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. • A novel method for statistical modeling and analysis of temporally-evolving shapes. • Elastic shape analysis represents a shape sequence by Euclidean time series. • Dynamic shape evolution is crucial aspect of cell migration in biology. • A detailed approach for modeling and classifying shape dynamics during cell motility.

The method proposed in this paper is a robust combination of multi-task learning and unsupervised domain adaptation for segmenting amoeboid cells in microscopy. A highlight of this work is the manner in which the model's hyperparameters are estimated. The detriments of ad-hoc parameter estimation are well known, but this issue remains largely unaddressed in the context of CNN-based segmentation. Using a novel min-max formulation of the segmentation cost function our proposed method analytically estimates the model's hyperparameters, while simultaneously learning the CNN weights during training. This end-to-end framework provides a consolidated mechanism to harness the potential of multi-task learning to isolate and segment clustered cells from low contrast brightfield images, and it simultaneously leverages deep domain adaptation to segment fluorescent cells without explicit pixel-level re- annotation of the data. Experimental validations on multi-cellular images strongly suggest the effectiveness of the proposed technique, and our quantitative results show at least 15% and 10% improvement in cell segmentation on brightfield and fluorescence images respectively compared to contemporary supervised segmentation methods.

We propose an image based PDE-constrained optimisation framework to compute the dynamical quantities of a cell nucleus undergoing deformation. It allows retrieving the displacement, strain and stress at each pixel of the nuclear domain, as well as the traction force on the boundary. It is based on a mechanical model of the nuclear components and a pair of images documenting the deformation of the cell nucleus. To test our approach, we provide a warping method that produces a second image from an initial one along with the expected mechanical quantities. Both quantitative and qualitative analysis conclude for a significant and consistent improvement of our method over optical flow techniques.

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.

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.

Detecting and segmenting individual cells from microscopy images is critical to various life science applications. Traditional cell segmentation tools are often ill-suited for applications in brightfield microscopy due to poor contrast and intensity heterogeneity, and only a small subset are applicable to segment cells in a cluster. In this regard, we introduce a novel supervised technique for cell segmentation in a multitask learning paradigm. A combination of a multi-task loss, based on the region and cell boundary detection, is employed for an improved prediction efficiency of the network. The learning problem is posed in a novel min-max framework which enables adaptive estimation of the hyper-parameters in an automatic fashion. The region and cell boundary predictions are combined via morphological operations and active contour model to segment individual cells. The proposed methodology is particularly suited to segment touching cells from brightfield microscopy images without manual interventions. Quantitatively, we observe an overall Dice score of 0.93 on the validation set, which is an improvement of over 15.9% on a recent unsupervised method, and outperforms the popular supervised U-net algorithm by at least 5.8% on average.

Variational deformable models have proven over the past decades a high efficiency for segmentation and tracking in 2-D sequences. Yet, their application to 3-D time-lapse images has been hampered by discretization issues, heavy computational loads and lack of proper user visualization and interaction, limiting their use for routine analysis of large data-sets. We propose here to address these limitations by reformulating the problem entirely in the discrete domain using 3-D active meshes, which express a surface as a discrete triangular mesh, and minimize the energy functional accordingly. By performing computations in the discrete domain, computational costs are drastically reduced, whilst the mesh formalism allows to benefit from real-time 3-D rendering and other GPU-based optimizations. Performance evaluations on both simulated and real biological data sets show that this novel framework outperforms current state-of-the-art methods, constituting a light and fast alternative to traditional variational models for segmentation and tracking applications.

This paper presents a segmentation and tracking method for quantitative analysis of cell dynamics from in vitro videomicroscopy data. The method is based on parametric active contours and includes several adaptations that address important difficulties of cellular imaging, particularly the presence of low-contrast boundary deformations known as pseudopods, and the occurence of multiple contacts between cells. First, we use an edge map based on the average intensity dispersion that takes advantage of relative background homogeneity to facilitate the detection of both pseudopods and interfaces between adjacent cells. Second, we introduce a repulsive interaction between contours that allows correct segmentation of objects in contact and overcomes the shortcomings of previously reported techniques to enforce contour separation. Our tracking technique was validated on a realistic data set by comparison with a manually defined ground-truth and was successfully applied to study the motility of amoebae in a biological research project.