A prototype system to keep track of the viewpoints and information in the independent views was implemented on MVDE hardware to support discussions on future command and control environments and to provide the necessary framework for conducting empirical studies (Paper II). Another prototype, the in situ tomographic display, was developed to support presentation of spatial 3D data (e.g., temperature or airflow) in 2D views in situ with working environments (Paper III). In addition to the visualization systems, a technique for high precision pen-based interaction in rear-projection display environments -- the PixelActiveSurface -- was developed (Papers IV and V).
The empirical studies evaluate how new forms of visualization in MVDEs with independent views affect the way information is perceived and can be shared in collaboration. The conclusion is that multiple independent views can provide more effective and efficient visualization when the following conditions are met: text is oriented towards the viewer (Paper VI), different aspects of information are coordinated between different views of the same display (Paper VIII) and correct views of 3D models are used to compare ordinal information and relations in spatial data (Paper VII). However, for the techniques to support co-located work efficiently, it is necessary that the type of work and the task to be solved are first properly analyzed and understood (Papers VII and IX).
This thesis presents methods for interactive segmentation and visualization where true 3D interaction with haptic feedback and stereo graphics is used. Well-known segmentation methods such as fast marching, fuzzy connectedness, live-wire, and deformable models, have been tailored and extended for implementation in a 3D environment where volume visualization and haptics are used to guide the user. The visualization is accelerated with graphics hardware and therefore allows for volume rendering in stereo at interactive rates. The haptic feedback is rendered with constraint-based direct volume haptics in order to convey information about the data that is hard to visualize and thereby facilitate the interaction. The methods have been applied to real medical images, e.g., 3D liver CT data and 4D breast MR data with good results. To provide a tool for future work in this area, a software toolkit containing the implementations of the developed methods has been made publicly available.
Efim Khalimsky's topology on the integers, invented in the 1970s, is a digital counterpart of the Euclidean topology on the real line. The Khalimsky topology became widely known to researchers in digital geometry and computer imagery during the early 1990s.
Suppose that a continuous function is defined on a subspace of an n-dimensional Khalimsky space. One question to ask is whether this function can be extended to a continuous function defined on the whole space. We solve this problem. A related problem is to characterize the subspaces on which every continuous function can be extended. Also this problem is solved.
We generalize and solve the extension problem for integer-valued, Khalimsky-continuous functions defined on arbitrary smallest-neighborhood spaces, also called Alexandrov spaces.
The notion of a digital straight line was clarified in 1974 by Azriel Rosenfeld. We introduce another type of digital straight line, a line that respects the Khalimsky topology in the sense that a line is a topological embedding of the Khalimsky line into the Khalimsky plane.
In higher dimensions, we generalize this construction to digital Khalimsky hyperplanes, surfaces and curves by digitization of real objects. In particular we study approximation properties and topological separation properties.
The last paper is about Khalimsky manifolds, spaces that are locally homeomorphic to n-dimensional Khalimsky space. We study different definitions and address basic questions such as uniqueness of dimension and existence of certain manifolds.
The world is 3D and modern imaging methods such as confocal microscopy provide 3D images. Hence, a large part of the work has dealt with the development of new and improved methods for quantitative analysis of 3D images, in particular fluorescently labeled skeletal muscle cells.
A geometrical model for robust segmentation of skeletal muscle fibers was developed. Images of the multinucleated muscle cells were pre-processed using a novel spatially modulated transform, producing images with reduced complexity and facilitating easy nuclei segmentation. Fibers from several mammalian species were modeled and features were computed based on cell nuclei positions. Features such as myonuclear domain size and nearest neighbor distance, were shown to correlate with body mass, and femur length. Human muscle fibers from young and old males, and females, were related to fiber type and extracted features, where myonuclear domain size variations were shown to increase with age irrespectively of fiber type and gender.
A segmentation method for severely clustered point-like signals was developed and applied to images of fluorescent probes, quantifying the amount and location of mitochondrial DNA within cells. A synthetic cell model was developed, to provide a controllable golden standard for performance evaluation of both expert manual and fully automated segmentations. The proposed method matches the correctness achieved by manual quantification.
An interactive segmentation procedure was successfully applied to treated testicle sections of boar, showing how a common industrial plastic softener significantly affects testosterone concentrations.
The two-dimensional hexagonal grid has some advantages over the traditionally used square grid. For example, less samples are needed to get the same reconstruction quality, it is less rotational dependent, and each picture element has only one type of neighbor which simplifies many algorithms. The corresponding three-dimensional grids are the face-centered cubic (fcc) grid and the body-centered cubic (bcc) grids.
In this thesis, image representations using non-standard grids is examined. The focus is on the fcc and bcc grids and tools for processing images on these grids, but distance functions and related algorithms (distance transforms and various representations of objects) are defined in a general framework allowing any point-lattice in any dimension. Formulas for point-to-point distance and conditions for metricity are given in the general case and parameter optimization is presented for the fcc and bcc grids. Some image acquisition and visualization techniques for the fcc and bcc grids are also presented. More theoretical results define distance functions for grids of arbitrary dimensions.
Less samples are needed to represent images on non-standard grids. Thus, the huge amount of data generated by for example computerized tomography can be reduced by representating the images on non-standard grids such as the fcc or bcc grids. The thesis gives a tool-box that can be used to acquire, process, and visualize images on high-dimensional, non-standard grids.