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.

中文翻译：

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曲率对谷物种子大小物体高光谱反射率图像的影响

用于农产品质量和安全检查的高光谱成像经常面临处理圆形表面的挑战。当对象像谷物一样小且相对于像素的空间维度的曲率很大时，这一挑战尤其明显。来自小麦粒大小的均匀照明物体边缘附近区域的漫反射光的强度将大大降低，历史上由兰伯特余弦定律建模，该定律以 16 世纪的约翰·兰伯特 (Johann Lambert) 的名字命名，他推测从无光泽表面上的一个点反射的能量与观察者的偏角有关。目前的研究是为了将反射光的预测朗伯响应与数学上可定义形状的曲面（即圆柱体和长椭球体）上的实际测量值进行比较，后者被引入作为小麦籽粒的近似值。使用台式高光谱成像系统扫描三个直径的炭黑掺杂和烧结 PTFE（0.16-0.99 标称反射率）圆柱体，最小的与小麦籽粒的小尺寸相当，以及暗灰色长球体同等大小和白麦粒。分析包括将沿曲面的单个像素的测量反射率 (940–1650 nm) 与根据兰伯特余弦定律确定的反射率进行比较。研究结果表明，中心像素对校正反应良好，