UC Santa Barbara

Cell boundary detection and segmentation enable the quantitative analysis of cellular organization, morphology, and dynamics, which are fundamental to understanding biological processes and disease mechanisms. Accurate detection and segmentation from time-lapse microscopy videos are essential for providing longitudinal information of cell boundaries. Popular unsupervised cell segmentation tools, such as ImageJ, require manual tuning of parameters and rely on restrictive assumptions about the shape of the objects. While recently developed supervised segmentation tools based on convolutional neural networks enhance accuracy, they depend on high-quality labeled images for training, making them unsuitable for segmenting new types of objects not in existing databases. To address these limitations, we developed an unsupervised cell segmentation algorithm from noisy microscopy images using fast Gaussian processes without the need for parameter tuning or restrictive assumptions about the shape of the object. We derived robust thresholding criteria that are adaptive for heterogeneous images containing distinct brightness at different parts to separate objects from the background, and employed watershed segmentation to distinguish touching cell objects. Both simulated studies and real-data analysis of large microscopy images demonstrate the scalability and accuracy of our approach compared with existing alternatives. Our method achieves consistently higher average precision scores than {\sf ImageJ} for both whole cell and cell nuclei segmentation. This unsupervised approach is particularly valuable for segmenting novel cell types where annotated training data is limited or unavailable, making it broadly applicable to diverse microscopy imaging tasks. We have also implemented this method into an R package, FastSegmentation, for scalable and accessible application. Beyond segmentation, we apply diffusion-based generative models to cell microscopy image analysis. We review denoising diffusion probabilistic models (DDPMs) and score-based generative models using stochastic differential equations (SDEs), including their theoretical foundations and training procedures. Through controlled experiments on simulated Gaussian mixture models and real cell microscopy images, we demonstrate that these models can effectively generate realistic cell images for data augmentation and denoise corrupted microscopy images while preserving cellular structures. These capabilities address critical challenges in biomedical imaging, where acquiring large labeled datasets is expensive, and images are often degraded by various noise sources during acquisition. Chapter 1 introduces cell microscopy segmentation challenges and available segmentation and smoothing methods, including the application of Gaussian processes (GP) for smoothing 2-dimensional (2D) data. Chapter 2 details the proposed unsupervised segmentation algorithm leveraging smoothing via GP, a novel data-driven threshold, and watershed for final segmentation. Chapter 3 presents the R package FastSegmentation, which contains readily available functions for implementing the segmentation process described in Chapter 2. Chapter 4 reviews DDPMs and score-based generative modeling using SDEs, presents simulation analysis of Gaussian mixture models, and demonstrates applications to cell microscopy image generation and denoising. Chapter 5 provides concluding remarks and future directions.