Non-rigid registration of 2-D/3-D dynamic data with feature alignment

In this work, we are computing the matching between 2D manifolds and 3D manifolds with temporal constraints, that is we are computing the matching among a time sequence of 2D/3D manifolds. It is solved by mapping all the manifolds to a common domain, then build their matching by composing the forward mapping and the inverse mapping. At first, we solve the matching problem between 2D manifolds with temporal constraints by using mesh-based registration method. We propose a surface parameterization method to compute the mapping between the 2D manifold and the common 2D planar domain. We can compute the matching among the time sequence of deforming geometry data through this common domain. Compared with previous work, our method is independent of the quality of mesh elements and more efficient for the time sequence data. Then we develop a global intensity-based registration method to solve the matching problem between 3D manifolds with temporal constraints. Our method is based on a 4D(3D+T) free-from B-spline deformation model which has both spatial and temporal smoothness. Compared with previous 4D image registration techniques, our method avoids some local minimum. Thus it can be solved faster and achieve better accuracy of landmark point predication. We demonstrate the efficiency of these works on the real applications. The first one is applied to the dynamic face registering and texture mapping. The second one is applied to lung tumor motion tracking in the medical image analysis. In our future work, we are developing more efficient mesh-based 4D registration method. It can be applied to tumor motion estimation and tracking, which can be used to calculate the read dose delivered to the lung and surrounding tissues. Thus this can support the online treatment of lung cancer radiotherapy

Local, Smooth, and Consistent Jacobi Set Simplification

The relation between two Morse functions defined on a common domain can be studied in terms of their Jacobi set. The Jacobi set contains points in the domain where the gradients of the functions are aligned. Both the Jacobi set itself as well as the segmentation of the domain it induces have shown to be useful in various applications. Unfortunately, in practice functions often contain noise and discretization artifacts causing their Jacobi set to become unmanageably large and complex. While there exist techniques to simplify Jacobi sets, these are unsuitable for most applications as they lack fine-grained control over the process and heavily restrict the type of simplifications possible. In this paper, we introduce a new framework that generalizes critical point cancellations in scalar functions to Jacobi sets in two dimensions. We focus on simplifications that can be realized by smooth approximations of the corresponding functions and show how this implies simultaneously simplifying contiguous subsets of the Jacobi set. These extended cancellations form the atomic operations in our framework, and we introduce an algorithm to successively cancel subsets of the Jacobi set with minimal modifications according to some user-defined metric. We prove that the algorithm is correct and terminates only once no more local, smooth and consistent simplifications are possible. We disprove a previous claim on the minimal Jacobi set for manifolds with arbitrary genus and show that for simply connected domains, our algorithm reduces a given Jacobi set to its simplest configuration.Comment: 24 pages, 19 figure

Vector field processing on triangle meshes

While scalar fields on surfaces have been staples of geometry processing, the use of tangent vector fields has steadily grown in geometry processing over the last two decades: they are crucial to encoding directions and sizing on surfaces as commonly required in tasks such as texture synthesis, non-photorealistic rendering, digital grooming, and meshing. There are, however, a variety of discrete representations of tangent vector fields on triangle meshes, and each approach offers different tradeoffs among simplicity, efficiency, and accuracy depending on the targeted application. This course reviews the three main families of discretizations used to design computational tools for vector field processing on triangle meshes: face-based, edge-based, and vertex-based representations. In the process of reviewing the computational tools offered by these representations, we go over a large body of recent developments in vector field processing in the area of discrete differential geometry. We also discuss the theoretical and practical limitations of each type of discretization, and cover increasingly-common extensions such as n-direction and n-vector fields. While the course will focus on explaining the key approaches to practical encoding (including data structures) and manipulation (including discrete operators) of finite-dimensional vector fields, important differential geometric notions will also be covered: as often in Discrete Differential Geometry, the discrete picture will be used to illustrate deep continuous concepts such as covariant derivatives, metric connections, or Bochner Laplacians

Heterogeneous volumetric data mapping and its medical applications

With the advance of data acquisition techniques, massive solid geometries are being collected routinely in scientific tasks, these complex and unstructured data need to be effectively correlated for various processing and analysis. Volumetric mapping solves bijective low-distortion correspondence between/among 3D geometric data, and can serve as an important preprocessing step in many tasks in compute-aided design and analysis, industrial manufacturing, medical image analysis, to name a few. This dissertation studied two important volumetric mapping problems: the mapping of heterogeneous volumes (with nonuniform inner structures/layers) and the mapping of sequential dynamic volumes. To effectively handle heterogeneous volumes, first, we studied the feature-aligned harmonic volumetric mapping. Compared to previous harmonic mapping, it supports the point, curve, and iso-surface alignment, which are important low-dimensional structures in heterogeneous volumetric data. Second, we proposed a biharmonic model for volumetric mapping. Unlike the conventional harmonic volumetric mapping that only supports positional continuity on the boundary, this new model allows us to have higher order continuity $C^1$ along the boundary surface. This suggests a potential model to solve the volumetric mapping of complex and big geometries through divide-and-conquer. We also studied the medical applications of our volumetric mapping in lung tumor respiratory motion modeling. We were building an effective digital platform for lung tumor radiotherapy based on effective volumetric CT/MRI image matching and analysis. We developed and integrated in this platform a set of geometric/image processing techniques including advanced image segmentation, finite element meshing, volumetric registration and interpolation. The lung organ/tumor and surrounding tissues are treated as a heterogeneous region and a dynamic 4D registration framework is developed for lung tumor motion modeling and tracking. Compared to the previous 3D pairwise registration, our new 4D parameterization model leads to a significantly improved registration accuracy. The constructed deforming model can hence approximate the deformation of the tissues and tumor

Visual Techniques for Geological Fieldwork Using Mobile Devices

Visual techniques in general and 3D visualisation in particular have seen considerable adoption within the last 30 years in the geosciences and geology. Techniques such as volume visualisation, for analysing subsurface processes, and photo-coloured LiDAR point-based rendering, to digitally explore rock exposures at the earth’s surface, were applied within geology as one of the first adopting branches of science. A large amount of digital, geological surface- and volume data is nowadays available to desktop-based workflows for geological applications such as hydrocarbon reservoir exploration, groundwater modelling, CO2 sequestration and, in the future, geothermal energy planning. On the other hand, the analysis and data collection during fieldwork has yet to embrace this ”digital revolution”: sedimentary logs, geological maps and stratigraphic sketches are still captured in each geologist’s individual fieldbook, and physical rocks samples are still transported to the lab for subsequent analysis. Is this still necessary, or are there extended digital means of data collection and exploration in the field ? Are modern digital interpretation techniques accurate and intuitive enough to relevantly support fieldwork in geology and other geoscience disciplines ? This dissertation aims to address these questions and, by doing so, close the technological gap between geological fieldwork and office workflows in geology. The emergence of mobile devices and their vast array of physical sensors, combined with touch-based user interfaces, high-resolution screens and digital cameras provide a possible digital platform that can be used by field geologists. Their ubiquitous availability increases the chances to adopt digital workflows in the field without additional, expensive equipment. The use of 3D data on mobile devices in the field is furthered by the availability of 3D digital outcrop models and the increasing ease of their acquisition. This dissertation assesses the prospects of adopting 3D visual techniques and mobile devices within field geology. The research of this dissertation uses previously acquired and processed digital outcrop models in the form of textured surfaces from optical remote sensing and photogrammetry. The scientific papers in this thesis present visual techniques and algorithms to map outcrop photographs in the field directly onto the surface models. Automatic mapping allows the projection of photo interpretations of stratigraphy and sedimentary facies on the 3D textured surface while providing the domain expert with simple-touse, intuitive tools for the photo interpretation itself. The developed visual approach, combining insight from all across the computer sciences dealing with visual information, merits into the mobile device Geological Registration and Interpretation Toolset (GRIT) app, which is assessed on an outcrop analogue study of the Saltwick Formation exposed at Whitby, North Yorkshire, UK. Although being applicable to a diversity of study scenarios within petroleum geology and the geosciences, the particular target application of the visual techniques is to easily provide field-based outcrop interpretations for subsequent construction of training images for multiple point statistics reservoir modelling, as envisaged within the VOM2MPS project. Despite the success and applicability of the visual approach, numerous drawbacks and probable future extensions are discussed in the thesis based on the conducted studies. Apart from elaborating on more obvious limitations originating from the use of mobile devices and their limited computing capabilities and sensor accuracies, a major contribution of this thesis is the careful analysis of conceptual drawbacks of established procedures in modelling, representing, constructing and disseminating the available surface geometry. A more mathematically-accurate geometric description of the underlying algebraic surfaces yields improvements and future applications unaddressed within the literature of geology and the computational geosciences to this date. Also, future extensions to the visual techniques proposed in this thesis allow for expanded analysis, 3D exploration and improved geological subsurface modelling in general.publishedVersio