Skeletonization and segmentation of binary voxel shapes

Preface. This dissertation is the result of research that I conducted between January 2005 and December 2008 in the Visualization research group of the Technische Universiteit Eindhoven. I am pleased to have the opportunity to thank a number of people that made this work possible. I owe my sincere gratitude to Alexandru Telea, my supervisor and first promotor. I did not consider pursuing a PhD until my Master’s project, which he also supervised. Due to our pleasant collaboration from which I learned quite a lot, I became convinced that becoming a doctoral student would be the right thing to do for me. Indeed, I can say it has greatly increased my knowledge and professional skills. Alex, thank you for our interesting discussions and the freedom you gave me in conducting my research. You made these four years a pleasant experience. I am further grateful to Jack vanWijk, my second promotor. Our monthly discussions were insightful, and he continuously encouraged me to take a more formal and scientific stance. I would also like to thank Prof. Jan de Graaf from the department of mathematics for our discussions on some of my conjectures. His mathematical rigor was inspiring. I am greatly indebted to the Netherlands Organisation for Scientific Research (NWO) for funding my PhD project (grant number 612.065.414). I thank Prof. Kaleem Siddiqi, Prof. Mark de Berg, and Dr. Remco Veltkamp for taking part in the core doctoral committee and Prof. Deborah Silver and Prof. Jos Roerdink for participating in the extended committee. Our Visualization group provides a great atmosphere to do research in. In particular, I would like to thank my fellow doctoral students Frank van Ham, Hannes Pretorius, Lucian Voinea, Danny Holten, Koray Duhbaci, Yedendra Shrinivasan, Jing Li, NielsWillems, and Romain Bourqui. They enabled me to take my mind of research from time to time, by discussing political and economical affairs, and more trivial topics. Furthermore, I would like to thank the senior researchers of our group, Huub van de Wetering, Kees Huizing, and Michel Westenberg. In particular, I thank Andrei Jalba for our fruitful collaboration in the last part of my work. On a personal level, I would like to thank my parents and sister for their love and support over the years, my friends for providing distractions outside of the office, and Michelle for her unconditional love and ability to light up my mood when needed

Higher-Order Regularization in Computer Vision

At the core of many computer vision models lies the minimization of an objective function consisting of a sum of functions with few arguments. The order of the objective function is defined as the highest number of arguments of any summand. To reduce ambiguity and noise in the solution, regularization terms are included into the objective function, enforcing different properties of the solution. The most commonly used regularization is penalization of boundary length, which requires a second-order objective function. Most of this thesis is devoted to introducing higher-order regularization terms and presenting efficient minimization schemes. One of the topics of the thesis covers a reformulation of a large class of discrete functions into an equivalent form. The reformulation is shown, both in theory and practical experiments, to be advantageous for higher-order regularization models based on curvature and second-order derivatives. Another topic is the parametric max-flow problem. An analysis is given, showing its inherent limitations for large-scale problems which are common in computer vision. The thesis also introduces a segmentation approach for finding thin and elongated structures in 3D volumes. Using a line-graph formulation, it is shown how to efficiently regularize with respect to higher-order differential geometric properties such as curvature and torsion. Furthermore, an efficient optimization approach for a multi-region model is presented which, in addition to standard regularization, is able to enforce geometric constraints such as inclusion or exclusion of different regions. The final part of the thesis deals with dense stereo estimation. A new regularization model is introduced, penalizing the second-order derivatives of a depth or disparity map. Compared to previous second-order approaches to dense stereo estimation, the new regularization model is shown to be more easily optimized

Doctor of Philosophy

dissertationImage segmentation entails the partitioning of an image domain, usually two or three dimensions, so that each partition or segment has some meaning that is relevant to the application at hand. Accurate image segmentation is a crucial challenge in many disciplines, including medicine, computer vision, and geology. In some applications, heterogeneous pixel intensities; noisy, ill-defined, or diffusive boundaries; and irregular shapes with high variability can make it challenging to meet accuracy requirements. Various segmentation approaches tackle such challenges by casting the segmentation problem as an energy-minimization problem, and solving it using efficient optimization algorithms. These approaches are broadly classified as either region-based or edge (surface)-based depending on the features on which they operate. The focus of this dissertation is on the development of a surface-based energy model, the design of efficient formulations of optimization frameworks to incorporate such energy, and the solution of the energy-minimization problem using graph cuts. This dissertation utilizes a set of four papers whose motivation is the efficient extraction of the left atrium wall from the late gadolinium enhancement magnetic resonance imaging (LGE-MRI) image volume. This dissertation utilizes these energy formulations for other applications, including contact lens segmentation in the optical coherence tomography (OCT) data and the extraction of geologic features in seismic data. Chapters 2 through 5 (papers 1 through 4) explore building a surface-based image segmentation model by progressively adding components to improve its accuracy and robustness. The first paper defines a parametric search space and its discrete formulation in the form of a multilayer three-dimensional mesh model within which the segmentation takes place. It includes a generative intensity model, and we optimize using a graph formulation of the surface net problem. The second paper proposes a Bayesian framework with a Markov random field (MRF) prior that gives rise to another class of surface nets, which provides better segmentation with smooth boundaries. The third paper presents a maximum a posteriori (MAP)-based surface estimation framework that relies on a generative image model by incorporating global shape priors, in addition to the MRF, within the Bayesian formulation. Thus, the resulting surface not only depends on the learned model of shapes,but also accommodates the test data irregularities through smooth deviations from these priors. Further, the paper proposes a new shape parameter estimation scheme, in closed form, for segmentation as a part of the optimization process. Finally, the fourth paper (under review at the time of this document) presents an extensive analysis of the MAP framework and presents improved mesh generation and generative intensity models. It also performs a thorough analysis of the segmentation results that demonstrates the effectiveness of the proposed method qualitatively, quantitatively, and clinically. Chapter 6, consisting of unpublished work, demonstrates the application of an MRF-based Bayesian framework to segment coupled surfaces of contact lenses in optical coherence tomography images. This chapter also shows an application related to the extraction of geological structures in seismic volumes. Due to the large sizes of seismic volume datasets, we also present fast, approximate surface-based energy minimization strategies that achieve better speed-ups and memory consumption

Segmentation and Fracture Detection in X-ray images for Traumatic Pelvic Injury

Due to the risk of complications such as hemorrhage, severe pelvic trauma is associated with a high mortality rate. Prompt medical treatment is therefore vital. However, the complexity of the injuries can make successful diagnosis and treatment challenging. By generating predictions and recommendations based on patient data, computer-aided decision support systems have the potential to assist physicians in improving outcomes. However, no current system considers features automatically extracted from medical images. This dissertation describes a system to extract diagnostic features from pelvic X-ray images that can be used as input to the prediction process; specifically, the presence of fracture and quantitative measures of displacement. Feature extraction requires prior identification of separate structures of interest within the pelvis. The proposed system therefore incorporates a hierarchical segmentation algorithm which is able to automatically extract multiple structures in a single pass, using a combination of anatomical knowledge and computational techniques such as directed Hough Transform. This algorithm also applies a novel Spline/ASM segmentation method which combines cubic spline interpolation with a deformable model approach which maintains curved contours and provides local control over segmentation. In order for the proposed system to be used as a component in a computerized decision support system, segmentation is designed to be entirely automatic. Furthermore, Spline/ASM is suitable for many other segmentation applications where the objects of interest show curved contours. After successful segmentation, fracture detection is performed on the pelvic ring and pubis structures, using an algorithm based on wavelet transform, anatomical information and boundary tracing. A method is also developed to calculate quantitative measures of symphysis pubis displacement that may indicate pelvic instability and prove useful in identifying fracture patterns. Finally, X-ray features are combined with patient demographics and physiological scores for generation of predictive rules for injury severity, with promising current results. This indicates the potential diagnostic value of the extracted features, and in turn the usefulness of the proposed radiograph analysis component in a larger decision support system

Example Based Caricature Synthesis

The likeness of a caricature to the original face image is an essential and often overlooked part of caricature production. In this paper we present an example based caricature synthesis technique, consisting of shape exaggeration, relationship exaggeration, and optimization for likeness. Rather than relying on a large training set of caricature face pairs, our shape exaggeration step is based on only one or a small number of examples of facial features. The relationship exaggeration step introduces two definitions which facilitate global facial feature synthesis. The first is the T-Shape rule, which describes the relative relationship between the facial elements in an intuitive manner. The second is the so called proportions, which characterizes the facial features in a proportion form. Finally we introduce a similarity metric as the likeness metric based on the Modified Hausdorff Distance (MHD) which allows us to optimize the configuration of facial elements, maximizing likeness while satisfying a number of constraints. The effectiveness of our algorithm is demonstrated with experimental results