Effect of curvature on hyperspectral reflectance images of cereal seed-sized objects

Hyperspectral imaging for quality and safety inspection of agricultural products is frequently confronted with the challenge of handling rounded surfaces. This challenge is especially noted when the objects are as small as cereal grains for which curvature with respect to the spatial dimension of a pixel is large. Diffusely reflected light from regions near the edges of a uniformly illuminated object the size of a wheat kernel will have its intensity reduced greatly, historically modelled by the Lambert Cosine Law, eponymously named after Johann Lambert of the sixteenth century, who theorised that the fraction of energy reflected from a spot on a matte surface is related to the declination angle of the observer. The current study was performed to compare the predicted Lambertian response of reflected light to actual measurement on curved surfaces of mathematically definable shapes, namely cylinders and prolate ellipsoids, with the latter introduced as an approximation to a wheat kernel. Carbon black-doped and sintered PTFE (0.16–0.99 nominal reflectance) cylinders of three diameters, with the smallest on par with the minor dimension of a wheat kernel, were scanned using a benchtop hyperspectral imaging system, as were dull gray-painted prolate spheroids of equivalent size and white wheat kernels. The analysis consisted of comparing the measured reflectances (940–1650 nm) from individual pixels along the curved surface with those determined according to the Lambert Cosine Law. The findings indicate that central pixels responded well to correction, with a greater departure from theory for pixels closest to the edges.