Measuring volume and density of a barley grain using ellipsoid approximation from a 2-D digital image

Abstract

A digital imaging method was developed to determine the size, weight, volume and density of individual barley grains. Calibrations were developed using morphological measurements based on 2-D digital images, and were validated using a range of bulk barley samples. The validation of the grain diameter (minor) and grain weight algorithms gave high correlation coefficients ( r = 0.93 and 0.97, respectively, P < 0.01), with low standard errors (0.09 mm and 1.37 mg, respectively) when compared to physical measurements. Estimated grain volume and density from image data, using three different mathematical approaches were compared: Model 1, a general ellipsoid; Model 2, a combination of two cone frustums with an ellipse top and base; and Model 3, a set of elliptical cylinders representing pixels along the image length. Derived grain volume data using Model 2 when compared to gas displacement volume measurements gave significant correlations ( r = 0.97, P < 0.01) with the lowest standard error (0.97 mm 3), in contrast to volume data estimated using Model 1 and Model 3. Even though Model 2 gave accurate and precise results for grain volume, Model 1 (with the slope adjusted) gave the highest correlation ( r = 0.63, P < 0.01) with the lowest standard error (0.055 mg/mm 3) for estimating grain density from image data, compared to gas displacement density measurements.