Subspace procrustes analysis

Postprint (author's final draft

Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach

Cardiac motion estimation is an important diagnostic tool to detect heart diseases and it has been explored with modalities such as MRI and conventional ultrasound (US) sequences. US cardiac motion estimation still presents challenges because of the complex motion patterns and the presence of noise. In this work, we propose a novel approach to estimate the cardiac motion using ultrafast ultrasound data. -- Our solution is based on a variational formulation characterized by the L2-regularized class. The displacement is represented by a lattice of b-splines and we ensure robustness by applying a maximum likelihood type estimator. While this is an important part of our solution, the main highlight of this paper is to combine a low-rank data representation with topology preservation. Low-rank data representation (achieved by finding the k-dominant singular values of a Casorati Matrix arranged from the data sequence) speeds up the global solution and achieves noise reduction. On the other hand, topology preservation (achieved by monitoring the Jacobian determinant) allows to radically rule out distortions while carefully controlling the size of allowed expansions and contractions. Our variational approach is carried out on a realistic dataset as well as on a simulated one. We demonstrate how our proposed variational solution deals with complex deformations through careful numerical experiments. While maintaining the accuracy of the solution, the low-rank preprocessing is shown to speed up the convergence of the variational problem. Beyond cardiac motion estimation, our approach is promising for the analysis of other organs that experience motion.Comment: 15 pages, 10 figures, Physics in Medicine and Biology, 201

Subspace procrustes analysis

Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Then, a non-rigid 2-D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can simultaneously model all rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more effcient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach.Preprin

Subspace Procrustes Analysis

Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Then, a non-rigid 2-D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can simultaneously model all rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more efficient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach

Extrinisic Calibration of a Camera-Arm System Through Rotation Identification

Determining extrinsic calibration parameters is a necessity in any robotic system composed of actuators and cameras. Once a system is outside the lab environment, parameters must be determined without relying on outside artifacts such as calibration targets. We propose a method that relies on structured motion of an observed arm to recover extrinsic calibration parameters. Our method combines known arm kinematics with observations of conics in the image plane to calculate maximum-likelihood estimates for calibration extrinsics. This method is validated in simulation and tested against a real-world model, yielding results consistent with ruler-based estimates. Our method shows promise for estimating the pose of a camera relative to an articulated arm's end effector without requiring tedious measurements or external artifacts. Index Terms: robotics, hand-eye problem, self-calibration, structure from motio

Learning associations between clinical information and motion-based descriptors using a large scale MR-derived cardiac motion atlas

The availability of large scale databases containing imaging and non-imaging data, such as the UK Biobank, represents an opportunity to improve our understanding of healthy and diseased bodily function. Cardiac motion atlases provide a space of reference in which the motion fields of a cohort of subjects can be directly compared. In this work, a cardiac motion atlas is built from cine MR data from the UK Biobank (~ 6000 subjects). Two automated quality control strategies are proposed to reject subjects with insufficient image quality. Based on the atlas, three dimensionality reduction algorithms are evaluated to learn data-driven cardiac motion descriptors, and statistical methods used to study the association between these descriptors and non-imaging data. Results show a positive correlation between the atlas motion descriptors and body fat percentage, basal metabolic rate, hypertension, smoking status and alcohol intake frequency. The proposed method outperforms the ability to identify changes in cardiac function due to these known cardiovascular risk factors compared to ejection fraction, the most commonly used descriptor of cardiac function. In conclusion, this work represents a framework for further investigation of the factors influencing cardiac health.Comment: 2018 International Workshop on Statistical Atlases and Computational Modeling of the Hear

Implementing a multi-model estimation method

This work is realized within the scope of a general attempt to understand parametric adaptation, regarding visual perception. The key idea is to analyze how we may use multi-model parametric estimation as a 1st step towards categorization. More generally, the goal is to formalize how the notion of ``objects'' or ``events'' in an application may be reduced to a choice in a hierarchy of parametric models used to estimate the underlying data categorization. These mechanisms are to be linked with what occurs in the cerebral cortex where object recognition corresponds to a parametric neuronal estimation (see for instanced Page 2000 for a discussion and Freedman et al 2001 for an example regarding the primate visual cortex). We thus hope to bring here an algorithmic element in relation with the ``grand-ma'' neuron modelization. We thus revisit the problem of parameter estimation in computer vision, presented here as a simple optimization problem, considering (i) non-linear implicit measurement equations and parameter constraints, plus (ii) robust estimation in the presence of outliers and (iii) multi-model comparisons. Here, (1) a projection algorithm based on generalizations of square-root decompositions allows an efficient and numerically stable local resolution of a set of non-linear equations. On the other hand, (2) a robust estimation module of a hierarchy of non-linear models has been designed and validated. A step ahead, the software architecture of the estimation module is discussed with the goal of being integrated in reactive software environments or within applications with time constraints

Multilevel analysis of nuclear dynamics in lamin perturbed fibroblasts

The nuclear lamina provides structural support to the nucleus and has a central role in defining nuclear organization. Defects in its filamentous constituents, the lamins, lead to a class of diseases collectively referred to as laminopathies. On the cellular level, lamin mutations affect the physical integrity of nuclei and nucleo-cytoskeletal interactions, resulting in increased susceptibility to mechanical stress and altered gene expression [1]. Most studies regarding the mechanical properties of the nucleus in laminopathic conditions are based on the induction of extracellular stress, such as strain or compression, and focus on nuclear integrity and/or nucleo-cytoskeletal interaction [2]. Far less is known about the role of nuclear organization and mobility under basal steady-state conditions. In this study, we quantitatively compared nuclear organization, nuclear deformation and chromatin mobility of fibroblasts from a Hutchinson-Gilford progeria patient with cells from a lamin A/C-deficient patient and wild-type dermal fibroblasts. To this end, we created a toolbox in imageJ for automatically analyzing both nuclear as well as subnuclear dynamics in living cells. Simultaneously, we developed a workflow for comparing cellular morphology and subcellular protein distribution in a high content fashion. We found that the absence of functional lamin A/C leads to increased nuclear plasticity on the hour and minute time scale but also to increased intranuclear mobility down to the seconds time scale. In contrast, progeria cells showed overall reduced nuclear dynamics. In addition, high content analysis revealed marked morphological and topological differences between different culture passages within a cell type and between different pathological variants of culture-age matched laminopathic cell types

Voxel-wise group analysis of DTI

pre-printDiffusion tensor MRI (DTI) is now a widely used modality to investigate the fiber tissues in vivo, especially the white matter in brain. An automatic pipeline is described in this paper to conduct a localized voxel-wise multiple-subject group comparison study of DTI. The pipeline consists of 3 steps: 1) Preprocessing, including image format converting, image quality check, eddy-current and motion artifact correction, skull stripping and tensor image estimation, 2) study-specific unbiased DTI atlas computation via affine followed by fluid nonlinear registration and warping of all individual DTI images into the common atlas space to achieve voxel-wise correspondence, 3) voxel-wise statistical analysis via heterogeneous linear regression and wild bootstrap technique for correcting for multiple comparisons. This pipeline was applied to process data from a fitness and aging study and preliminary results are presented. The results show that this fully automatic pipeline is suitable for voxel-wise group DTI analysis