Temporal ordering and registration of images in studies of developmental dynamics

Abstract

Progress of development is commonly reconstructed from imaging snapshots of chemical or mechanical processes in fixed tissues. As a first step in these reconstructions, snapshots must be spatially registered and ordered in time. Currently, image registration and ordering are often done manually, requiring a significant amount of expertise with a specific system. However, as the sizes of imaging data sets grow, these tasks become increasingly difficult, especially when the images are noisy and the developmental changes being examined are subtle. To address these challenges, we present an automated approach to simultaneously register and temporally order imaging data sets. The approach is based on vector diffusion maps, a manifold learning technique that does not require a priori knowledge of image features or a parametric model of the developmental dynamics. We illustrate this approach by registering and ordering data from imaging studies of pattern formation and morphogenesis in three model systems. We also provide software to aid in the application of our methodology to other experimental data sets.

Reconstruction of normal forms by learning informed observation geometries from data

“…While we only use indices for the trials and the measurement channels, we did keep the sequential parametrization of the measurements by time (here, at equal time intervals); this is not necessary, and one could use only labels also in the time axis (denoting what measurements were obtained at the same moment in time but without knowing the actual time stamp). This would lead to the correct ordering of the measurement snapshots without providing actual time stamps for them (43). More generally, semisupervised learning and "manifold completion" tools can be used to fruitfully fill in missing data, interpolate, and (modestly) extrapolate the input-output functions learned here.…”

Multiple Penalized Principal Curves: Analysis and Computation

“…Edges that are about to be added in the reconnection step (described in Section 4.2.1) are shown as dashed blue lines. Here we consider data generated as noisy samples of the spiral t ↦ (t cos(t), t sin(t)), t ∈ [3,14], shown as a dashed line in Figure 9(b). 2000 points are drawn uniformly with respect to arc length along the spiral.…”

Synthesizing developmental trajectories

“…A critical assumption in finding the mappings is that the multivariable dynamics of the patterning process are both low-dimensional and smooth with respect to the underlying parameters. This assumption is supported by studies with mathematical models of specific biological systems and by computational analysis of datasets from imaging studies of development [19,20]. More formally, we consider a set of data points (x 1 , .…”