Spherical harmonics texture extraction for versatile analysis of biological objects
Authors: Gros Oane , Passmore Josiah B. , Borst Noa , Kutra Dominik , Nijenhuis Wilco , Fuqua Timothy , Kapitein Lukas C. , Crocker Justin , Kreshuk Anna , Köhler Simone 
Published: July 2024

The characterization of phenotypes in cells or organisms from microscopy data largely depends on differences in the spatial distribution of image intensity. Multiple methods exist for quantifying the intensity distribution - or image texture - across objects in natural images. However, many of these texture extraction methods do not directly adapt to 3D microscopy data. Here, we presentSpherical Textureextraction, which measures the variance in intensity per angular wavelength by calculating the Spherical Harmonics or Fourier power spectrum of a spherical or circular projection of the angular mean intensity of the object. This method provides a 20-value characterization that quantifies the scale of features in the spherical projection of the intensity distribution, giving a different signal if the intensity is, for example, clustered in parts of the volume or spread across the entire volume. We apply this method to different systems and demonstrate its ability to describe various biological problems through feature extraction. TheSpherical Textureextraction characterizes biologically defined gene expression patterns inDrosophila melanogasterembryos, giving a quantitative read-out for pattern formation. Our method can also quantify morphological differences inCaenorhabditis elegansgermline nuclei, which lack a predefined pattern. We show that the classification of germline nuclei using theirSpherical Textureoutperforms a convolutional neural net when training data is limited. Additionally, we use a similar pipeline on 2D cell migration data to extract polarization direction, quantifying the alignment of fluorescent markers to the migration direction. We implemented theSpherical Texturemethod as a plugin inilastik, making it easy to install and apply to any segmented 3D or 2D dataset. Additionally, this technique can also easily be applied through a Python package to provide extra feature extraction for any object classification pipeline or downstream analysis.

Author summary

We introduce a novel method to extract quantitative data from microscopy images by precisely measuring the distribution of intensities within objects in both 3D or 2D. This method is easily accessible through the object classification workflow ofilastik, provided the original image is segmented into separate objects. The method is specifically designed to analyze mostly convex objects, focusing on the variation in fluorescence intensity caused by differences in their shapes or patterns.

We demonstrate the versatility of our method by applying it to very different biological samples. Specifically, we showcase its effectiveness in quantifying the patterning inD. melanogasterembryos, in classifying the nuclei inC. elegansgermlines, and in extracting polarization information from individual migratory cells. Through these examples, we illustrate that our technique can be employed across different biological scales. Furthermore, we highlight the multiple ways in which the data generated by our method can be used, including quantifying the strength of a specific pattern, employing machine learning to classify diverse morphologies, or extracting directionality or polarization from fluorescence intensity.