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

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,{kappa} . 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 Kappas 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.