Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2018 Mar 15;145(6):dev156778. doi: 10.1242/dev.156778

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

© 2018. Published by The Company of Biologists Ltd

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution and reproduction in any medium provided that the original work is properly attributed.

PMC Copyright notice

Fig. 2. — LOCO-EFA retrieves correctly the cell shape's dominant spatial frequency. (A) EFA decomposes a two-dimensional cell outline into an infinite summation of related ellipses or modes that can also be used to approximate the cell outline. (B) Each EFA harmonic is decomposed into two counter-rotating circles. (C) Mode is composed of the counter-clockwise rotating n+1th harmonic circle and the clockwise rotating n−1th circle. (D) The combined amplitude contribution to L_n (yellow line) of the two counter-rotating circles with radii and also depends on the offset in their starting points and the offset of the overall (mode 1) starting point, which together determine the initial phase shift (green dots) in the amplitude contribution of each rotor. (E,F) Comparison of closed contour reconstruction through either EFA (E) or LOCO-EFA (F). Although both approximations converge to the original six-lobed star shape (labelled ‘Original’), the reconstruction using EFA harmonics (E) generates a spurious shape after addition of the fifth harmonic and only recovers the original shape after the seventh harmonic, whereas the LOCO-EFA (F) reconstitutes the original shape precisely at the sixth mode, matching the protrusion number. The number of modes used for each sequential reconstruction is indicated below each shape. (G) LOCO-EFA reconstruction of a real cell taking the first n modes into account, as indicated below the panels. (H) Determination of the level of mismatch between the original cell shape and the Nth mode truncated LOCO-EFA approximation, by applying the XOR (exclusive OR) function (see supplementary Materials and Methods).

Inline graphic — LOCO-EFA retrieves correctly the cell shape's dominant spatial frequency. (A) EFA decomposes a two-dimensional cell outline into an infinite summation of related ellipses or modes that can also be used to approximate the cell outline. (B) Each EFA harmonic is decomposed into two counter-rotating circles. (C) Mode is composed of the counter-clockwise rotating n+1th harmonic circle and the clockwise rotating n−1th circle. (D) The combined amplitude contribution to L_n (yellow line) of the two counter-rotating circles with radii and also depends on the offset in their starting points and the offset of the overall (mode 1) starting point, which together determine the initial phase shift (green dots) in the amplitude contribution of each rotor. (E,F) Comparison of closed contour reconstruction through either EFA (E) or LOCO-EFA (F). Although both approximations converge to the original six-lobed star shape (labelled ‘Original’), the reconstruction using EFA harmonics (E) generates a spurious shape after addition of the fifth harmonic and only recovers the original shape after the seventh harmonic, whereas the LOCO-EFA (F) reconstitutes the original shape precisely at the sixth mode, matching the protrusion number. The number of modes used for each sequential reconstruction is indicated below each shape. (G) LOCO-EFA reconstruction of a real cell taking the first n modes into account, as indicated below the panels. (H) Determination of the level of mismatch between the original cell shape and the Nth mode truncated LOCO-EFA approximation, by applying the XOR (exclusive OR) function (see supplementary Materials and Methods).