Segmentation and Restoration of Images on Surfaces by Parametric Active Contours with Topology Changes

In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are mathematically described using a parametric approach. For image restoration, a diffusion equation with Neumann boundary conditions is solved in a postprocessing step in the individual regions. Numerical schemes are presented which allow to efficiently compute segmentations and denoised versions of images on surfaces. Also topology changes of the evolving curves are detected and performed using a fast sub-routine. Finally, several experiments are presented where the developed methods are applied on different artificial and real images defined on different surfaces

Image feature analysis using the Multiresolution Fourier Transform

The problem of identifying boundary contours or line structures is widely recognised as an important component in many applications of image analysis and computer vision. Typical solutions to the problem employ some form of edge detection followed by line following or, more commonly in recent years, Hough transforms. Because of the processing requirements of such methods and to try to improve the robustness of the algorithms, a number of authors have explored the use of multiresolution approaches to the problem. Non-parametric, iterative approaches such as relaxation labelling and "Snakes" have also been used. This thesis presents a boundary detection algorithm based on a multiresolution image representation, the Multiresolution Fourier Transform (MFT), which represents an image over a range of spatial/spatial-frequency resolutions. A quadtree based image model is described in which each leaf is a region which can be modelled using one of a set of feature classes. Consideration is given to using linear and circular arc features for this modelling, and frequency domain models are developed for them. A general model based decision process is presented and shown to be applicable to detecting local image features, selecting the most appropriate scale for modelling each region of the image and linking the local features into the region boundary structures of the image. The use of a consistent inference process for all of the subtasks used in the boundary detection represents a significant improvement over the adhoc assemblies of estimation and detection that have been common in previous work. Although the process is applied using a restricted set of local features, the framework presented allows for expansion of the number of boundary feature models and the possible inclusion of models of region properties. Results are presented demonstrating the effective application of these procedures to a number of synthetic and natural images

Computational models for image contour grouping

Contours are one dimensional curves which may correspond to meaningful entities such as object boundaries. Accurate contour detection will simplify many vision tasks such as object detection and image recognition. Due to the large variety of image content and contour topology, contours are often detected as edge fragments at first, followed by a second step known as {u0300}{u0300}contour grouping'' to connect them. Due to ambiguities in local image patches, contour grouping is essential for constructing globally coherent contour representation. This thesis aims to group contours so that they are consistent with human perception. We draw inspirations from Gestalt principles, which describe perceptual grouping ability of human vision system. In particular, our work is most relevant to the principles of closure, similarity, and past experiences. The first part of our contribution is a new computational model for contour closure. Most of existing contour grouping methods have focused on pixel-wise detection accuracy and ignored the psychological evidences for topological correctness. This chapter proposes a higher-order CRF model to achieve contour closure in the contour domain. We also propose an efficient inference method which is guaranteed to find integer solutions. Tested on the BSDS benchmark, our method achieves a superior contour grouping performance, comparable precision-recall curves, and more visually pleasant results. Our work makes progresses towards a better computational model of human perceptual grouping. The second part is an energy minimization framework for salient contour detection problem. Region cues such as color/texture homogeneity, and contour cues such as local contrast, are both useful for this task. In order to capture both kinds of cues in a joint energy function, topological consistency between both region and contour labels must be satisfied. Our technique makes use of the topological concept of winding numbers. By using a fast method for winding number computation, we find that a small number of linear constraints are sufficient for label consistency. Our method is instantiated by ratio-based energy functions. Due to cue integration, our method obtains improved results. User interaction can also be incorporated to further improve the results. The third part of our contribution is an efficient category-level image contour detector. The objective is to detect contours which most likely belong to a prescribed category. Our method, which is based on three levels of shape representation and non-parametric Bayesian learning, shows flexibility in learning from either human labeled edge images or unlabelled raw images. In both cases, our experiments obtain better contour detection results than competing methods. In addition, our training process is robust even with a considerable size of training samples. In contrast, state-of-the-art methods require more training samples, and often human interventions are required for new category training. Last but not least, in Chapter 7 we also show how to leverage contour information for symmetry detection. Our method is simple yet effective for detecting the symmetric axes of bilaterally symmetric objects in unsegmented natural scene images. Compared with methods based on feature points, our model can often produce better results for the images containing limited texture

A Novel Free Form Femoral Cutting Guide

Knee arthoplasty is a common procedure that requires the removal of damaged bone and cartilage from the distal femur so that a reconstructive implant may be installed. Traditionally, a five planar resection has been accomplished with a universal cutting box and navigated with either metal jigs or optically tracked computer navigation systems. Free form, or curved, resections have been made possible with surgical robots which control the resection pathway and serve as the navigation system. The free form femoral cutting guide serves as a non powered framework to guide a standard surgical drill along an anatomically defined pathway, resulting in the removal of distal femoral cartilage. It is fixed via attachment to a bone mounted base component, which is positioned with a patient specific jig. To operate, the surgeon slides the surgical drill along a pair of interlocked tracks. One track controls motion in the anteroposterior (AP) direction and one track controls motion in the mediolateral (ML) direction. Combining both motions results in the removal of cartilage from the area of the distal femur for unilateral or total knee arthoplasty

Incorporating Cardiac Substructures Into Radiation Therapy For Improved Cardiac Sparing

Growing evidence suggests that radiation therapy (RT) doses to the heart and cardiac substructures (CS) are strongly linked to cardiac toxicities, though only the heart is considered clinically. This work aimed to utilize the superior soft-tissue contrast of magnetic resonance (MR) to segment CS, quantify uncertainties in their position, assess their effect on treatment planning and an MR-guided environment. Automatic substructure segmentation of 12 CS was completed using a novel hybrid MR/computed tomography (CT) atlas method and was improved upon using a 3-dimensional neural network (U-Net) from deep learning. Intra-fraction motion due to respiration was then quantified. The inter-fraction setup uncertainties utilizing a novel MR-linear accelerator were also quantified. Treatment planning comparisons were performed with and without substructure inclusions and methods to reduce radiation dose to sensitive CS were evaluated. Lastly, these described technologies (deep learning U-Net) were translated to an MR-linear accelerator and a segmentation pipeline was created. Automatic segmentations from the hybrid MR/CT atlas was able to generate accurate segmentations for the chambers and great vessels (Dice similarity coefficient (DSC) \u3e 0.75) but coronary artery segmentations were unsuccessful (DSC\u3c0.3). After implementing deep learning, DSC for the chambers and great vessels was ≥0.85 along with an improvement in the coronary arteries (DSC\u3e0.5). Similar accuracy was achieved when implementing deep learning for MR-guided RT. On average, automatic segmentations required ~10 minutes to generate per patient and deep learning only required 14 seconds. The inclusion of CS in the treatment planning process did not yield statistically significant changes in plan complexity, PTV, or OAR dose. Automatic segmentation results from deep learning pose major efficiency and accuracy gains for CS segmentation offering high potential for rapid implementation into radiation therapy planning for improved cardiac sparing. Introducing CS into RT planning for MR-guided RT presented an opportunity for more effective sparing with limited increase in plan complexity

Incorporating Cardiac Substructures Into Radiation Therapy For Improved Cardiac Sparing

Growing evidence suggests that radiation therapy (RT) doses to the heart and cardiac substructures (CS) are strongly linked to cardiac toxicities, though only the heart is considered clinically. This work aimed to utilize the superior soft-tissue contrast of magnetic resonance (MR) to segment CS, quantify uncertainties in their position, assess their effect on treatment planning and an MR-guided environment. Automatic substructure segmentation of 12 CS was completed using a novel hybrid MR/computed tomography (CT) atlas method and was improved upon using a 3-dimensional neural network (U-Net) from deep learning. Intra-fraction motion due to respiration was then quantified. The inter-fraction setup uncertainties utilizing a novel MR-linear accelerator were also quantified. Treatment planning comparisons were performed with and without substructure inclusions and methods to reduce radiation dose to sensitive CS were evaluated. Lastly, these described technologies (deep learning U-Net) were translated to an MR-linear accelerator and a segmentation pipeline was created. Automatic segmentations from the hybrid MR/CT atlas was able to generate accurate segmentations for the chambers and great vessels (Dice similarity coefficient (DSC) \u3e 0.75) but coronary artery segmentations were unsuccessful (DSC\u3c0.3). After implementing deep learning, DSC for the chambers and great vessels was ≥0.85 along with an improvement in the coronary arteries (DSC\u3e0.5). Similar accuracy was achieved when implementing deep learning for MR-guided RT. On average, automatic segmentations required ~10 minutes to generate per patient and deep learning only required 14 seconds. The inclusion of CS in the treatment planning process did not yield statistically significant changes in plan complexity, PTV, or OAR dose. Automatic segmentation results from deep learning pose major efficiency and accuracy gains for CS segmentation offering high potential for rapid implementation into radiation therapy planning for improved cardiac sparing. Introducing CS into RT planning for MR-guided RT presented an opportunity for more effective sparing with limited increase in plan complexity

Effective 3D Geometric Matching for Data Restoration and Its Forensic Application

3D geometric matching is the technique to detect the similar patterns among multiple objects. It is an important and fundamental problem and can facilitate many tasks in computer graphics and vision, including shape comparison and retrieval, data fusion, scene understanding and object recognition, and data restoration. For example, 3D scans of an object from different angles are matched and stitched together to form the complete geometry. In medical image analysis, the motion of deforming organs is modeled and predicted by matching a series of CT images. This problem is challenging and remains unsolved, especially when the similar patterns are 1) small and lack geometric saliency; 2) incomplete due to the occlusion of the scanning and damage of the data. We study the reliable matching algorithm that can tackle the above difficulties and its application in data restoration. Data restoration is the problem to restore the fragmented or damaged model to its original complete state. It is a new area and has direct applications in many scientific fields such as Forensics and Archeology. In this dissertation, we study novel effective geometric matching algorithms, including curve matching, surface matching, pairwise matching, multi-piece matching and template matching. We demonstrate its applications in an integrated digital pipeline of skull reassembly, skull completion, and facial reconstruction, which is developed to facilitate the state-of-the-art forensic skull/facial reconstruction processing pipeline in law enforcement

Combinatorial Solutions for Shape Optimization in Computer Vision

This thesis aims at solving so-called shape optimization problems, i.e. problems where the shape of some real-world entity is sought, by applying combinatorial algorithms. I present several advances in this field, all of them based on energy minimization. The addressed problems will become more intricate in the course of the thesis, starting from problems that are solved globally, then turning to problems where so far no global solutions are known. The first two chapters treat segmentation problems where the considered grouping criterion is directly derived from the image data. That is, the respective data terms do not involve any parameters to estimate. These problems will be solved globally. The first of these chapters treats the problem of unsupervised image segmentation where apart from the image there is no other user input. Here I will focus on a contour-based method and show how to integrate curvature regularity into a ratio-based optimization framework. The arising optimization problem is reduced to optimizing over the cycles in a product graph. This problem can be solved globally in polynomial, effectively linear time. As a consequence, the method does not depend on initialization and translational invariance is achieved. This is joint work with Daniel Cremers and Simon Masnou. I will then proceed to the integration of shape knowledge into the framework, while keeping translational invariance. This problem is again reduced to cycle-finding in a product graph. Being based on the alignment of shape points, the method actually uses a more sophisticated shape measure than most local approaches and still provides global optima. It readily extends to tracking problems and allows to solve some of them in real-time. I will present an extension to highly deformable shape models which can be included in the global optimization framework. This method simultaneously allows to decompose a shape into a set of deformable parts, based only on the input images. This is joint work with Daniel Cremers. In the second part segmentation is combined with so-called correspondence problems, i.e. the underlying grouping criterion is now based on correspondences that have to be inferred simultaneously. That is, in addition to inferring the shapes of objects, one now also tries to put into correspondence the points in several images. The arising problems become more intricate and are no longer optimized globally. This part is divided into two chapters. The first chapter treats the topic of real-time motion segmentation where objects are identified based on the observations that the respective points in the video will move coherently. Rather than pre-estimating motion, a single energy functional is minimized via alternating optimization. The main novelty lies in the real-time capability, which is achieved by exploiting a fast combinatorial segmentation algorithm. The results are furthermore improved by employing a probabilistic data term. This is joint work with Daniel Cremers. The final chapter presents a method for high resolution motion layer decomposition and was developed in combination with Daniel Cremers and Thomas Pock. Layer decomposition methods support the notion of a scene model, which allows to model occlusion and enforce temporal consistency. The contributions are twofold: from a practical point of view the proposed method allows to recover fine-detailed layer images by minimizing a single energy. This is achieved by integrating a super-resolution method into the layer decomposition framework. From a theoretical viewpoint the proposed method introduces layer-based regularity terms as well as a graph cut-based scheme to solve for the layer domains. The latter is combined with powerful continuous convex optimization techniques into an alternating minimization scheme. Lastly I want to mention that a significant part of this thesis is devoted to the recent trend of exploiting parallel architectures, in particular graphics cards: many combinatorial algorithms are easily parallelized. In Chapter 3 we will see a case where the standard algorithm is hard to parallelize, but easy for the respective problem instances

Pulmonary Image Segmentation and Registration Algorithms: Towards Regional Evaluation of Obstructive Lung Disease

Pulmonary imaging, including pulmonary magnetic resonance imaging (MRI) and computed tomography (CT), provides a way to sensitively and regionally measure spatially heterogeneous lung structural-functional abnormalities. These unique imaging biomarkers offer the potential for better understanding pulmonary disease mechanisms, monitoring disease progression and response to therapy, and developing novel treatments for improved patient care. To generate these regional lung structure-function measurements and enable broad clinical applications of quantitative pulmonary MRI and CT biomarkers, as a first step, accurate, reproducible and rapid lung segmentation and registration methods are required. In this regard, we first developed a 1H MRI lung segmentation algorithm that employs complementary hyperpolarized 3He MRI functional information for improved lung segmentation. The 1H-3He MRI joint segmentation algorithm was formulated as a coupled continuous min-cut model and solved through convex relaxation, for which a dual coupled continuous max-flow model was proposed and a max-flow-based efficient numerical solver was developed. Experimental results on a clinical dataset of 25 chronic obstructive pulmonary disease (COPD) patients ranging in disease severity demonstrated that the algorithm provided rapid lung segmentation with high accuracy, reproducibility and diminished user interaction. We then developed a general 1H MRI left-right lung segmentation approach by exploring the left-to-right lung volume proportion prior. The challenging volume proportion-constrained multi-region segmentation problem was approximated through convex relaxation and equivalently represented by a max-flow model with bounded flow conservation conditions. This gave rise to a multiplier-based high performance numerical implementation based on convex optimization theories. In 20 patients with mild- to-moderate and severe asthma, the approach demonstrated high agreement with manual segmentation, excellent reproducibility and computational efficiency. Finally, we developed a CT-3He MRI deformable registration approach that coupled the complementary CT-1H MRI registration. The joint registration problem was solved by exploring optical-flow techniques, primal-dual analyses and convex optimization theories. In a diverse group of patients with asthma and COPD, the registration approach demonstrated lower target registration error than single registration and provided fast regional lung structure-function measurements that were strongly correlated with a reference method. Collectively, these lung segmentation and registration algorithms demonstrated accuracy, reproducibility and workflow efficiency that all may be clinically-acceptable. All of this is consistent with the need for broad and large-scale clinical applications of pulmonary MRI and CT