Finite element surface registration incorporating curvature, volume preservation, and statistical model information

We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models

The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch

Recent and forthcoming advances in instrumentation, and giant new surveys, are creating astronomical data sets that are not amenable to the methods of analysis familiar to astronomers. Traditional methods are often inadequate not merely because of the size in bytes of the data sets, but also because of the complexity of modern data sets. Mathematical limitations of familiar algorithms and techniques in dealing with such data sets create a critical need for new paradigms for the representation, analysis and scientific visualization (as opposed to illustrative visualization) of heterogeneous, multiresolution data across application domains. Some of the problems presented by the new data sets have been addressed by other disciplines such as applied mathematics, statistics and machine learning and have been utilized by other sciences such as space-based geosciences. Unfortunately, valuable results pertaining to these problems are mostly to be found only in publications outside of astronomy. Here we offer brief overviews of a number of concepts, techniques and developments, some "old" and some new. These are generally unknown to most of the astronomical community, but are vital to the analysis and visualization of complex datasets and images. In order for astronomers to take advantage of the richness and complexity of the new era of data, and to be able to identify, adopt, and apply new solutions, the astronomical community needs a certain degree of awareness and understanding of the new concepts. One of the goals of this paper is to help bridge the gap between applied mathematics, artificial intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in Astronomy, special issue "Robotic Astronomy

Advanced Algorithms for 3D Medical Image Data Fusion in Specific Medical Problems

Fúze obrazu je dnes jednou z nejběžnějších avšak stále velmi diskutovanou oblastí v lékařském zobrazování a hraje důležitou roli ve všech oblastech lékařské péče jako je diagnóza, léčba a chirurgie. V této dizertační práci jsou představeny tři projekty, které jsou velmi úzce spojeny s oblastí fúze medicínských dat. První projekt pojednává o 3D CT subtrakční angiografii dolních končetin. V práci je využito kombinace kontrastních a nekontrastních dat pro získání kompletního cévního stromu. Druhý projekt se zabývá fúzí DTI a T1 váhovaných MRI dat mozku. Cílem tohoto projektu je zkombinovat stukturální a funkční informace, které umožňují zlepšit znalosti konektivity v mozkové tkáni. Třetí projekt se zabývá metastázemi v CT časových datech páteře. Tento projekt je zaměřen na studium vývoje metastáz uvnitř obratlů ve fúzované časové řadě snímků. Tato dizertační práce představuje novou metodologii pro klasifikaci těchto metastáz. Všechny projekty zmíněné v této dizertační práci byly řešeny v rámci pracovní skupiny zabývající se analýzou lékařských dat, kterou vedl pan Prof. Jiří Jan. Tato dizertační práce obsahuje registrační část prvního a klasifikační část třetího projektu. Druhý projekt je představen kompletně. Další část prvního a třetího projektu, obsahující specifické předzpracování dat, jsou obsaženy v disertační práci mého kolegy Ing. Romana Petera.Image fusion is one of today´s most common and still challenging tasks in medical imaging and it plays crucial role in all areas of medical care such as diagnosis, treatment and surgery. Three projects crucially dependent on image fusion are introduced in this thesis. The first project deals with the 3D CT subtraction angiography of lower limbs. It combines pre-contrast and contrast enhanced data to extract the blood vessel tree. The second project fuses the DTI and T1-weighted MRI brain data. The aim of this project is to combine the brain structural and functional information that purvey improved knowledge about intrinsic brain connectivity. The third project deals with the time series of CT spine data where the metastases occur. In this project the progression of metastases within the vertebrae is studied based on fusion of the successive elements of the image series. This thesis introduces new methodology of classifying metastatic tissue. All the projects mentioned in this thesis have been solved by the medical image analysis group led by Prof. Jiří Jan. This dissertation concerns primarily the registration part of the first project and the classification part of the third project. The second project is described completely. The other parts of the first and third project, including the specific preprocessing of the data, are introduced in detail in the dissertation thesis of my colleague Roman Peter, M.Sc.

Semi-Automatic Segmentation of Normal Female Pelvic Floor Structures from Magnetic Resonance Images

Stress urinary incontinence (SUI) and pelvic organ prolapse (POP) are important health issues affecting millions of American women. Investigation of the cause of SUI and POP requires a better understand of the anatomy of female pelvic floor. In addition, pre-surgical planning and individualized treatment plans require development of patient-specific three-dimensional or virtual reality models. The biggest challenge in building those models is to segment pelvic floor structures from magnetic resonance images because of their complex shapes, which make manual segmentation labor-intensive and inaccurate. In this dissertation, a quick and reliable semi-automatic segmentation method based on a shape model is proposed. The model is built on statistical analysis of the shapes of structures in a training set. A local feature map of the target image is obtained by applying a filtering pipeline, including contrast enhancement, noise reduction, smoothing, and edge extraction. With the shape model and feature map, automatic segmentation is performed by matching the model to the border of the structure using an optimization technique called evolution strategy. Segmentation performance is evaluated by calculating a similarity coefficient between semi-automatic and manual segmentation results. Taguchi analysis is performed to investigate the significance of segmentation parameters and provide tuning trends for better performance. The proposed method was successfully tested on both two-dimensional and three-dimensional image segmentation using the levator ani and obturator muscles as examples. Although the method is designed for segmentation of female pelvic floor structures, it can also be applied to other structures or organs without large shape variatio

Semi-Automatic Segmentation of Normal Female Pelvic Floor Structures from Magnetic Resonance Images

Stress urinary incontinence (SUI) and pelvic organ prolapse (POP) are important health issues affecting millions of American women. Investigation of the cause of SUI and POP requires a better understand of the anatomy of female pelvic floor. In addition, pre-surgical planning and individualized treatment plans require development of patient-specific three-dimensional or virtual reality models. The biggest challenge in building those models is to segment pelvic floor structures from magnetic resonance images because of their complex shapes, which make manual segmentation labor-intensive and inaccurate. In this dissertation, a quick and reliable semi-automatic segmentation method based on a shape model is proposed. The model is built on statistical analysis of the shapes of structures in a training set. A local feature map of the target image is obtained by applying a filtering pipeline, including contrast enhancement, noise reduction, smoothing, and edge extraction. With the shape model and feature map, automatic segmentation is performed by matching the model to the border of the structure using an optimization technique called evolution strategy. Segmentation performance is evaluated by calculating a similarity coefficient between semi-automatic and manual segmentation results. Taguchi analysis is performed to investigate the significance of segmentation parameters and provide tuning trends for better performance. The proposed method was successfully tested on both two-dimensional and three-dimensional image segmentation using the levator ani and obturator muscles as examples. Although the method is designed for segmentation of female pelvic floor structures, it can also be applied to other structures or organs without large shape variatio