Multi-scale and multi-spectral shape analysis: from 2d to 3d

Shape analysis is a fundamental aspect of many problems in computer graphics and computer vision, including shape matching, shape registration, object recognition and classification. Since the SIFT achieves excellent matching results in 2D image domain, it inspires us to convert the 3D shape analysis to 2D image analysis using geometric maps. However, the major disadvantage of geometric maps is that it introduces inevitable, large distortions when mapping large, complex and topologically complicated surfaces to a canonical domain. It is demanded for the researchers to construct the scale space directly on the 3D shape. To address these research issues, in this dissertation, in order to find the multiscale processing for the 3D shape, we start with shape vector image diffusion framework using the geometric mapping. Subsequently, we investigate the shape spectrum field by introducing the implementation and application of Laplacian shape spectrum. In order to construct the scale space on 3D shape directly, we present a novel idea to solve the diffusion equation using the manifold harmonics in the spectral point of view. Not only confined on the mesh, by using the point-based manifold harmonics, we rigorously derive our solution from the diffusion equation which is the essential of the scale space processing on the manifold. Built upon the point-based manifold harmonics transform, we generalize the diffusion function directly on the point clouds to create the scale space. In virtue of the multiscale structure from the scale space, we can detect the feature points and construct the descriptor based on the local neighborhood. As a result, multiscale shape analysis directly on the 3D shape can be achieved

Visual Exploration And Information Analytics Of High-Dimensional Medical Images

Data visualization has transformed how we analyze increasingly large and complex data sets. Advanced visual tools logically represent data in a way that communicates the most important information inherent within it and culminate the analysis with an insightful conclusion. Automated analysis disciplines - such as data mining, machine learning, and statistics - have traditionally been the most dominant fields for data analysis. It has been complemented with a near-ubiquitous adoption of specialized hardware and software environments that handle the storage, retrieval, and pre- and postprocessing of digital data. The addition of interactive visualization tools allows an active human participant in the model creation process. The advantage is a data-driven approach where the constraints and assumptions of the model can be explored and chosen based on human insight and confirmed on demand by the analytic system. This translates to a better understanding of data and a more effective knowledge discovery. This trend has become very popular across various domains, not limited to machine learning, simulation, computer vision, genetics, stock market, data mining, and geography. In this dissertation, we highlight the role of visualization within the context of medical image analysis in the field of neuroimaging. The analysis of brain images has uncovered amazing traits about its underlying dynamics. Multiple image modalities capture qualitatively different internal brain mechanisms and abstract it within the information space of that modality. Computational studies based on these modalities help correlate the high-level brain function measurements with abnormal human behavior. These functional maps are easily projected in the physical space through accurate 3-D brain reconstructions and visualized in excellent detail from different anatomical vantage points. Statistical models built for comparative analysis across subject groups test for significant variance within the features and localize abnormal behaviors contextualizing the high-level brain activity. Currently, the task of identifying the features is based on empirical evidence, and preparing data for testing is time-consuming. Correlations among features are usually ignored due to lack of insight. With a multitude of features available and with new emerging modalities appearing, the process of identifying the salient features and their interdependencies becomes more difficult to perceive. This limits the analysis only to certain discernible features, thus limiting human judgments regarding the most important process that governs the symptom and hinders prediction. These shortcomings can be addressed using an analytical system that leverages data-driven techniques for guiding the user toward discovering relevant hypotheses. The research contributions within this dissertation encompass multidisciplinary fields of study not limited to geometry processing, computer vision, and 3-D visualization. However, the principal achievement of this research is the design and development of an interactive system for multimodality integration of medical images. The research proceeds in various stages, which are important to reach the desired goal. The different stages are briefly described as follows: First, we develop a rigorous geometry computation framework for brain surface matching. The brain is a highly convoluted structure of closed topology. Surface parameterization explicitly captures the non-Euclidean geometry of the cortical surface and helps derive a more accurate registration of brain surfaces. We describe a technique based on conformal parameterization that creates a bijective mapping to the canonical domain, where surface operations can be performed with improved efficiency and feasibility. Subdividing the brain into a finite set of anatomical elements provides the structural basis for a categorical division of anatomical view points and a spatial context for statistical analysis. We present statistically significant results of our analysis into functional and morphological features for a variety of brain disorders. Second, we design and develop an intelligent and interactive system for visual analysis of brain disorders by utilizing the complete feature space across all modalities. Each subdivided anatomical unit is specialized by a vector of features that overlap within that element. The analytical framework provides the necessary interactivity for exploration of salient features and discovering relevant hypotheses. It provides visualization tools for confirming model results and an easy-to-use interface for manipulating parameters for feature selection and filtering. It provides coordinated display views for visualizing multiple features across multiple subject groups, visual representations for highlighting interdependencies and correlations between features, and an efficient data-management solution for maintaining provenance and issuing formal data queries to the back end

Surface-guided computing to analyze subcellular morphology and membrane-associated signals in 3D

Signal transduction and cell function are governed by the spatiotemporal organization of membrane-associated molecules. Despite significant advances in visualizing molecular distributions by 3D light microscopy, cell biologists still have limited quantitative understanding of the processes implicated in the regulation of molecular signals at the whole cell scale. In particular, complex and transient cell surface morphologies challenge the complete sampling of cell geometry, membrane-associated molecular concentration and activity and the computing of meaningful parameters such as the cofluctuation between morphology and signals. Here, we introduce u-Unwrap3D, a framework to remap arbitrarily complex 3D cell surfaces and membrane-associated signals into equivalent lower dimensional representations. The mappings are bidirectional, allowing the application of image processing operations in the data representation best suited for the task and to subsequently present the results in any of the other representations, including the original 3D cell surface. Leveraging this surface-guided computing paradigm, we track segmented surface motifs in 2D to quantify the recruitment of Septin polymers by blebbing events; we quantify actin enrichment in peripheral ruffles; and we measure the speed of ruffle movement along topographically complex cell surfaces. Thus, u-Unwrap3D provides access to spatiotemporal analyses of cell biological parameters on unconstrained 3D surface geometries and signals.Comment: 49 pages, 10 figure

Visualizing Natural Image Statistics

Natural image statistics is an important area of research in cognitive sciences and computer vision. Visualization of statistical results can help identify clusters and anomalies as well as analyze deviation, distribution and correlation. Furthermore, they can provide visual abstractions and symbolism for categorized data. In this paper, we begin our study of visualization of image statistics by considering visual representations of power spectra, which are commonly used to visualize different categories of images. We show that they convey a limited amount of statistical information about image categories and their support for analytical tasks is ineffective. We then introduce several new visual representations, which convey different or more information about image statistics. We apply ANOVA to the image statistics to help select statistically more meaningful measurements in our design process. A task-based user evaluation was carried out to compare the new visual representations with the conventional power spectra plots. Based on the results of the evaluation, we made further improvement of visualizations by introducing composite visual representations of image statistics

Doctor of Philosophy

dissertationStochastic methods, dense free-form mapping, atlas construction, and total variation are examples of advanced image processing techniques which are robust but computationally demanding. These algorithms often require a large amount of computational power as well as massive memory bandwidth. These requirements used to be ful lled only by supercomputers. The development of heterogeneous parallel subsystems and computation-specialized devices such as Graphic Processing Units (GPUs) has brought the requisite power to commodity hardware, opening up opportunities for scientists to experiment and evaluate the in uence of these techniques on their research and practical applications. However, harnessing the processing power from modern hardware is challenging. The di fferences between multicore parallel processing systems and conventional models are signi ficant, often requiring algorithms and data structures to be redesigned signi ficantly for efficiency. It also demands in-depth knowledge about modern hardware architectures to optimize these implementations, sometimes on a per-architecture basis. The goal of this dissertation is to introduce a solution for this problem based on a 3D image processing framework, using high performance APIs at the core level to utilize parallel processing power of the GPUs. The design of the framework facilitates an efficient application development process, which does not require scientists to have extensive knowledge about GPU systems, and encourages them to harness this power to solve their computationally challenging problems. To present the development of this framework, four main problems are described, and the solutions are discussed and evaluated: (1) essential components of a general 3D image processing library: data structures and algorithms, as well as how to implement these building blocks on the GPU architecture for optimal performance; (2) an implementation of unbiased atlas construction algorithms|an illustration of how to solve a highly complex and computationally expensive algorithm using this framework; (3) an extension of the framework to account for geometry descriptors to solve registration challenges with large scale shape changes and high intensity-contrast di fferences; and (4) an out-of-core streaming model, which enables developers to implement multi-image processing techniques on commodity hardware