University of Macau / Faculty of Science and Technology / Department of Electromechanical Engineering

University of Macau / Faculty of Science and Technology / Department of Computer and Information Science

University of Macau / Faculty of Science and Technology / Department of Computer and Information Science

University of Macau / Faculty of Science and Technology / Department of Computer and Information Science

Topology-related issues are becoming increasingly important in Computer Graphics. This research examines the use of topological analysis for solving two important problems in 3D Graphics: surface parameterization, and vector field design on surfaces. Many applications, such as high-quality and interactive image synthesis, benefit from the solutions to these problems. Surface parameterization refers to segmenting a 3D surface into a number of patches and unfolding them onto a plane. A surface parameterization allows surface properties to be sampled and stored in a texture map for high-quality and interactive display. One of the most important quality measurements for surface parameterization is stretch, which causes an uneven sampling rate across the surface and needs to be avoided whenever possible. In this thesis, I present an automatic parameterization technique that segments the surface according to the handles and large protrusions in the surface. This results in a small number of large patches that can be unfolded with relatively little stretch. To locate the handles and large protrusions, I make use of topological analysis of a distance-based function on the surface. Vector field design refers to creating continuous vector fields on 3D surfaces with control over vector field topology, such as the number and location of the singularities. Many graphics applications make use of an input vector field. The singularities in the input vector field often cause visual artifacts for these applications, such as texture synthesis and non-photorealistic rendering. In this thesis, I describe a vector field design system for both planar domains and 3D mesh surfaces. The system provides topological editing operations that allow the user to control the number and location of the singularities in the vector field. For the system to work for 3D meshes surface, I present a novel piecewise interpolating scheme that produces a continuous vector field based on the vector values defined at the vertices of the mesh. I demonstrate the effectiveness of the system through several graphics applications: painterly rendering of still images, pencil-sketches of surfaces, and texture synthesis.

In this thesis, we propose and evaluate two novel scale-based decomposable representations of shape for the segmentation and morphometric analysis of anatomical structures in medical imaging. We propose two representations that are adapted to a particular class of anatomical structures and allow for a richer shape description and a more fine-grained control over the deformation of models based on these representations, when compared to previous techniques. In the first part of this thesis, we introduce the concept of a scale-space shape filter for implicit shape representations that measures the deviation from a tubular shape in a local neighborhood of points, given a particular scale of analysis. We use these filters for the segmentation of blood vessels, and introduce the notion of segmentation with a soft shape prior, where the segmented model is not globally constrained to a predefined shape space, but is penalized locally if it deviates strongly from a tubular structure. Using this filter, we derive a region-based active contour segmentation algorithm for tubular structures that penalizes leakages. We present results on synthetic and real 2D and 3D datasets. In the second part of this thesis, we present a novel multi-scale parametric shape representation using spherical wavelets. Our proposed shape representation encodes shape variations in a population at various scales to be used as prior in a probabilistic segmentation framework. We derive a probabilistic active surface segmentation algorithm using the multi-scale prior coefficients as parameters for our optimization procedure. One nice benefit of this algorithm is that the optimization method can be applied in a coarse-to-fine manner. We present results on 3D sub-cortical brain structures. We also present a novel method of statistical surface-based morphometry based on the use of non-parametric permutation tests and the spherical wavelet shape representation. As an application, we analyze two sub-cortical brain structures, the caudate nucleus and hippocampus.

Breast cancer is a major health concern in the United States. Mammography is the gold standard for screening breast cancer and screen-film technology is still widely used in the screening for breast cancer. However, screen-film systems have limited dynamic range and contrasts compared to digital systems, and do not offer integrated image processing capabilities. Recently, digital mammography has seen an upsurge in clinical adoption but current digital mammography systems are limited in terms of their spatial resolution. Therefore, high-resolution digital mammography systems with superior signal-to-noise ratio and contrast characteristics need to be explored. A monolithic, single module high-resolution (39 um) digital x-ray platform (Fairchild Imaging Inc., Milpitas, CA) was developed and characterized for digital mammography. The architecture was extended to a large area (16 x 24-cm) multi-module solid-state imager with variable resolution (39 and 78-um). In addition, a four module (16 x 16-cm) imaging architecture with 78-um pixel was explored for high-resolution contrast enhanced digital mammography for the detection of malignancy-associated angiogenesis. Simulations based on the cascaded linear systems framework were performed in order to characterize the physical properties of the imaging platforms such as the modulation transfer function (MTF), noise power spectra (NPS), and detective quantum efficiency (DQE). Experimental measurements of imager performance was also conducted and compared to model predicted results. Further, perceptual analysis of the prototype imaging platform for digital mammography was performed. Various imaging platforms were successfully developed and investigated to identify essential parameters for high-resolution digital x-ray breast imaging. The single module prototype exhibited physical characteristics that are favorable for digital mammography. Good agreement between model and experimental results were observed demonstrating the utility of such models for further system improvement. The large area 16 x 24-cm prototype demonstrated superior contrast-detail characteristics compared to a clinical FFDM system (100 um pixel) at both 39 and 78-um pixel sizes. Both experimental and theoretical results pointed towards the feasibility of contrast enhanced mammography at mean x-ray glandular dose levels substantially lower than mammography under the conditions investigated. Qualitative analysis of contrast enhanced digital mammography indicated favorable image quality.

This thesis is concerned with modeling geometric patterns. Specifically, a clear and practical definition for regular patterns is proposed. Based on this definition, this thesis proposes the following modeling setting to describe the semantic transfer of a model between various forms of pattern regularity: (1) recognition or identification of patterns in digital models of 3D assemblies and scenes, (2) pattern regularization, (3) pattern modification and editing by varying the repetition parameters, and (4) establishing exceptions (designed irregularities) in regular patterns. In line with this setting, this thesis describes a representation and approach for designing and editing hierarchical assemblies based on grouped, nested, and recursively nested patterns. Based on this representation, this thesis presents the OCTOR approach for specifying, recording, and producing exceptions in regular patterns. To support editing of free-form shape patterns on surfaces, this thesis also presents the imprint-mapping approach which can be used to identify, extract, process, and apply relief features on surfaces. Pattern regularization, modification, and exceptions are addressed for the case of relief features on surfaces.

Medical image analysis aims at developing techniques to extract information from medical images. Among its many sub-fields, image registration and segmentation are two important topics. In this report, we present four pieces of work, addressing different problems as well as coupling them into a unified framework of shape based image segmentation. Specifically: 1. We link the image registration with the point set registration, and propose a globally optimal diffeomorphic registration technique for point set registration. 2. We propose an image segmentation technique which incorporates the robust statistics of the image and the multiple contour evolution. Therefore, the method is able to simultaneously extract multiple targets from the image. 3. By combining the image registration, statistical learning, and image segmentation, we perform a shape based method which not only utilizes the image information but also the shape knowledge. 4. A multi-scale shape representation based on the wavelet transformation is proposed. In particular, the shape is represented by wavelet coefficients in a hierarchical way in order to decompose the shape variance in multiple scales. Furthermore, the statistical shape learning and shape based segmentation is performed under such multi-scale shape representation framework.

In this work, our goal is to track visual targets using residual vector quantization (RVQ). We compare our results with principal components analysis (PCA) and tree structured vector quantization (TSVQ) based tracking. This work is significant since PCA is commonly used in the Pattern Recognition, Machine Learning and Computer Vision communities. On the other hand, TSVQ is commonly used in the Signal Processing and data compression communities. RVQ with more than two stages has not received much attention due to the difficulty in producing stable designs. In this work, we bring together these different approaches into an integrated tracking framework and show that RVQ tracking performs best according to multiple criteria on publicly available datasets. Moreover, an advantage of our approach is a learning-based tracker that builds the target model while it tracks, thus avoiding the costly step of building target models prior to tracking.