No abstract

In this paper, we give a detailed analysis of the accuracy of Zernike moments in terms of their discretization errors and the reconstruction power. It is found that there is an inherent limitation in the precision of computing the Zernike moments due to the geometric nature of a circular domain. This is explained by relating the accuracy issue to a celebrated problem in analytic number theory of evaluating the lattice points within a circle.

An algorithm for high-precision numerical computation of Zernike moments is presented. The algorithm, based on the introduced polar pixel tiling scheme, does not exhibit the geometric error and numerical integration error which are inherent in conventional methods based on Cartesian coordinates. This yields a dramatic improvement of the Zernike moments accuracy in terms of their reconstruction and invariance properties. The introduced image tiling requires an interpolation algorithm which turns out to be of the second order importance compared to the discretization error. Various comparisons are made between the accuracy of the proposed method and that of commonly used techniques. The results reveal the great advantage of our approach.

No abstract

When a constraint is removed, confluent cells migrate directionally into the available space. How the migration directionality and speed increase are initiated at the leading edge and propagate into neighboring cells are not well understood. Using a quantitative visualization technique — Particle Image Velocimetry (PIV) — we revealed that migration directionality and speed had strikingly different dynamics. Migration directionality increases as a wave propagating from the leading edge into the cell sheet, while the increase in cell migration speed is maintained only at the leading edge. The overall directionality steadily increases with time as cells migrate into the cell-free space, but migration speed remains largely the same. A Particle-Based Compass (PBC) model suggests cellular interplay (which depends on cell-cell distance) and migration speed are sufficient to capture the dynamics of migration directionality revealed experimentally. Extracellular Ca2+ regulated both migration speed and directionality, but in a significantly different way, suggested by the correlation between directionality and speed only in some dynamic ranges. Our experimental and modeling results reveal distinct directionality and speed dynamics in collective migration, and these factors can be regulated by extracellular Ca2+ through cellular interplay. Quantitative visualization using PIV and our PBC model thus provide a powerful approach to dissect the mechanisms of collective cell migration.