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  1. Free, publicly-accessible full text available June 1, 2023
  2. Free, publicly-accessible full text available April 1, 2023
  3. We consider the problem of characterizing shape populations using highly frequent representative shapes. Framing such shapes as statistical modes – shapes that correspond to (significant) local maxima of the underlying pdfs – we develop a frequency-based, nonparametric approach for estimating sample modes. Using an elastic shape metric, we define ϵ-neighborhoods in the shape space and shortlist shapes that are central and have the most neighbors. A critical issue – How to automatically select the threshold ϵ? – is resolved using a combination of ANOVA and empirical mode distribution. The resulting modal set, in turn, helps characterize the shape population and performs better than the traditional cluster means. We demonstrate this framework using amoeba shapes from brightfield microscopy images and highlight its advantages over existing ideas.
    Free, publicly-accessible full text available March 28, 2023
  4. Free, publicly-accessible full text available March 1, 2023
  5. Summary This paper develops a functional hybrid factor regression modelling framework to handle the heterogeneity of many large-scale imaging studies, such as the Alzheimer’s disease neuroimaging initiative study. Despite the numerous successes of those imaging studies, such heterogeneity may be caused by the differences in study environment, population, design, protocols or other hidden factors, and it has posed major challenges in integrative analysis of imaging data collected from multicentres or multistudies. We propose both estimation and inference procedures for estimating unknown parameters and detecting unknown factors under our new model. The asymptotic properties of both estimation and inference procedures are systematically investigated. The finite-sample performance of our proposed procedures is assessed by using Monte Carlo simulations and a real data example on hippocampal surface data from the Alzheimer’s disease study.
    Free, publicly-accessible full text available February 1, 2023
  6. Despite enormous structural variability exhibited in 3D chromosomal conformations at a global scale, there is a significant commonality of structures visible at smaller, local levels. We hypothesize that chromosomal conformations are representable as concatenations of a handful of prototypical shapelets, termed shape letters. This is akin to expressing complicated sentences in a language using only a small set of letters. Our goal is to organize the vast variability of 3D chromosomal conformation by constructing a set of predominant shape letters, termed a shape alphabet, using statistical shape analysis of curvelets taken from training conformations. This paper utilizes conformations generated from Integrative Genome Modeling to develop a shape alphabet as follows: it first segments 3D conformations into curvelets according to their Topologically Associated Domains. It then clusters these segments, estimates mean shapes, and refines and reorders these shapes into a Chromosome Shape Alphabet. The paper demonstrates effectiveness of this construction by successfully representing independent test conformations taken from IGM and other methods such as SIMBA3D, both symbolically and structurally, using the constructed alphabet.
    Free, publicly-accessible full text available December 9, 2022
  7. Elastic Riemannian metrics have been used successfully for statistical treatments of functional and curve shape data. However, this usage suffers from a significant restriction: the function boundaries are assumed to be fixed and matched. Functional data often comes with unmatched boundaries, {\it e.g.}, in dynamical systems with variable evolution rates, such as COVID-19 infection rate curves associated with different geographical regions. Here, we develop a Riemannian framework that allows for partial matching, comparing, and clustering functions under phase variability {\it and} uncertain boundaries. We extend past work by (1) Defining a new diffeomorphism group G over the positive reals that is the semidirect product of a time-warping group and a time-scaling group; (2) Introducing a metric that is invariant to the action of G; (3) Imposing a Riemannian Lie group structure on G to allow for an efficient gradient-based optimization for elastic partial matching; and (4) Presenting a modification that, while losing the metric property, allows one to control the amount of boundary disparity in the registration. We illustrate this framework by registering and clustering shapes of COVID-19 rate curves, identifying basic patterns, minimizing mismatch errors, and reducing variability within clusters compared to previous methods.
  8. The problem of using covariates to predict shapes of objects in a regression setting is important in many fields. A formal statistical approach, termed Geodesic regression model, is commonly used for modeling and analyzing relationships between Euclidean predictors and shape responses. Despite its popularity, this model faces several key challenges, including (i) misalignment of shapes due to pre-processing steps, (ii) difficulties in shape alignment due to imaging heterogeneity, and (iii) lack of spatial correlation in shape structures. This paper proposes a comprehensive geodesic factor regression model that addresses all these challenges. Instead of using shapes as extracted from pre-registered data, it takes a more fundamental approach, incorporating alignment step within the proposed regression model and learns them using both pre-shape and covariate data. Additionally, it specifies spatial correlation structures using low-dimensional representations, including latent factors on the tangent space and isotropic error terms. The proposed framework results in substantial improvements in regression performance, as demonstrated through simulation studies and a real data analysis on Corpus Callosum contour data obtained from the ADNI study.
  9. Registering functions (curves) using time warpings (re-parameterizations) is central to many computer vision and shape analysis solutions. While traditional registration methods minimize penalized-L2 norm, the elastic Riemannian metric and square-root velocity functions (SRVFs) have resulted in significant improvements in terms of theory and practical performance. This solution uses the dynamic programming algorithm to minimize the L2 norm between SRVFs of given functions. However, the computational cost of this elastic dynamic programming framework – O(nT 2 k) – where T is the number of time samples along curves, n is the number of curves, and k < T is a parameter – limits its use in applications involving big data. This paper introduces a deep-learning approach, named SRVF Registration Net or SrvfRegNet to overcome these limitations. SrvfRegNet architecture trains by optimizing the elastic metric-based objective function on the training data and then applies this trained network to the test data to perform fast registration. In case the training and the test data are from different classes, it generalizes to the test data using transfer learning, i.e., retraining of only the last few layers of the network. It achieves the state-of-the-art alignment performance albeit at much reduced computational cost. We demonstrate themore »efficiency and efficacy of this framework using several standard curve datasets.« less