Algorithmic statistics of retinal images

There has been a tremendous amount of image processing and machine learning research to measure and classify disease progression from live optical coherence tomography (OCT) imaging of the retina. The images considered here are large, complex, three-dimensional (3-D) and difficult to visualize effectively. Many current supervised machine learning approaches, \emph{e.g.} neural networks, are non-metric meaning that any features or measurements generated can introduce systematic distortion that may be correlated with underlying non-meaningful physiological differences. Here we present a metric learning approach using the normalized compression distance (NCD) combined with anisotropic structure-enhancing filters to quantify and visualize the principal differences among a collection of 3-D retinal images. We validate the NCD-measured structural differences between pairs of images against the physician-measured change in visual field function, achieving a prediction error of $\sim$ 0.5 dB, more accurate than non-metric deep learning approaches. The normalized compression vectors (NCV) are proposed as a feature set measuring visual differences among a collection of 3-D microscopy images. The utility of the NCV for visualizing and measuring patterns of change is demonstrated for a human with moderate non-progressing glaucoma and for a non-human primate model using intraocular pressure setting manipulation. We conclude with a brief simulation of non-metric embedding features, \emph{e.g.} from neural networks, introducing class-correlated statistical distortion.

The cell signaling structure function

Live cell microscopy captures 5-D $(x,y,z,channel,time)$ movies that display patterns of cellular motion and signaling dynamics. We present here an approach to finding spatiotemporal patterns of cell signaling dynamics in 5-D live cell microscopy movies unique in requiring no a priori knowledge of expected pattern dynamics, and no training data. The proposed cell signaling structure function (SSF) is a Kolmogorov structure function that optimally measures cell signaling state as nuclear intensity w.r.t. surrounding cytoplasm, a significant improvement compared to the current state-of-the-art cytonuclear ratio. SSF kymographs store at each spatiotemporal cell centroid the SSF value, or a functional output such as velocity. Patterns of similarity are identified via the metric normalized compression distance (NCD). The NCD is a reproducing kernel for a Hilbert space that represents the input SSF kymographs as points in a low dimensional embedding that optimally captures the pattern similarity identified by the NCD throughout the space. The only parameter is the expected cell radii ($\mu m$). A new formulation of the cluster structure function optimally estimates how meaningful an embedding from the RKHS representation. Results are presented quantifying the impact of ERK and AKT signaling between different oncogenic mutations, and by the relation between ERK signaling and cellular velocity patterns for movies of 2-D monolayers of human breast epithelial (MCF10A) cells, 3-D MCF10A spheroids under optogenetic manipulation of ERK, and human induced pluripotent stem cells .