Rotated Fourier transform (RFT) enables the quantification of anisotropic structure in high-moisture plant-protein extrudates

When producing plant-protein-based meat analogues via high moisture extrusion (HME), the structure of extrudates is determined by complex interactions between ingredient composition and processing conditions. To facilitate consumers in their transition towards a diet higher in plant-based proteins, the food industry aims to closely mimic the structure of meat of animal origin. Currently, insights into the structuring process are gained, for example, by imaging samples using MRI or confocal microscopy. Existing software for analysing these images, however, often lacks the ability to quantitively analyse structure and anisotropy. Here, we present a new image processing method, named Rotated Fourier Transform (RFT), that enables the quantification of anisotropic structures of extrudates from multimodal images acquired at different length scales. RFT can provide a single measure of structural anisotropy, namely the weighted order parameter (WOP), for either the entire image or subregions thereof. RFT utilises Fourier transforms to obtain the dominant angles representing the structural orientation detected within the image. For each dominant angle, we further calculate an amplitude relative to the background within each sub-image. These amplitudes depend on the signal-to-noise levels of the corresponding angular features, which enables reducing the influence of insignificant features on the WOP. Here, we used RFT to quantify anisotropy in images of soy protein concentrate HME samples. We identified both anisotropic and isotropic regions and further showed that the relative spatial extent of the anisotropic region, perpendicular to the flow direction, increases along the cooling die. While applied in this paper to the specific case of soy HME samples, RFT is a generic method applicable to any image displaying anisotropic features. Thus, RFT is a powerful and robust tool for comprehensive quantification of food structures and beyond.