Interactive visualization tools for topological exploration

Thesis (Ph.D.) - Indiana University, Computer Science, 1992This thesis concerns using computer graphics methods to visualize mathematical objects. Abstract mathematical concepts are extremely difficult to visualize, particularly when higher dimensions are involved; I therefore concentrate on subject areas such as the topology and geometry of four dimensions which provide a very challenging domain for visualization techniques. In the first stage of this research, I applied existing three-dimensional computer graphics techniques to visualize projected four-dimensional mathematical objects in an interactive manner. I carried out experiments with direct object manipulation and constraint-based interaction and implemented tools for visualizing mathematical transformations. As an application, I applied these techniques to visualizing the conjecture known as Fermat's Last Theorem. Four-dimensional objects would best be perceived through four-dimensional eyes. Even though we do not have four-dimensional eyes, we can use computer graphics techniques to simulate the effect of a virtual four-dimensional camera viewing a scene where four-dimensional objects are being illuminated by four-dimensional light sources. I extended standard three-dimensional lighting and shading methods to work in the fourth dimension. This involved replacing the standard "z-buffer" algorithm by a "w-buffer" algorithm for handling occlusion, and replacing the standard "scan-line" conversion method by a new "scan-plane" conversion method. Furthermore, I implemented a new "thickening" technique that made it possible to illuminate surfaces correctly in four dimensions. Our new techniques generate smoothly shaded, highlighted view-volume images of mathematical objects as they would appear from a four-dimensional viewpoint. These images reveal fascinating structures of mathematical objects that could not be seen with standard 3D computer graphics techniques. As applications, we generated still images and animation sequences for mathematical objects such as the Steiner surface, the four-dimensional torus, and a knotted 2-sphere. The images of surfaces embedded in 4D that have been generated using our methods are unique in the history of mathematical visualization. Finally, I adapted these techniques to visualize volumetric data (3D scalar fields) generated by other scientific applications. Compared to other volume visualization techniques, this method provides a new approach that researchers can use to look at and manipulate certain classes of volume data

Detailed and Practical 3D Reconstruction with Advanced Photometric Stereo Modelling

Object 3D reconstruction has always been one of the main objectives of computer vision. After many decades of research, most techniques are still unsuccessful at recovering high resolution surfaces, especially for objects with limited surface texture. Moreover, most shiny materials are particularly hard to reconstruct. Photometric Stereo (PS), which operates by capturing multiple images under changing illumination has traditionally been one of the most successful techniques at recovering a large amount of surface details, by exploiting the relationship between shading and local shape. However, using PS has been highly impractical because most approaches are only applicable in a very controlled lab setting and limited to objects experiencing diffuse reflection. Nevertheless, recent advances in differential modelling have made complicated Photometric Stereo models possible and variational optimisations for these kinds of models show remarkable resilience to real world imperfections such as non-Gaussian noise and other outliers. Thus, a highly accurate, photometric-based reconstruction system is now possible. The contribution of this thesis is threefold. First of all, the Photometric Stereo model is extended in order to be able to deal with arbitrary ambient lighting. This is a step towards acquisition in a non-fully controlled lab setting. Secondly, the need for a priori knowledge of the light source brightness and attenuation characteristics is relaxed as an alternating optimisation procedure is proposed which is able to estimate these parameters. This extension allows for quick acquisition with inexpensive LEDs that exhibit unpredictable illumination characteristics (flickering etc). Finally, a volumetric parameterisation is proposed which allows one to tackle the multi-view Photometric Stereo problem in a similar manner, in a simple unified differential model. This final extension allows for complete object reconstruction merging information from multiple images taken from multiple viewpoints and variable illumination. The theoretical work in this thesis is experimentally evaluated in a number of challenging real world experiments, with data captured by custom-made hardware. In addition, the applicability of the generality of the proposed models is demonstrated by presenting a differential model for the shape of polarisation problem, which leads to a unified optimisation problem, fusing information from both methods. This allows for the acquisition of geometrical information about objects such as semi-transparent glass, hitherto hard to deal with

Shadow segmentation and tracking in real-world conditions

Visual information, in the form of images and video, comes from the interaction of light with objects. Illumination is a fundamental element of visual information. Detecting and interpreting illumination effects is part of our everyday life visual experience. Shading for instance allows us to perceive the three-dimensional nature of objects. Shadows are particularly salient cues for inferring depth information. However, we do not make any conscious or unconscious effort to avoid them as if they were an obstacle when we walk around. Moreover, when humans are asked to describe a picture, they generally omit the presence of illumination effects, such as shadows, shading, and highlights, to give a list of objects and their relative position in the scene. Processing visual information in a way that is close to what the human visual system does, thus being aware of illumination effects, represents a challenging task for computer vision systems. Illumination phenomena interfere in fact with fundamental tasks in image analysis and interpretation applications, such as object extraction and description. On the other hand, illumination conditions are an important element to be considered when creating new and richer visual content that combines objects from different sources, both natural and synthetic. When taken into account, illumination effects can play an important role in achieving realism. Among illumination effects, shadows are often integral part of natural scenes and one of the elements contributing to naturalness of synthetic scenes. In this thesis, the problem of extracting shadows from digital images is discussed. A new analysis method for the segmentation of cast shadows in still and moving images without the need of human supervision is proposed. The problem of separating moving cast shadows from moving objects in image sequences is particularly relevant for an always wider range of applications, ranging from video analysis to video coding, and from video manipulation to interactive environments. Therefore, particular attention has been dedicated to the segmentation of shadows in video. The validity of the proposed approach is however also demonstrated through its application to the detection of cast shadows in still color images. Shadows are a difficult phenomenon to model. Their appearance changes with changes in the appearance of the surface they are cast upon. It is therefore important to exploit multiple constraints derived from the analysis of the spectral, geometric and temporal properties of shadows to develop effective techniques for their extraction. The proposed method combines an analysis of color information and of photometric invariant features to a spatio-temporal verification process. With regards to the use of color information for shadow analysis, a complete picture of the existing solutions is provided, which points out the fundamental assumptions, the adopted color models and the link with research problems such as computational color constancy and color invariance. The proposed spatial verification does not make any assumption about scene geometry nor about object shape. The temporal analysis is based on a novel shadow tracking technique. On the basis of the tracking results, a temporal reliability estimation of shadows is proposed which allows to discard shadows which do not present time coherence. The proposed approach is general and can be applied to a wide class of applications and input data. The proposed cast shadow segmentation method has been evaluated on a number of different video data representing indoor and outdoor real-world environments. The obtained results have confirmed the validity of the approach, in particular its ability to deal with different types of content and its robustness to different physically important independent variables, and have demonstrated the improvement with respect to the state of the art. Examples of application of the proposed shadow segmentation tool to the enhancement of video object segmentation, tracking and description operations, and to video composition, have demonstrated the advantages of a shadow-aware video processing

Investigating the use of 3D digitisation for public facing applications in cultural heritage institutions

This thesis contains research into the use of 3D digitisation technologies by cultural heritage institutions in public facing applications. It is particularly interested in those technologies that can be adopted by institutions with limited budget and no previous experience in 3D digitisation. Whilst there has been research in the area of 3D imaging by museums and cultural heritage institutions, the majority is concerned with the use of the technology for academic or professional, curatorial purposes and on technical comparisons of the various technologies used for capture. Similarly, research conducted on the use of 3D models for public facing and public engagement applications has tended to focus on the various capture technologies, while little has been published on processing raw data for public facing applications – a time-consuming and potentially costly procedure. This research will investigate the issues encountered through the entire 3D digitisation workflow, from capture through processing to dissemination, focusing on the specific problems inherent in public facing projects and the heterogeneous and often problematic nature of museum objects. There has been little research published on the efficacy of 3D models both as providers of informational content and as public engagement tools used to fulfil a cultural heritage institution’s public facing remit. This research assesses the utility of interactive 3D models, as well as rendered animations of 3D content used as in-gallery exhibits and disseminated online. It finds that there is a prima facie case for believing that 3D models may be used to further a museum’s engagement and educational aims, and that there is an appetite among the general public for the use of this type of content in cultural heritage applications. The research will also compare a variety of methods for assessing the success of models

Material Visualisation for Virtual Reality: The Perceptual Investigations

Material representation plays a significant role in design visualisation and evaluation. On one hand, the simulated material properties determine the appearance of product prototypes in digitally rendered scenes. On the other hand, those properties are perceived by the viewers in order to make important design decisions. As an approach to simulate a more realistic environment, Virtual Reality (VR) provides users a vivid impression of depth and embodies them into an immersive environment. However, the scientific understanding of material perception and its applications in VR is still fairly limited. This leads to this thesis’s research question on whether the material perception in VR is different from that in traditional 2D displays, as well as the potential of using VR as a design tool to facilitate material evaluation.       This thesis is initiated from studying the perceptual difference of rendered materials between VR and traditional 2D viewing modes. Firstly, through a pilot study, it is confirmed that users have different perceptual experiences of the same material in the two viewing modes. Following that initial finding, the research investigates in more details the perceptual difference with psychophysics methods, which help in quantifying the users’ perceptual responses. Using the perceptual scale as a measuring means, the research analyses the users’ judgment and recognition of the material properties under VR and traditional 2D display environments. In addition, the research also elicits the perceptual evaluation criteria to analyse the emotional aspects of materials. The six perceptual criteria are in semantic forms, including rigidity, formality, fineness, softness, modernity, and irregularity.       The results showed that VR could support users in making a more refined judgment of material properties. That is to say, the users perceive better the minute changes of material properties under immersive viewing conditions. In terms of emotional aspects, VR is advantageous in signifying the effects induced by visual textures, while the 2D viewing mode is more effective for expressing the characteristics of plain surfaces. This thesis has contributed to the deeper understanding of users’ perception of material appearances in Virtual Reality, which is critical in achieving an effective design visualisation using such a display medium

Modeling and Simulation in Engineering

This book provides an open platform to establish and share knowledge developed by scholars, scientists, and engineers from all over the world, about various applications of the modeling and simulation in the design process of products, in various engineering fields. The book consists of 12 chapters arranged in two sections (3D Modeling and Virtual Prototyping), reflecting the multidimensionality of applications related to modeling and simulation. Some of the most recent modeling and simulation techniques, as well as some of the most accurate and sophisticated software in treating complex systems, are applied. All the original contributions in this book are jointed by the basic principle of a successful modeling and simulation process: as complex as necessary, and as simple as possible. The idea is to manipulate the simplifying assumptions in a way that reduces the complexity of the model (in order to make a real-time simulation), but without altering the precision of the results