Brain Warping Research Articles

Maps with Least Distortion Between Surfaces: From Geography to Brain Warping

The mathematical problem of cartography is that of finding maps that optimize distortion, in a sense that needs to be made precise. Indeed, the word ``distortion is attached to a variety of parameters: distances, areas and angles, and the general problem is to find mappings that are closest to mappings that make a compromise between these parameters among all mappings from a given subset of the sphere onto the Euclidean plane. Furthermore, geographers usually had additional constraints on the desired maps, such as preserving distances along a certain meridian---or along all meridians, or of sending parallels (circles centered at the poles) to parallel straight lines, or to concentric circles, or to other types of ``parallel curves in the plane. We shall mention examples of mappings from the sphere to the Euclidean plane satisfying such requirements. The various approaches to the question of maps with minimal distortion from (subsets of) the sphere onto the Euclidean plane acted as a motivation for Euler, Lagrange, Gauss, Chebyshev and other geometers to study general maps between differentiable surfaces. Furthermore, geography gave rise to an early version of extremal quasiconformal mappings, as a particular class of least-distortion mappings. This took place in the nineteenth century, before quasiconformal mappings were officially introduced in the late 1920s as a tool in conformal geometry and before they led to the first known metric on Teichmuller space. Thurston's theory of best Lipschitz maps, developed in his paper ``Minimal stretch maps between hyperbolic surfaces, is also based on the idea of studying maps with least distortion between surfaces. It led him to the definition of another metric on Teichmuller space, the Thurston metric, which is today an active research topic. We shall discuss all this in the present paper. We shall also see how least distortion maps occur in art, biology and the medical sciences, and in particular in brain imaging.

A framework to study the cortical folding patterns

This paper describes a decade-long research program focused on the variability of the cortical folding patterns. The program has developed a framework of using artificial neuroanatomists that are trained to identify sulci from a database. The framework relies on a renormalization of the brain warping problem, which consists in matching the cortices at the scale of the folds. Another component of the program is the search for the alphabet of the folding patterns, namely, a list of indivisible elementary sulci. The search relies on the study of the cortical folding process using antenatal imaging and on backward simulations of morphogenesis aimed at revealing traces of the embryologic dimples in the mature cortical surface. The importance of sulcal-based morphometry is illustrated by a simple study of the correlates of handedness on asymmetry indices. The study shows for instance that the central sulcus is larger in the dominant hemisphere.

Conceptual, methodological, and statistical challenges in brain imaging studies of developmentally based psychopathologies.

Brain imaging studies in developmentally based psychopathologies most often use magnetic resonance imaging (MRI) to study regional volumes, task-related activity, neurometabolite concentrations, or the paths of fiber tracts within the brain. Methodological challenges for the use of MRI in studying these disorders include understanding the ultrastructural correlates of brain structure and function that are below the limits of resolution of this imaging modality and developing better methods for approximating the anatomical boundaries of the cytoarchitectonic units that are defined by those ultrastructural characteristics. Conceptual challenges include distinguishing findings that represent pathophysiologically central causes from compensatory and epiphenomenal effects, a difficulty that stems directly from the inherently correlational nature of imaging data. The promise of functional imaging studies must capitalize on the specificity of the cognitive and behavioral probes that are used to illuminate core features of the pathophysiology of developmental disorders, while recognizing the assumptions and limitations of the subtraction paradigms that are used to isolate the brain functions of interest. Statistical challenges include incorporating adequate statistical models for scaling effects within the brain, as well as modeling important demographic correlates that contribute to the substantial interindividual variability inherent in most imaging data. Statistical analyses need to consider the substantial intercorrelation of measures across the brain and the importance of correcting for multiple statistical comparisons, as well as the need for improved methods for brain warping and for assessing effective connectivity in functional imaging studies.

Handbook of Medical Imaging. Processing and Analysis

I Enhancement Fundametal Enhancement Techniques Adaptive Image Filtering Enhancement by Multiscale Nonlinear Operators Medical Image Enhancement with Hybrid Filters. II Segmentation Overview and Fundamentals of Medical Image Segmentation Image Segmentation by Fuzzy Clustering: Methods and Issues Segmentation with Neural Networks Deformable Models Shape Constraints in Deformable Models Gradient Vector Flow Deformable Models Fully Automated Hybrid Segmentation of the Brain Volumetric Segmentation Partial Volume Segmentation with Voxel Histograms. III Quantification Two-dimensional Shape and Texture Quantification Texture Analysis in Three Dimensions as a Cue to Medical Diagnosis Computational Neuroanatomy Using Shape Transformation Morphometry of Arterial Trees and Microvascular Networks Image-Based Computational Biomechanics of the Musculoskeletal System Three-Dimensional Bone Angle Quantification Database Selection and Feature Extraction for Neural Networks Quantitative Image Analysis for Estimation of Breast Cancer Risk Classification of Breast Lesions in Mammograms Quantitative Analysis of Cardiac Function Image Processing and Analysis in Tagged Cardiac MRI Image Interpolation and Resampling. IV Registration The Physical Basis of Spatial Distortions in Magnetic Resonance Images Physical and Biological Bases of Spatial Distortiobns in Positron Emission Tomography Images Biological Underpinnings of Anatomic Consistency and Variability in the Human Brain Spatial Transformation Models Validation of Registration Accuracy Landmark-based Registration using Features Identified Through Differential Geometry Registration of Contours using Chamfer Matching Within-Modality Registration using Intensity-Based Cost Functions Across-Modality Registration using Intensity-Based Cost Functions Talairach Space as a Tool for Intersubject Standardization in the Brain Warping Strategies for Intersubject Registration Optimizing the Resampling of Registered Images Clinical Applications of Image Registration Registration for Image-Guided Surgery Image Registration and the Construction of Multidimensional Brain Atlases. V Visualization Visualization Pathways in Biomedicine Three-Dimensional Visualization in Medicine and Biology Volume Visualization in Medicine Fast Isosurface Extraction Methods for Large Image Data Sets Morphometric Methods for Virtual Endoscopy. VI Compression Storage and Communication Fundamentals and Standards of Compression and Communication Medical Image Archive and Retrieval Image Standardization in PACS Quality Evaluation for Compressed Medical Images: Fundamentals Quality Evaluation for Compressed Medical Images: Diagnostic Accuracy Quality Evaluation for Compressed Medical Images: Statistical Issues Three-Dimensional Image Compression with Wavelet Transforms Medical Image Processing and Analysis Software. Index

Three-dimensional multimodal brain warping using the demons algorithm and adaptive intensity corrections.

This paper presents an original method for three-dimensional elastic registration of multimodal images. We propose to make use of a scheme that iterates between correcting for intensity differences between images and performing standard monomodal registration. The core of our contribution resides in providing a method that finds the transformation that maps the intensities of one image to those of another. It makes the assumption that there are at most two functional dependencies between the intensities of structures present in the images to register, and relies on robust estimation techniques to evaluate these functions. We provide results showing successful registration between several imaging modalities involving segmentations, T1 magnetic resonance (MR), T2 MR, proton density (PD) MR and computed tomography (CT). We also argue that our intensity modeling may be more appropriate than mutual information (MI) in the context of evaluating high-dimensional deformations, as it puts more constraints on the parameters to be estimated and, thus, permits a better search of the parameter space.