(376d) Registration and Dimensionality Reduction Algorithms for the Analysis of Drosophila Embryogenesis Images

Authors: 
Dsilva, C., Princeton University
Lim, B., University of Pennsylvania
Singer, A., Princeton University
Shvartsman, S. Y., Princeton University
Kevrekidis, I. G., Princeton University

Over the past several years, there have been significant algorithmic developments in image analysis. These include new algorithms for image registration [1], as well as methods to compute image features which are both informative and invariant to symmetries such as translations and rotations [2, 3]. Simultaneously, dimensionality reduction techniques, such as principal component analysis and diffusion maps [4], have proven useful in uncovering patterns and structure in large, complex data sets. Vector diffusion maps [5] is a recently developed algorithm that combines diffusion maps and the factoring out of symmetries in a single algorithmic step, which simultaneously registers and extracts low-dimensional structure from imaging data sets. We discuss these algorithms and apply them to imaging data collected from studies of Drosophila embryogenesis to extract parsimonious descriptions of developmental dynamic pattern formation processes.

[1] Singer, A. "Angular synchronization by eigenvectors and semidefinite programming." Applied and computational harmonic analysis 30.1 (2011): 20-36.

[2] Mallat, Stéphane. "Group invariant scattering." Communications on Pure and Applied Mathematics 65.10 (2012): 1331-1398.

[3] Zhao, Zhizhen, and Amit Singer. "Fourier–Bessel rotational invariant eigenimages." JOSA A 30.5 (2013): 871-877.

[4] Coifman, Ronald R., et al. "Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps." Proceedings of the National Academy of Sciences of the United States of America 102.21 (2005): 7426-7431.

[5] Singer, Amit, and H‐T. Wu. "Vector diffusion maps and the connection Laplacian." Communications on pure and applied mathematics 65.8 (2012): 1067-1144.