Multi-object segmentation using coupled nonparametric shape and relative pose priors

We present a new method for multi-object segmentation in a maximum a posteriori estimation framework. Our method is motivated by the observation that neighboring or coupling objects in images generate configurations and co-dependencies which could potentially aid in segmentation if properly exploited. Our approach employs coupled shape and inter-shape pose priors that are computed using training images in a nonparametric multi-variate kernel density estimation framework. The coupled shape prior is obtained by estimating the joint shape distribution of multiple objects and the inter-shape pose priors are modeled via standard moments. Based on such statistical models, we formulate an optimization problem for segmentation, which we solve by an algorithm based on active contours. Our technique provides significant improvements in the segmentation of weakly contrasted objects in a number of applications. In particular for medical image analysis, we use our method to extract brain Basal Ganglia structures, which are members of a complex multi-object system posing a challenging segmentation problem. We also apply our technique to the problem of handwritten character segmentation. Finally, we use our method to segment cars in urban scenes

Nonparametric joint shape learning for customized shape modeling

We present a shape optimization approach to compute patient-specific models in customized prototyping applications. We design a coupled shape prior to model the transformation between a related pair of surfaces, using a nonparametric joint probability density estimation. The coupled shape prior forces with the help of application-specific data forces and smoothness forces drive a surface deformation towards a desired output surface. We demonstrate the usefulness of the method for generating customized shape models in applications of hearing aid design and pre-operative to intra-operative anatomic surface estimation

Coupled non-parametric shape and moment-based inter-shape pose priors for multiple basal ganglia structure segmentation

This paper presents a new active contour-based, statistical method for simultaneous volumetric segmentation of multiple subcortical structures in the brain. In biological tissues, such as the human brain, neighboring structures exhibit co-dependencies which can aid in segmentation, if properly analyzed and modeled. Motivated by this observation, we formulate the segmentation problem as a maximum a posteriori estimation problem, in which we incorporate statistical prior models on the shapes and inter-shape (relative) poses of the structures of interest. This provides a principled mechanism to bring high level information about the shapes and the relationships of anatomical structures into the segmentation problem. For learning the prior densities we use a nonparametric multivariate kernel density estimation framework. We combine these priors with data in a variational framework and develop an active contour-based iterative segmentation algorithm. We test our method on the problem of volumetric segmentation of basal ganglia structures in magnetic resonance (MR) images. We present a set of 2D and 3D experiments as well as a quantitative performance analysis. In addition, we perform a comparison to several existent segmentation methods and demonstrate the improvements provided by our approach in terms of segmentation accuracy

Modeling Multi-object Configurations via Medial/Skeletal Linking Structures

We introduce a method for modeling a configuration of objects in 2D or 3D images using a mathematical "skeletal linking structure" which will simultaneously capture the individual shape features of the objects and their positional information relative to one another. The objects may either have smooth boundaries and be disjoint from the others or share common portions of their boundaries with other objects in a piecewise smooth manner. These structures include a special class of "Blum medial linking structures," which are intrinsically associated to the configuration and build upon the Blum medial axes of the individual objects. We give a classification of the properties of Blum linking structures for generic configurations. The skeletal linking structures add increased flexibility for modeling configurations of objects by relaxing the Blum conditions and they extend in a minimal way the individual "skeletal structures" which have been previously used for modeling individual objects and capturing their geometric properties. This allows for the mathematical methods introduced for single objects to be significantly extended to the entire configuration of objects. These methods not only capture the internal shape structures of the individual objects but also the external structure of the neighboring regions of the objects

Medial/skeletal linking structures for multi-region configurations

We consider a generic configuration of regions, consisting of a collection of distinct compact regions $\{\Omega_i\}$ in $\mathbb{R}^{n+1}$ which may be either smooth regions disjoint from the others or regions which meet on their piecewise smooth boundaries $\mathcal{B}_i$ in a generic way. We introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions' individual shapes and geometric properties as well as the "positional geometry" of the collection. The linking structure extends in a minimal way the individual "skeletal structures" on each of the regions, allowing us to significantly extend the mathematical methods introduced for single regions to the configuration. We prove for a generic configuration of regions the existence of a special type of Blum linking structure which builds upon the Blum medial axes of the individual regions. This requires proving several transversality theorems for certain associated "multi-distance" and "height-distance" functions for such configurations. We show that by relaxing the conditions on the Blum linking structures we obtain the more general class of skeletal linking structures which still capture the geometric properties. In addition to yielding geometric invariants which capture the shapes and geometry of individual regions, the linking structures are used to define invariants which measure positional properties of the configuration such as: measures of relative closeness of neighboring regions and relative significance of the individual regions for the configuration. These invariants, which are computed by formulas involving "skeletal linking integrals" on the internal skeletal structures, are then used to construct a "tiered linking graph," which identifies subconfigurations and provides a hierarchical ordering of the regions.Comment: 135 pages, 36 figures. Version to appear in Memoirs of the Amer. Math. So

Computational Anatomy for Multi-Organ Analysis in Medical Imaging: A Review

The medical image analysis field has traditionally been focused on the development of organ-, and disease-specific methods. Recently, the interest in the development of more 20 comprehensive computational anatomical models has grown, leading to the creation of multi-organ models. Multi-organ approaches, unlike traditional organ-specific strategies, incorporate inter-organ relations into the model, thus leading to a more accurate representation of the complex human anatomy. Inter-organ relations are not only spatial, but also functional and physiological. Over the years, the strategies 25 proposed to efficiently model multi-organ structures have evolved from the simple global modeling, to more sophisticated approaches such as sequential, hierarchical, or machine learning-based models. In this paper, we present a review of the state of the art on multi-organ analysis and associated computation anatomy methodology. The manuscript follows a methodology-based classification of the different techniques 30 available for the analysis of multi-organs and multi-anatomical structures, from techniques using point distribution models to the most recent deep learning-based approaches. With more than 300 papers included in this review, we reflect on the trends and challenges of the field of computational anatomy, the particularities of each anatomical region, and the potential of multi-organ analysis to increase the impact of 35 medical imaging applications on the future of healthcare.Comment: Paper under revie

Coupled non-parametric shape and moment-based inter-shape pose priors for multiple basal ganglia structure segmentation

Brain tissue and structure segmentation in magnetic resonance (MR) images is a fundamental problem in clinical studies of brain structure and function. Due to limitations such as low contrast, partial volume effects, and field inhomogeneities, the delineation of subcortical (basal ganglia) structures such as caudate nucleus, putamen, and thalamus from white matter, gray matter and cerebrospinal fluid (CSF) is a very challenging problem. This thesis presents a new method for simultaneous segmentation of multiple brain structures. We formulate the segmentation problem as a maximum a posteriori estimation problem, in which we incorporate statistical prior models on the shapes and relative poses of the structures of interest. Our method is motivated by the observation that neighboring or coupling structures in medical images generate configurations and co-dependencies which could potentially aid in segmentation if properly exploited. Our coupled shape priors are learned through nonparametric multivariate kernel density estimation based on training data. Relative pose priors are modeled via standard moments. Given this framework, the segmentation problems turns into an optimization problem, which we solve using active contours. We present experimental results on synthetic data as well as on a rich set of real MR images demonstrating the effectiveness of the proposed method in segmenting basal ganglia structures as well as improvements it provides over existing approaches

Coupled Shape Models for the Diagnosis of Organ Motion Restriction

Annähernd 30% der weltweiten Todesfälle sind auf Erkrankungen des Herzens und der Lunge zurückzuführen, wobei die meisten dieser Erkrankungen während ihres Verlaufs die Mobilität des betroffenen Organs verändern. Viele dieser To-desfälle könnten durch eine frühzeitige Erkennung und Behandlung der Erkran-kung vermieden werden. Deshalb wurden im Zuge dieser Arbeit Methoden ent-wickelt, um aus Segmentierungen von dynamischen Magnetresonanztomogra-phie-Daten quantitative Kennzahlen für die funktionale Analyse der Herz- und Lungenbewegung zu generieren. Ein automatisiertes Segmentierungsverfahren basierend auf gekoppelten Formmodellen wurde entwickelt, welches wechsel-seitige Informationen der Form und Geometrie mehrerer korrelierter Objekte mit einbezieht, und somit 40% bessere Ergebnisse im Vergleich zur Verwendung einzelner Modelle erzielte. Im Fall des Herzens wurde ein Volumenberechnungs-fehler von unter 13% erreicht, was in der Größenordnung der Interobserver-Variabilität liegt. Für die Lunge konnte ein Volumenfehler von unter 70ml gezeigt werden. Aus den Segmentierungsergebnissen wurden funktionale Parameter der lokalen Organdynamik abgeleitet und visualisiert, die gegen konventionelle Diag-nosemethoden evaluiert wurden und dabei gute Übereinstimmung zeigen, dar-über hinaus jedoch eine lokal und regionale Mobilitätscharakterisierung erlau-ben