A Joint Transformation and Residual Image Descriptor for Morphometric Image Analysis using an Equivalence Class Formulation

Existing computational anatomy methodologies for morphometric analysis of medical images are often based solely on the shape transformation, typically being a diffeomorphism, that warps these images to a common template or vice versa. However, anatomical differences as well as changes induced by pathology, prevent the warping transformation from producing an exact correspondence. The residual image captures information that is not reflected by the diffeomorphism, and therefore allows us to maintain the entire morphological profile for analysis. In this paper we present a morphological descriptor which combines the warping transformation with the residual image in an equivalence class formulation, to characterize morphology of anatomical structures. Equivalence classes are formed by pairs of transformation and residual, for different levels of smoothness of the warping transformation. These pairs belong to the same equivalence class, since they jointly reconstruct the exact same morphology. Moreover, pattern classification methods are trained on the entire equivalence class, instead of a single pair, in order to become more robust to a variety of factors that affect the warping transformation, including the anatomy being measured. This joint descriptor is evaluated by statistical testing and estimation of class separation by classification, initially for 2-D synthetic images with simulated atrophy and subsequently for a volumetric dataset consisting of schizophrenia patients and healthy controls. Results of class separation indicate that this joint descriptor produces generally better and more robust class separation than using each of the components separately

Two and three dimensional segmentation of multimodal imagery

The role of segmentation in the realms of image understanding/analysis, computer vision, pattern recognition, remote sensing and medical imaging in recent years has been significantly augmented due to accelerated scientific advances made in the acquisition of image data. This low-level analysis protocol is critical to numerous applications, with the primary goal of expediting and improving the effectiveness of subsequent high-level operations by providing a condensed and pertinent representation of image information. In this research, we propose a novel unsupervised segmentation framework for facilitating meaningful segregation of 2-D/3-D image data across multiple modalities (color, remote-sensing and biomedical imaging) into non-overlapping partitions using several spatial-spectral attributes. Initially, our framework exploits the information obtained from detecting edges inherent in the data. To this effect, by using a vector gradient detection technique, pixels without edges are grouped and individually labeled to partition some initial portion of the input image content. Pixels that contain higher gradient densities are included by the dynamic generation of segments as the algorithm progresses to generate an initial region map. Subsequently, texture modeling is performed and the obtained gradient, texture and intensity information along with the aforementioned initial partition map are used to perform a multivariate refinement procedure, to fuse groups with similar characteristics yielding the final output segmentation. Experimental results obtained in comparison to published/state-of the-art segmentation techniques for color as well as multi/hyperspectral imagery, demonstrate the advantages of the proposed method. Furthermore, for the purpose of achieving improved computational efficiency we propose an extension of the aforestated methodology in a multi-resolution framework, demonstrated on color images. Finally, this research also encompasses a 3-D extension of the aforementioned algorithm demonstrated on medical (Magnetic Resonance Imaging / Computed Tomography) volumes

Task-Optimal Registration Cost Functions

In this paper, we propose a framework for learning the parameters of registration cost functions – such as the tradeoff between the regularization and image similiarity term – with respect to a specific task. Assuming the existence of labeled training data, we specialize the framework for the task of localizing hidden labels via image registration. We learn the parameters of the weighted sum of squared differences (wSSD) image similarity term that are optimal for the localization of Brodmann areas (BAs) in a new subject based on cortical geometry. We demonstrate state-of-the-art localization of V1, V2, BA44 and BA45

Image analysis for extracapsular hip fracture surgery

PhD ThesisDuring the implant insertion phase of extracapsular hip fracture surgery, a surgeon visually inspects digital radiographs to infer the best position for the implant. The inference is made by “eye-balling”. This clearly leaves room for trial and error which is not ideal for the patient. This thesis presents an image analysis approach to estimating the ideal positioning for the implant using a variant of the deformable templates model known as the Constrained Local Model (CLM). The Model is a synthesis of shape and local appearance models learned from a set of annotated landmarks and their corresponding local patches extracted from digital femur x-rays. The CLM in this work highlights both Principal Component Analysis (PCA) and Probabilistic PCA as regularisation components; the PPCA variant being a novel adaptation of the CLM framework that accounts for landmark annotation error which the PCA version does not account for. Our CLM implementation is used to articulate 2 clinical metrics namely: the Tip-Apex Distance and Parker’s Ratio (routinely used by clinicians to assess the positioning of the surgical implant during hip fracture surgery) within the image analysis framework. With our model, we were able to automatically localise signi cant landmarks on the femur, which were subsequently used to measure Parker’s Ratio directly from digital radiographs and determine an optimal placement for the surgical implant in 87% of the instances; thereby, achieving fully automatic measurement of Parker’s Ratio as opposed to manual measurements currently performed in the surgical theatre during hip fracture surgery

Statistical shape analysis for bio-structures : local shape modelling, techniques and applications

A Statistical Shape Model (SSM) is a statistical representation of a shape obtained from data to study variation in shapes. Work on shape modelling is constrained by many unsolved problems, for instance, difficulties in modelling local versus global variation. SSM have been successfully applied in medical image applications such as the analysis of brain anatomy. Since brain structure is so complex and varies across subjects, methods to identify morphological variability can be useful for diagnosis and treatment. The main objective of this research is to generate and develop a statistical shape model to analyse local variation in shapes. Within this particular context, this work addresses the question of what are the local elements that need to be identified for effective shape analysis. Here, the proposed method is based on a Point Distribution Model and uses a combination of other well known techniques: Fractal analysis; Markov Chain Monte Carlo methods; and the Curvature Scale Space representation for the problem of contour localisation. Similarly, Diffusion Maps are employed as a spectral shape clustering tool to identify sets of local partitions useful in the shape analysis. Additionally, a novel Hierarchical Shape Analysis method based on the Gaussian and Laplacian pyramids is explained and used to compare the featured Local Shape Model. Experimental results on a number of real contours such as animal, leaf and brain white matter outlines have been shown to demonstrate the effectiveness of the proposed model. These results show that local shape models are efficient in modelling the statistical variation of shape of biological structures. Particularly, the development of this model provides an approach to the analysis of brain images and brain morphometrics. Likewise, the model can be adapted to the problem of content based image retrieval, where global and local shape similarity needs to be measured

Virtual Morphology and Evolutionary Morphometrics in the new millenium.

EDITED VOLUME; abstract N/

Statistical shape analysis for bio-structures : local shape modelling, techniques and applications

A Statistical Shape Model (SSM) is a statistical representation of a shape obtained from data to study variation in shapes. Work on shape modelling is constrained by many unsolved problems, for instance, difficulties in modelling local versus global variation. SSM have been successfully applied in medical image applications such as the analysis of brain anatomy. Since brain structure is so complex and varies across subjects, methods to identify morphological variability can be useful for diagnosis and treatment. The main objective of this research is to generate and develop a statistical shape model to analyse local variation in shapes. Within this particular context, this work addresses the question of what are the local elements that need to be identified for effective shape analysis. Here, the proposed method is based on a Point Distribution Model and uses a combination of other well known techniques: Fractal analysis; Markov Chain Monte Carlo methods; and the Curvature Scale Space representation for the problem of contour localisation. Similarly, Diffusion Maps are employed as a spectral shape clustering tool to identify sets of local partitions useful in the shape analysis. Additionally, a novel Hierarchical Shape Analysis method based on the Gaussian and Laplacian pyramids is explained and used to compare the featured Local Shape Model. Experimental results on a number of real contours such as animal, leaf and brain white matter outlines have been shown to demonstrate the effectiveness of the proposed model. These results show that local shape models are efficient in modelling the statistical variation of shape of biological structures. Particularly, the development of this model provides an approach to the analysis of brain images and brain morphometrics. Likewise, the model can be adapted to the problem of content based image retrieval, where global and local shape similarity needs to be measured.EThOS - Electronic Theses Online ServiceConsejo Nacional de Ciencia y Tecnología (Mexico) (CONACYT)GBUnited Kingdo

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity