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This paper presents a generative statistical model for analyzing time series of planar shapes. Using elastic shape analysis, we separate object kinematics (rigid motions and speed variability) from morphological evolution, representing the latter through transported velocity fields (TVFs). A principal component analysis (PCA) based dimensionality reduction of the TVF representation provides a finite-dimensional Euclidean framework, enabling traditional time-series analysis. We then fit a vector auto-regressive (VAR) model to the TVF-PCA time series, capturing the statistical dynamics of shape evolution. To characterize morphological changes,we use VAR model parameters for model comparison, synthesis, and sequence classification. Leveraging these parameters, along with machine learning classifiers, we achieve high classification accuracy. Extensive experiments on cell motility data validate our approach, demonstrating its effectiveness in modeling and classifying migrating cells based on morphological evolution—marking a novel contribution to the field. 

This paper addresses the problem of characterizing statistical distributions of cellular shape populations using shape samples from microscopy image data. This problem is challenging because of the nonlinearity and high-dimensionality of shape manifolds. The paper develops an efficient, nonparametric approach using ideas from k-modal mixtures and kernel estimators. It uses elastic shape analysis of cell boundaries to estimate statistical modes and clusters given shapes around those modes. (Notably, it uses a combination of modal distributions and ANOVA to determine k automatically.) A population is then characterized as k-modal mixture relative to this estimated clustering and a chosen kernel (e.g., a Gaussian or a flat kernel). One can compare and analyze populations using the Fisher-Rao metric between their estimated distributions. We demonstrate this approach for classifying shapes associated with migrations of entamoeba histolytica under different experimental conditions. This framework remarkably captures salient shape patterns and separates shape data for different experimental settings, even when it is difficult to discern class differences visually. 

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. 

Statistical analysis of shape evolution during cell migration is important for gaining insights into biological processes. This paper develops a time-series model for temporal evolution of cellular shapes during cell motility. It uses elastic shape analysis to represent and analyze shapes of cell boundaries (as planar closed curves), thus separating cell shape changes from cell kinematics. Specifically, it utilizes Transported Square-Root Velocity Field (TSRVF), to map non-Euclidean shape sequences into a Euclidean time series. It then uses PCA to reduce Euclidean dimensions and imposes a Vector Auto-Regression (VAR) model on the resulting low-dimensional time series. Finally, it presents some results from VAR-based statistical analysis: estimation of model parameters and diagnostics, synthesis of new shape sequences, and predictions of future shapes given past shapes.