Domain adaptation based transfer learning approach for solving PDEs on complex geometries

In machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods are sub-fields within machine learning that are concerned with solving the inescapable problem of insufficient training data by relaxing the domain dependence hypothesis. In this contribution, this issue has been addressed and by making a novel combination of both the methods we develop a computationally efficient and practical algorithm to solve boundary value problems based on nonlinear partial differential equations. We adopt a meshfree analysis framework to integrate the prevailing geometric modelling techniques based on NURBS and present an enhanced deep collocation approach that also plays an important role in the accuracy of solutions. We start with a brief introduction on how these methods expand upon this framework. We observe an excellent agreement between these methods and have shown that how fine-tuning a pre-trained network to a specialized domain may lead to an outstanding performance compare to the existing ones. As proof of concept, we illustrate the performance of our proposed model on several benchmark problems. © 2022, The Author(s)

Testing SPECT Motion Correction Algorithms

Frequently, testing of Single Photon Emission Computed Tomography (SPECT) motion correction algorithms is done either by using simplistic deformations that do not accurately simulate true patient motion or by applying the algorithms directly to data acquired from a real patient, where the true internal motion is unknown. In this work, we describe a way to combine these two approaches by using imaging data acquired from real volunteers to simulate the data that the motion correction algorithms would normally observe. The goal is to provide an assessment framework which can both: simulate realistic SPECT acquisitions that incorporate realistic body deformations and provide a ground truth volume to compare against. Every part of the motion correction algorithm needs to be exercised: from parameter estimation of the motion model, to the final reconstruction results. In order to build the ground truth anthropomorphic numerical phantoms, we acquire high resolution MRI scans and motion observation data of a volunteer in multiple different configurations. We then extract the organ boundaries using thresholding, active contours, and morphology. Phantoms of radioactivity uptake and density inside the body can be generated from these boundaries to be used to simulate SPECT acquisitions. We present results on extraction of the ribs, lungs, heart, spine, and the rest of the soft tissue in the thorax using our segmentation approach. In general, extracting the lungs, heart, and ribs in images that do not contain the spine works well, but the spine could be better extracted using other methods that we discuss. We also go in depth into the software development component of this work, describing the C++ coding framework we used and the High Level Interactive GUI Language (HLING). HLING solved a lot of problems but introduced a fair bit of its own. We include a set of requirements to provide a foundation for the next attempt at developing a declarative and minimally restrictive methodology for writing interactive image processing applications in C++ based on lessons learned during the development of HLING

Mesh modification using deformation gradients

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 117-131).Computer-generated character animation, where human or anthropomorphic characters are animated to tell a story, holds tremendous potential to enrich education, human communication, perception, and entertainment. However, current animation procedures rely on a time consuming and difficult process that requires both artistic talent and technical expertise. Despite the tremendous amount of artistry, skill, and time dedicated to the animation process, there are few techniques to help with reuse. Although individual aspects of animation are well explored, there is little work that extends beyond the boundaries of any one area. As a consequence, the same procedure must be followed for each new character without the opportunity to generalize or reuse technical components. This dissertation describes techniques that ease the animation process by offering opportunities for reuse and a more intuitive animation formulation. A differential specification of arbitrary deformation provides a general representation for adapting deformation to different shapes, computing semantic correspondence between two shapes, and extrapolating natural deformation from a finite set of examples.(cont.) Deformation transfer adds a general-purpose reuse mechanism to the animation pipeline by transferring any deformation of a source triangle mesh onto a different target mesh. The transfer system uses a correspondence algorithm to build a discrete many-to-many mapping between the source and target triangles that permits transfer between meshes of different topology. Results demonstrate retargeting both kinematic poses and non-rigid deformations, as well as transfer between characters of different topological and anatomical structure. Mesh-based inverse kinematics extends the idea of traditional skeleton-based inverse kinematics to meshes by allowing the user to pose a mesh via direct manipulation. The user indicates the dass of meaningful deformations by supplying examples that can be created automatically with deformation transfer, sculpted, scanned, or produced by any other means. This technique is distinguished from traditional animation methods since it avoids the expensive character setup stage. It is distinguished from existing mesh editing algorithms since the user retains the freedom to specify the class of meaningful deformations. Results demonstrate an intuitive interface for posing meshes that requires only a small amount of user effort.by Robert Walker Sumner.Ph.D

Facial Modelling and animation trends in the new millennium : a survey

M.Sc (Computer Science)Facial modelling and animation is considered one of the most challenging areas in the animation world. Since Parke and Waters’s (1996) comprehensive book, no major work encompassing the entire field of facial animation has been published. This thesis covers Parke and Waters’s work, while also providing a survey of the developments in the field since 1996. The thesis describes, analyses, and compares (where applicable) the existing techniques and practices used to produce the facial animation. Where applicable, the related techniques are grouped in the same chapter and described in a chronological fashion, outlining their differences, as well as their advantages and disadvantages. The thesis is concluded by exploratory work towards a talking head for Northern Sotho. Facial animation and lip synchronisation of a fragment of Northern Sotho is done by using software tools primarily designed for English.Computin

A Methodological Approach to Knowledge-Based Engineering Systems for Manufacturing

A survey of implementations of the knowledge-based engineering approach in different technological sectors is presented. The main objectives and techniques of examined applications are pointed out to illustrate the trends and peculiarities for a number of manufacturing field. Existing methods for the development of these engineering systems are then examined in order to identify critical aspects when applied to manufacturing. A new methodological approach is proposed to overcome some specific limitations that emerged from the above-mentioned survey. The aim is to provide an innovative method for the implementation of knowledge-based engineering applications in the field of industrial production. As a starting point, the field of application of the system is defined using a spatial representation. The conceptual design phase is carried out with the aid of a matrix structure containing the most relevant elements of the system and their relations. In particular, objectives, descriptors, inputs and actions are defined and qualified using categorical attributes. The proposed method is then applied to three case studies with different locations in the applicability space. All the relevant elements of the detailed implementation of these systems are described. The relations with assumptions made during the design are highlighted to validate the effectiveness of the proposed method. The adoption of case studies with notably different applications also reveals the versatility in the application of the method

Similarity Assessment and Retrieval of CAD Models

Ph.DDOCTOR OF PHILOSOPH

Hierarchical processing, editing and rendering of acquired geometry

La représentation des surfaces du monde réel dans la mémoire d’une machine peut désormais être obtenue automatiquement via divers périphériques de capture tels que les scanners 3D. Ces nouvelles sources de données, précises et rapides, amplifient de plusieurs ordres de grandeur la résolution des surfaces 3D, apportant un niveau de précision élevé pour les applications nécessitant des modèles numériques de surfaces telles que la conception assistée par ordinateur, la simulation physique, la réalité virtuelle, l’imagerie médicale, l’architecture, l’étude archéologique, les effets spéciaux, l’animation ou bien encore les jeux video. Malheureusement, la richesse de la géométrie produite par ces méthodes induit une grande, voire gigantesque masse de données à traiter, nécessitant de nouvelles structures de données et de nouveaux algorithmes capables de passer à l’échelle d’objets pouvant atteindre le milliard d’échantillons. Dans cette thèse, je propose des solutions performantes en temps et en espace aux problèmes de la modélisation, du traitement géométrique, de l’édition intéractive et de la visualisation de ces surfaces 3D complexes. La méthodologie adoptée pendant l’élaboration transverse de ces nouveaux algorithmes est articulée autour de 4 éléments clés : une approche hiérarchique systématique, une réduction locale de la dimension des problèmes, un principe d’échantillonage-reconstruction et une indépendance à l’énumération explicite des relations topologiques aussi appelée approche basée-points. En pratique, ce manuscrit propose un certain nombre de contributions, parmi lesquelles : une nouvelle structure hiérarchique hybride de partitionnement, l’Arbre Volume-Surface (VS-Tree) ainsi que de nouveaux algorithmes de simplification et de reconstruction ; un système d’édition intéractive de grands objets ; un noyau temps-réel de synthèse géométrique par raffinement et une structure multi-résolution offrant un rendu efficace de grands objets. Ces structures, algorithmes et systèmes forment une chaîne capable de traiter les objets en provenance du pipeline d’acquisition, qu’ils soient représentés par des nuages de points ou des maillages, possiblement non 2-variétés. Les solutions obtenues ont été appliquées avec succès aux données issues des divers domaines d’application précités.Digital representations of real-world surfaces can now be obtained automatically using various acquisition devices such as 3D scanners and stereo camera systems. These new fast and accurate data sources increase 3D surface resolution by several orders of magnitude, borrowing higher precision to applications which require digital surfaces. All major computer graphics applications can take benefit of this automatic modeling process, including: computer-aided design, physical simulation, virtual reality, medical imaging, architecture, archaeological study, special effects, computer animation and video games. Unfortunately, the richness of the geometry produced by these media comes at the price of a large, possibility gigantic, amount of data which requires new efficient data structures and algorithms offering scalability for processing such objects. This thesis proposes time and space efficient solutions for modeling, editing and rendering such complex surfaces, solving these problems with new algorithms sharing 4 fundamental elements: a systematic hierarchical approach, a local dimension reduction, a sampling-reconstruction paradigm and a pointbased basis. Basically, this manuscript proposes several contributions, including: a new hierarchical space subdivision structure, the Volume-Surface Tree, for geometry processing such as simplification and reconstruction; a streaming system featuring new algorithms for interactive editing of large objects, an appearancepreserving multiresolution structure for efficient rendering of large point-based surfaces, and a generic kernel for real-time geometry synthesis by refinement. These elements form a pipeline able to process acquired geometry, either represented by point clouds or non-manifold meshes. Effective results have been successfully obtained with data coming from the various applications mentioned

Geometric modelling and shape optimisation of pharmaceutical tablets. Geometric modelling and shape optimisation of pharmaceutical tablets using partial differential equations.

Pharmaceutical tablets have been the most dominant form for drug delivery and they need to be strong enough to withstand external stresses due to packaging and loading conditions before use. The strength of the produced tablets, which is characterised by their compressibility and compactibility, is usually deter-mined through a physical prototype. This process is sometimes quite expensive and time consuming. Therefore, simulating this process before hand can over-come this problem. A technique for shape modelling of pharmaceutical tablets based on the use of Partial Differential Equations is presented in this thesis. The volume and the sur-face area of the generated parametric tablet in various shapes have been es-timated numerically. This work also presents an extended formulation of the PDE method to a higher dimensional space by increasing the number of pa-rameters responsible for describing the surface in order to generate a solid tab-let. The shape and size of the generated solid tablets can be changed by ex-ploiting the analytic expressions relating the coefficients associated with the PDE method. The solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load has been utilised in order to model a displace-ment component of a compressed PDE-based representation of a flat-faced round tablet. The simulation results, which are analysed using the Heckel model, show that the developed model is capable of predicting the compressibility of pharmaceutical powders since it fits the experimental data accurately. The opti-mal design of pharmaceutical tablets with particular volume and maximum strength has been obtained using an automatic design optimisation which is performed by combining the PDE method and a standard method for numerical optimisation

A new 3D modelling paradigm for discrete model

Until few years ago, 3D modelling was a topic confined into a professional environment. Nowadays technological innovations, the 3D printer among all, have attracted novice users to this application field. This sudden breakthrough was not supported by adequate software solutions. The 3D editing tools currently available do not assist the non-expert user during the various stages of generation, interaction and manipulation of 3D virtual models. This is mainly due to the current paradigm that is largely supported by two-dimensional input/output devices and strongly affected by obvious geometrical constraints. We have identified three main phases that characterize the creation and management of 3D virtual models. We investigated these directions evaluating and simplifying the classic editing techniques in order to propose more natural and intuitive tools in a pure 3D modelling environment. In particular, we focused on freehand sketch-based modelling to create 3D virtual models, interaction and navigation in a 3D modelling environment and advanced editing tools for free-form deformation and objects composition. To pursuing these goals we wondered how new gesture-based interaction technologies can be successfully employed in a 3D modelling environments, how we could improve the depth perception and the interaction in 3D environments and which operations could be developed to simplify the classical virtual models editing paradigm. Our main aims were to propose a set of solutions with which a common user can realize an idea in a 3D virtual model, drawing in the air just as he would on paper. Moreover, we tried to use gestures and mid-air movements to explore and interact in 3D virtual environment, and we studied simple and effective 3D form transformations. The work was carried out adopting the discrete representation of the models, thanks to its intuitiveness, but especially because it is full of open challenges