large point cloud surface models. For a realistic visualization of the models, transparency and shadows are essential features. We propose a method for point cloud rendering with transparency and shadows at interactive rates. Our approach does not require any global or local surface reconstruction method, but operates directly on the point cloud. All passes are executed in image space and no pre-computation steps are required. The underlying technique for our approach is a depth peeling method for point cloud surface representations. Having detected a sorted sequence of surface layers, they can be blended front to back with given opacity values to obtain renderings with transparency. These computation steps achieve interactive frame rates. For renderings with shadows, we determine a point cloud shadow texture that stores for each point of a point cloud whether it is lit by a given light source. The extraction of the layer of lit points is obtained using the depth peeling technique, again. For the shadow texture computation, we also apply a Monte-Carlo integration method to approximate light from an area light source, leading to soft shadows. Shadow computations for point light sources are executed at interactive frame rates. Shadow computations for area light sources are performed at interactive or near-interactive frame rates depending on the approximation quality.

Level-set methods have become a valuable and well-established field of visualization over the last decades. Different implementations addressing different design goals and different data types exist. In particular, level sets can be used to extract isosurfaces from scalar volume data that fulfill certain smoothness criteria. Recently, such an approach has been generalized to operate on unstructured point-based volume data, where data points are not arranged on a regular grid nor are they connected in form of a mesh. Utilizing this new development, one can avoid an interpolation to a regular grid which inevitably introduces interpolation errors. However, the global processing of the level-set function can be slow when dealing with unstructured point-based volume data sets containing several million data points. We propose an improved level-set approach that performs the process of the level-set function locally. As for isosurface extraction we are only interested in the zero level set, values are only updated in regions close to the zero level set. In each iteration of the level-set process, the zero level set is extracted using direct isosurface extraction from unstructured point-based volume data and a narrow band around the zero level set is constructed. The band consists of two parts: an inner and an outer band. The inner band contains all data points within a small area around the zero level set. These points are updated when executing the level set step. The outer band encloses the inner band providing all those neighbors of the points of the inner band that are necessary to approximate gradients and mean curvature. Neighborhood information is obtained using an efficient kd-tree scheme, gradients and mean curvature are estimated using a four-dimensional least-squares fitting approach. Comparing ourselves to the global approach, we demonstrate that this local level-set approach for unstructured point-based volume data achieves a significant speed-up of one order of magnitude for data sets in the range of several million data points with equivalent quality and robustness.

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