Computer Science

Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions, or they do not correctly account for intrinsic curvature, which leads to unnatural-looking behavior away from the boundary. This leads to an unfortunate trade-off: one can either have natural behavior in the interior, or a distortion-free result at the boundary, but not both. We introduce a generalized Hessian energy for curved surfaces, expressed in terms of the covariant one-form Dirichlet energy, the Gaussian curvature, and the exterior derivative. Energy minimizers solve the Laplace-Beltrami biharmonic equation, correctly accounting for intrinsic curvature, leading to natural-looking isolines. On the boundary, minimizers are as-linear-as-possible, which reduces the distortion of isolines at the boundary. We discretize the covariant one-form Dirichlet energy using Crouzeix-Raviart finite elements, arriving at a discrete formulation of the Hessian energy for applications on curved surfaces. We observe convergence of the discretization in our experiments.

A novel square equal-area map projection is proposed. The projection combines closed-form forward and inverse solutions with relatively low angular distortion and minimal cusps, a combination of properties not manifested by any previously published square equal-area projection. Thus, the new projection has lower angular distortion than any previously published square equal-area projection with a closed-form solution. Utilizing a quincuncial arrangement, the new projection places the north pole at the center of the square and divides the south pole between its four corners; the projection can be seamlessly tiled. The existence of closed-form solutions makes the projection suitable for real-time visualization applications, both in cartography and in other areas, such as for the display of panoramic images.

Synthetic apertures find applications in many fields, such as radar, radio telescopes, microscopy, sonar, ultrasound, LiDAR, and optical imaging. They approximate the signal of a single hypothetical wide aperture sensor with either an array of static small aperture sensors or a single moving small aperture sensor. Common sense in synthetic aperture sampling is that a dense sampling pattern within a wide aperture is required to reconstruct a clear signal. In this article we show that there exists practical limits to both, synthetic aperture size and number of samples for the application of occlusion removal. This leads to an understanding on how to design synthetic aperture sampling patterns and sensors in a most optimal and practically efficient way. We apply our findings to airborne optical sectioning which uses camera drones and synthetic aperture imaging to computationally remove occluding vegetation or trees for inspecting ground surfaces.

{When visualizing data in a realistically rendered 3D virtual environment, it is often important to represent not only the 3D scene but also overlaid information about additional, abstract data. These overlays must be usefully visible, i.e. be readable enough to convey the information they represent, but remain unobtrusive to avoid cluttering the view. We take a step toward establishing guidelines for designing such overlays by studying the relationship between three different patterns (filled, striped and dotted patterns), two pattern densities, the presence or not of a solid outline, two types of background (blank and with trees), and the opacity of the overlay. For each combination of factors, participants set the faintest and the strongest acceptable opacity values. Results from this first study suggest that i) ranges of acceptable opacities are around 20-70%, that ii) ranges can be extended by 5% by using an outline, and that iii) ranges shift based on features like pattern and density.

Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and computer vision. Relative to Euclidean distance computation, these tasks are complicated by the influence of curvature on the behavior of shortest paths, as well as the fact that the representation of the domain may itself be approximate. In spite of the difficulty of this problem, recent literature has developed a wide variety of sophisticated methods that enable rapid queries of geodesic information, even on relatively large models. This survey reviews the major categories of approaches to the computation of geodesic paths and distances, highlighting common themes and opportunities for future improvement.

Researchers have now achieved great success on dealing with 2D images using deep learning. In recent years, 3D computer vision and Geometry Deep Learning gain more and more attention. Many advanced techniques for 3D shapes have been proposed for different applications. Unlike 2D images, which can be uniformly represented by regular grids of pixels, 3D shapes have various representations, such as depth and multi-view images, voxel-based representation, point-based representation, mesh-based representation, implicit surface representation, etc. However, the performance for different applications largely depends on the representation used, and there is no unique representation that works well for all applications. Therefore, in this survey, we review recent development in deep learning for 3D geometry from a representation perspective, summarizing the advantages and disadvantages of different representations in different applications. We also present existing datasets in these representations and further discuss future research directions.

This thesis surveys the research in patch-based synthesis and algorithms for finding correspondences between small local regions of images. We additionally explore a large kind of applications of this new fast randomized matching technique. One of the algorithms we have studied in particular is PatchMatch, can find similar regions or "patches" of an image one to two orders of magnitude faster than previous techniques. The algorithmic program is driven by applying mathematical properties of nearest neighbors in natural images. It is observed that neighboring correspondences tend to be similar or "coherent" and use this observation in algorithm in order to quickly converge to an approximate solution. The algorithm is the most general form can find k-nearest neighbor matching, using patches that translate, rotate, or scale, using arbitrary descriptors, and between two or more images. Speed-ups are obtained over various techniques in an exceeding range of those areas. We have explored many applications of PatchMatch matching algorithm. In computer graphics, we have explored removing unwanted objects from images, seamlessly moving objects in images, changing image aspect ratios, and video summarization. In computer vision we have explored denoising images, object detection, detecting image forgeries, and detecting symmetries. We conclude by discussing the restrictions of our algorithmic program, GPU implementation and areas for future analysis.

Many computer science disciplines (e.g., combinatorial optimization, natural language processing, and information retrieval) use standard or established test suites for evaluating algorithms. In visualization, similar approaches have been adopted in some areas (e.g., volume visualization), while user testimonies and empirical studies have been the dominant means of evaluation in most other areas, such as designing colormaps. In this paper, we propose to establish a test suite for evaluating the design of colormaps. With such a suite, the users can observe the effects when different continuous colormaps are applied to planar scalar fields that may exhibit various characteristic features, such as jumps, local extrema, ridge or valley lines, different distributions of scalar values, different gradients, different signal frequencies, different levels of noise, and so on. The suite also includes an expansible collection of real-world data sets including the most popular data for colormap testing in the visualization literature. The test suite has been integrated into a web-based application for creating continuous colormaps (this https URL), facilitating close inter-operation between design and evaluation processes. This new facility complements traditional evaluation methods such as user testimonies and empirical studies.

In this work, a new and innovative way of spatial computing that appeared recently in the bibliography called True Augmented Reality (AR), is employed in cultural heritage preservation. This innovation could be adapted by the Virtual Museums of the future to enhance the quality of experience. It emphasises, the fact that a visitor will not be able to tell, at a first glance, if the artefact that he/she is looking at is real or not and it is expected to draw the visitors' interest. True AR is not limited to artefacts but extends even to buildings or life-sized character simulations of statues. It provides the best visual quality possible so that the users will not be able to tell the real objects from the augmented ones. Such applications can be beneficial for future museums, as with True AR, 3D models of various exhibits, monuments, statues, characters and buildings can be reconstructed and presented to the visitors in a realistic and innovative way. We also propose our Virtual Reality Sample application, a True AR playground featuring basic components and tools for generating interactive Virtual Museum applications, alongside a 3D reconstructed character (the priest of Asinou church) facilitating the storyteller of the augmented experience.

Smoothed particle hydrodynamics (SPH) has been extensively studied in computer graphics to animate fluids with versatile effects. However, SPH still suffers from two numerical difficulties: the particle deficiency problem, which will deteriorate the simulation accuracy, and the particle clumping problem, which usually leads to poor stability of particle simulations. We propose to solve these two problems by developing an approximate projection method for incompressible free-surface flows under a variational staggered particle framework. After particle discretization, we first categorize all fluid particles into four subsets. Then according to the classification, we propose to solve the particle deficiency problem by analytically imposing free surface boundary conditions on both the Laplacian operator and the source term. To address the particle clumping problem, we propose to extend the Taylor-series consistent pressure gradient model with kernel function correction and semi-analytical boundary conditions. Compared to previous approximate projection method [1], our incompressibility solver is stable under both compressive and tensile stress states, no pressure clumping or iterative density correction (e.g., a density constrained pressure approach) is necessary to stabilize the solver anymore. Motivated by the Helmholtz free energy functional, we additionally introduce an iterative particle shifting algorithm to improve the accuracy. It significantly reduces particle splashes near the free surface. Therefore, high-fidelity simulations of the formation and fragmentation of liquid jets and sheets are obtained for both the two-jets and milk-crown examples.