Kappa ( κ ): Analysis of Curvature in Biological Image Data using B-splines

This is the authors' abstract. We don't add key points for this paper.

Curvature is a central morphological feature of tissues, cells, and sub-cellular structures. A challenge for computational biology is to measure the curvature of these structures from biological image data. We present an open-source Fiji plugin for measuring curvature using B-splines. The plugin is named Kappa after the Greek symbol for curvature, κ . Kappa is semi-automated: users create an initialization curve by a point-click method, and the initialization curve is fit to the underlying data using an iterative minimization algorithm. We demonstrate Kappa’s applicability on images of cytoskeletal filaments in vitro , the cell wall of budding yeast, and whole worms moving in an agar dish. In order to verify the accuracy and precision of Kappa, we created a bank of synthetic images of known curvature using sine waves and golden spirals, which we digitized with different signal-to-noise ratios (SNR), pixel sizes, and point-spread functions (PSF). For synthetic images with characteristics similar to real data, the measured curvatures of those images show a high correlation with the theoretical curvatures. Our fitting algorithms perform better with higher SNR, smaller pixel sizes, and especially PSFs equivalent to super-resolution microscopy data (surprise, surprise). Kappa is freely available under the MIT license for simple integration into Fiji-based workflows. The source code and documentation can be found on GitHub at https://github.com/brouhardlab/Kappa .