Evaluation of variations in the shape of grain types using principal components analysis of the elliptic Fourier descriptors

Abstract

The variation in the shape of cereal grains, namely; barley, oat, rye and wheat (Canada Western Amber Durum and Canada Western Red Spring), were quantitatively evaluated using principal components analysis (PCA) based on elliptic Fourier descriptors. Grain image boundary contours were extracted from the digital images of kernels, expressed as chain-coded points and then approximated by 13 elliptic Fourier coefficients. After normalization of the size, rotation and starting point of the contours, four groups of coefficients namely; invariant, symmetrical, asymmetric and standardized Fourier coefficients were analyzed separately using PCA. The PCA based on the symmetric Fourier coefficients captured the shape variability of different grains with fewer principal components (PCs) than the rest. Results suggest that the major shape variations of grains can be summarized by the first two, five, eight and seventeen PCs of the symmetric, standardized, invariant and asymmetric Fourier coefficients, respectively, capturing about 99% of shape variations. The effect of growing regions on kernel shapes was also studied and results revealed that the shape variability is well captured by the PCA of the symmetric coefficients of the standardized Fourier descriptors.