Modeling small objects under uncertainties : novel algorithms and applications.

Active Shape Models (ASM), Active Appearance Models (AAM) and Active Tensor Models (ATM) are common approaches to model elastic (deformable) objects. These models require an ensemble of shapes and textures, annotated by human experts, in order identify the model order and parameters. A candidate object may be represented by a weighted sum of basis generated by an optimization process. These methods have been very effective for modeling deformable objects in biomedical imaging, biometrics, computer vision and graphics. They have been tried mainly on objects with known features that are amenable to manual (expert) annotation. They have not been examined on objects with severe ambiguities to be uniquely characterized by experts. This dissertation presents a unified approach for modeling, detecting, segmenting and categorizing small objects under uncertainty, with focus on lung nodules that may appear in low dose CT (LDCT) scans of the human chest. The AAM, ASM and the ATM approaches are used for the first time on this application. A new formulation to object detection by template matching, as an energy optimization, is introduced. Nine similarity measures of matching have been quantitatively evaluated for detecting nodules less than 1 em in diameter. Statistical methods that combine intensity, shape and spatial interaction are examined for segmentation of small size objects. Extensions of the intensity model using the linear combination of Gaussians (LCG) approach are introduced, in order to estimate the number of modes in the LCG equation. The classical maximum a posteriori (MAP) segmentation approach has been adapted to handle segmentation of small size lung nodules that are randomly located in the lung tissue. A novel empirical approach has been devised to simultaneously detect and segment the lung nodules in LDCT scans. The level sets methods approach was also applied for lung nodule segmentation. A new formulation for the energy function controlling the level set propagation has been introduced taking into account the specific properties of the nodules. Finally, a novel approach for classification of the segmented nodules into categories has been introduced. Geometric object descriptors such as the SIFT, AS 1FT, SURF and LBP have been used for feature extraction and matching of small size lung nodules; the LBP has been found to be the most robust. Categorization implies classification of detected and segmented objects into classes or types. The object descriptors have been deployed in the detection step for false positive reduction, and in the categorization stage to assign a class and type for the nodules. The AAMI ASMI A TM models have been used for the categorization stage. The front-end processes of lung nodule modeling, detection, segmentation and classification/categorization are model-based and data-driven. This dissertation is the first attempt in the literature at creating an entirely model-based approach for lung nodule analysis

Rekonstruktion und skalierbare Detektion und Verfolgung von 3D Objekten

The task of detecting objects in images is essential for autonomous systems to categorize, comprehend and eventually navigate or manipulate its environment. Since many applications demand not only detection of objects but also the estimation of their exact poses, 3D CAD models can prove helpful since they provide means for feature extraction and hypothesis refinement. This work, therefore, explores two paths: firstly, we will look into methods to create richly-textured and geometrically accurate models of real-life objects. Using these reconstructions as a basis, we will investigate on how to improve in the domain of 3D object detection and pose estimation, focusing especially on scalability, i.e. the problem of dealing with multiple objects simultaneously.Objekterkennung in Bildern ist für ein autonomes System von entscheidender Bedeutung, um seine Umgebung zu kategorisieren, zu erfassen und schließlich zu navigieren oder zu manipulieren. Da viele Anwendungen nicht nur die Erkennung von Objekten, sondern auch die Schätzung ihrer exakten Positionen erfordern, können sich 3D-CAD-Modelle als hilfreich erweisen, da sie Mittel zur Merkmalsextraktion und Verfeinerung von Hypothesen bereitstellen. In dieser Arbeit werden daher zwei Wege untersucht: Erstens werden wir Methoden untersuchen, um strukturreiche und geometrisch genaue Modelle realer Objekte zu erstellen. Auf der Grundlage dieser Konstruktionen werden wir untersuchen, wie sich der Bereich der 3D-Objekterkennung und der Posenschätzung verbessern lässt, wobei insbesondere die Skalierbarkeit im Vordergrund steht, d.h. das Problem der gleichzeitigen Bearbeitung mehrerer Objekte

Computational methods for the analysis of functional 4D-CT chest images.

Medical imaging is an important emerging technology that has been intensively used in the last few decades for disease diagnosis and monitoring as well as for the assessment of treatment effectiveness. Medical images provide a very large amount of valuable information that is too huge to be exploited by radiologists and physicians. Therefore, the design of computer-aided diagnostic (CAD) system, which can be used as an assistive tool for the medical community, is of a great importance. This dissertation deals with the development of a complete CAD system for lung cancer patients, which remains the leading cause of cancer-related death in the USA. In 2014, there were approximately 224,210 new cases of lung cancer and 159,260 related deaths. The process begins with the detection of lung cancer which is detected through the diagnosis of lung nodules (a manifestation of lung cancer). These nodules are approximately spherical regions of primarily high density tissue that are visible in computed tomography (CT) images of the lung. The treatment of these lung cancer nodules is complex, nearly 70% of lung cancer patients require radiation therapy as part of their treatment. Radiation-induced lung injury is a limiting toxicity that may decrease cure rates and increase morbidity and mortality treatment. By finding ways to accurately detect, at early stage, and hence prevent lung injury, it will have significant positive consequences for lung cancer patients. The ultimate goal of this dissertation is to develop a clinically usable CAD system that can improve the sensitivity and specificity of early detection of radiation-induced lung injury based on the hypotheses that radiated lung tissues may get affected and suffer decrease of their functionality as a side effect of radiation therapy treatment. These hypotheses have been validated by demonstrating that automatic segmentation of the lung regions and registration of consecutive respiratory phases to estimate their elasticity, ventilation, and texture features to provide discriminatory descriptors that can be used for early detection of radiation-induced lung injury. The proposed methodologies will lead to novel indexes for distinguishing normal/healthy and injured lung tissues in clinical decision-making. To achieve this goal, a CAD system for accurate detection of radiation-induced lung injury that requires three basic components has been developed. These components are the lung fields segmentation, lung registration, and features extraction and tissue classification. This dissertation starts with an exploration of the available medical imaging modalities to present the importance of medical imaging in today’s clinical applications. Secondly, the methodologies, challenges, and limitations of recent CAD systems for lung cancer detection are covered. This is followed by introducing an accurate segmentation methodology of the lung parenchyma with the focus of pathological lungs to extract the volume of interest (VOI) to be analyzed for potential existence of lung injuries stemmed from the radiation therapy. After the segmentation of the VOI, a lung registration framework is introduced to perform a crucial and important step that ensures the co-alignment of the intra-patient scans. This step eliminates the effects of orientation differences, motion, breathing, heart beats, and differences in scanning parameters to be able to accurately extract the functionality features for the lung fields. The developed registration framework also helps in the evaluation and gated control of the radiotherapy through the motion estimation analysis before and after the therapy dose. Finally, the radiation-induced lung injury is introduced, which combines the previous two medical image processing and analysis steps with the features estimation and classification step. This framework estimates and combines both texture and functional features. The texture features are modeled using the novel 7th-order Markov Gibbs random field (MGRF) model that has the ability to accurately models the texture of healthy and injured lung tissues through simultaneously accounting for both vertical and horizontal relative dependencies between voxel-wise signals. While the functionality features calculations are based on the calculated deformation fields, obtained from the 4D-CT lung registration, that maps lung voxels between successive CT scans in the respiratory cycle. These functionality features describe the ventilation, the air flow rate, of the lung tissues using the Jacobian of the deformation field and the tissues’ elasticity using the strain components calculated from the gradient of the deformation field. Finally, these features are combined in the classification model to detect the injured parts of the lung at an early stage and enables an earlier intervention

Geometric modeling of non-rigid 3D shapes : theory and application to object recognition.

One of the major goals of computer vision is the development of flexible and efficient methods for shape representation. This is true, especially for non-rigid 3D shapes where a great variety of shapes are produced as a result of deformations of a non-rigid object. Modeling these non-rigid shapes is a very challenging problem. Being able to analyze the properties of such shapes and describe their behavior is the key issue in research. Also, considering photometric features can play an important role in many shape analysis applications, such as shape matching and correspondence because it contains rich information about the visual appearance of real objects. This new information (contained in photometric features) and its important applications add another, new dimension to the problem\u27s difficulty. Two main approaches have been adopted in the literature for shape modeling for the matching and retrieval problem, local and global approaches. Local matching is performed between sparse points or regions of the shape, while the global shape approaches similarity is measured among entire models. These methods have an underlying assumption that shapes are rigidly transformed. And Most descriptors proposed so far are confined to shape, that is, they analyze only geometric and/or topological properties of 3D models. A shape descriptor or model should be isometry invariant, scale invariant, be able to capture the fine details of the shape, computationally efficient, and have many other good properties. A shape descriptor or model is needed. This shape descriptor should be: able to deal with the non-rigid shape deformation, able to handle the scale variation problem with less sensitivity to noise, able to match shapes related to the same class even if these shapes have missing parts, and able to encode both the photometric, and geometric information in one descriptor. This dissertation will address the problem of 3D non-rigid shape representation and textured 3D non-rigid shapes based on local features. Two approaches will be proposed for non-rigid shape matching and retrieval based on Heat Kernel (HK), and Scale-Invariant Heat Kernel (SI-HK) and one approach for modeling textured 3D non-rigid shapes based on scale-invariant Weighted Heat Kernel Signature (WHKS). For the first approach, the Laplace-Beltrami eigenfunctions is used to detect a small number of critical points on the shape surface. Then a shape descriptor is formed based on the heat kernels at the detected critical points for different scales. Sparse representation is used to reduce the dimensionality of the calculated descriptor. The proposed descriptor is used for classification via the Collaborative Representation-based Classification with a Regularized Least Square (CRC-RLS) algorithm. The experimental results have shown that the proposed descriptor can achieve state-of-the-art results on two benchmark data sets. For the second approach, an improved method to introduce scale-invariance has been also proposed to avoid noise-sensitive operations in the original transformation method. Then a new 3D shape descriptor is formed based on the histograms of the scale-invariant HK for a number of critical points on the shape at different time scales. A Collaborative Classification (CC) scheme is then employed for object classification. The experimental results have shown that the proposed descriptor can achieve high performance on the two benchmark data sets. An important observation from the experiments is that the proposed approach is more able to handle data under several distortion scenarios (noise, shot-noise, scale, and under missing parts) than the well-known approaches. For modeling textured 3D non-rigid shapes, this dissertation introduces, for the first time, a mathematical framework for the diffusion geometry on textured shapes. This dissertation presents an approach for shape matching and retrieval based on a weighted heat kernel signature. It shows how to include photometric information as a weight over the shape manifold, and it also propose a novel formulation for heat diffusion over weighted manifolds. Then this dissertation presents a new discretization method for the weighted heat kernel induced by the linear FEM weights. Finally, the weighted heat kernel signature is used as a shape descriptor. The proposed descriptor encodes both the photometric, and geometric information based on the solution of one equation. Finally, this dissertation proposes an approach for 3D face recognition based on the front contours of heat propagation over the face surface. The front contours are extracted automatically as heat is propagating starting from a detected set of landmarks. The propagation contours are used to successfully discriminate the various faces. The proposed approach is evaluated on the largest publicly available database of 3D facial images and successfully compared to the state-of-the-art approaches in the literature. This work can be extended to the problem of dense correspondence between non-rigid shapes. The proposed approaches with the properties of the Laplace-Beltrami eigenfunction can be utilized for 3D mesh segmentation. Another possible application of the proposed approach is the view point selection for 3D objects by selecting the most informative views that collectively provide the most descriptive presentation of the surface

Shape Analysis Using Spectral Geometry

Shape analysis is a fundamental research topic in computer graphics and computer vision. To date, more and more 3D data is produced by those advanced acquisition capture devices, e.g., laser scanners, depth cameras, and CT/MRI scanners. The increasing data demands advanced analysis tools including shape matching, retrieval, deformation, etc. Nevertheless, 3D Shapes are represented with Euclidean transformations such as translation, scaling, and rotation and digital mesh representations are irregularly sampled. The shape can also deform non-linearly and the sampling may vary. In order to address these challenging problems, we investigate Laplace-Beltrami shape spectra from the differential geometry perspective, focusing more on the intrinsic properties. In this dissertation, the shapes are represented with 2 manifolds, which are differentiable. First, we discuss in detail about the salient geometric feature points in the Laplace-Beltrami spectral domain instead of traditional spatial domains. Simultaneously, the local shape descriptor of a feature point is the Laplace-Beltrami spectrum of the spatial region associated to the point, which are stable and distinctive. The salient spectral geometric features are invariant to spatial Euclidean transforms, isometric deformations and mesh triangulations. Both global and partial matching can be achieved with these salient feature points. Next, we introduce a novel method to analyze a set of poses, i.e., near-isometric deformations, of 3D models that are unregistered. Different shapes of poses are transformed from the 3D spatial domain to a geometry spectral one where all near isometric deformations, mesh triangulations and Euclidean transformations are filtered away. Semantic parts of that model are then determined based on the computed geometric properties of all the mapped vertices in the geometry spectral domain while semantic skeleton can be automatically built with joints detected. Finally we prove the shape spectrum is a continuous function to a scale function on the conformal factor of the manifold. The derivatives of the eigenvalues are analytically expressed with those of the scale function. The property applies to both continuous domain and discrete triangle meshes. On the triangle meshes, a spectrum alignment algorithm is developed. Given two closed triangle meshes, the eigenvalues can be aligned from one to the other and the eigenfunction distributions are aligned as well. This extends the shape spectra across non-isometric deformations, supporting a registration-free analysis of general motion data

View generated database

This document represents the final report for the View Generated Database (VGD) project, NAS7-1066. It documents the work done on the project up to the point at which all project work was terminated due to lack of project funds. The VGD was to provide the capability to accurately represent any real-world object or scene as a computer model. Such models include both an accurate spatial/geometric representation of surfaces of the object or scene, as well as any surface detail present on the object. Applications of such models are numerous, including acquisition and maintenance of work models for tele-autonomous systems, generation of accurate 3-D geometric/photometric models for various 3-D vision systems, and graphical models for realistic rendering of 3-D scenes via computer graphics

Digital Image Processing

This book presents several recent advances that are related or fall under the umbrella of 'digital image processing', with the purpose of providing an insight into the possibilities offered by digital image processing algorithms in various fields. The presented mathematical algorithms are accompanied by graphical representations and illustrative examples for an enhanced readability. The chapters are written in a manner that allows even a reader with basic experience and knowledge in the digital image processing field to properly understand the presented algorithms. Concurrently, the structure of the information in this book is such that fellow scientists will be able to use it to push the development of the presented subjects even further

Developing advanced mathematical models for detecting abnormalities in 2D/3D medical structures.

Detecting abnormalities in two-dimensional (2D) and three-dimensional (3D) medical structures is among the most interesting and challenging research areas in the medical imaging field. Obtaining the desired accurate automated quantification of abnormalities in medical structures is still very challenging. This is due to a large and constantly growing number of different objects of interest and associated abnormalities, large variations of their appearances and shapes in images, different medical imaging modalities, and associated changes of signal homogeneity and noise for each object. The main objective of this dissertation is to address these problems and to provide proper mathematical models and techniques that are capable of analyzing low and high resolution medical data and providing an accurate, automated analysis of the abnormalities in medical structures in terms of their area/volume, shape, and associated abnormal functionality. This dissertation presents different preliminary mathematical models and techniques that are applied in three case studies: (i) detecting abnormal tissue in the left ventricle (LV) wall of the heart from delayed contrast-enhanced cardiac magnetic resonance images (MRI), (ii) detecting local cardiac diseases based on estimating the functional strain metric from cardiac cine MRI, and (iii) identifying the abnormalities in the corpus callosum (CC) brain structure—the largest fiber bundle that connects the two hemispheres in the brain—for subjects that suffer from developmental brain disorders. For detecting the abnormal tissue in the heart, a graph-cut mathematical optimization model with a cost function that accounts for the object’s visual appearance and shape is used to segment the the inner cavity. The model is further integrated with a geometric model (i.e., a fast marching level set model) to segment the outer border of the myocardial wall (the LV). Then the abnormal tissue in the myocardium wall (also called dead tissue, pathological tissue, or infarct area) is identified based on a joint Markov-Gibbs random field (MGRF) model of the image and its region (segmentation) map that accounts for the pixel intensities and the spatial interactions between the pixels. Experiments with real in-vivo data and comparative results with ground truth (identified by a radiologist) and other approaches showed that the proposed framework can accurately detect the pathological tissue and can provide useful metrics for radiologists and clinicians. To estimate the strain from cardiac cine MRI, a novel method based on tracking the LV wall geometry is proposed. To achieve this goal, a partial differential equation (PDE) method is applied to track the LV wall points by solving the Laplace equation between the LV contours of each two successive image frames over the cardiac cycle. The main advantage of the proposed tracking method over traditional texture-based methods is its ability to track the movement and rotation of the LV wall based on tracking the geometric features of the inner, mid-, and outer walls of the LV. This overcomes noise sources that come from scanner and heart motion. To identify the abnormalities in the CC from brain MRI, the CCs are aligned using a rigid registration model and are segmented using a shape-appearance model. Then, they are mapped to a simple unified space for analysis. This work introduces a novel cylindrical mapping model, which is conformal (i.e., one to one transformation and bijective), that enables accurate 3D shape analysis of the CC in the cylindrical domain. The framework can detect abnormalities in all divisions of the CC (i.e., splenium, rostrum, genu and body). In addition, it offers a whole 3D analysis of the CC abnormalities instead of only area-based analysis as done by previous groups. The initial classification results based on the centerline length and CC thickness suggest that the proposed CC shape analysis is a promising supplement to the current techniques for diagnosing dyslexia. The proposed techniques in this dissertation have been successfully tested on complex synthetic and MR images and can be used to advantage in many of today’s clinical applications of computer-assisted medical diagnostics and intervention

Using Surfaces and Surface Relations in an Early Cognitive Vision System

The final publication is available at Springer via http://dx.doi.org/10.1007/s00138-015-0705-yWe present a deep hierarchical visual system with two parallel hierarchies for edge and surface information. In the two hierarchies, complementary visual information is represented on different levels of granularity together with the associated uncertainties and confidences. At all levels, geometric and appearance information is coded explicitly in 2D and 3D allowing to access this information separately and to link between the different levels. We demonstrate the advantages of such hierarchies in three applications covering grasping, viewpoint independent object representation, and pose estimation.European Community’s Seventh Framework Programme FP7/IC

Robustness and Accuracy of Feature-Based Single Image 2-D–3-D Registration Without Correspondences for Image-Guided Intervention

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