A simple algorithm to measure the volume‐weighted and number‐weighted mean volume of particles

Abstract

SummaryAn algorithm is presented which offers an alternative approach for measuring volume‐ and number‐weighted mean volume and standard deviation of particles. Using a computer‐assisted manual method the following intermediate steps are performed automatically: generation of linear probes emanating from the sampling point of the object and intersecting the profile periphery, measurement of their lengths, and measurement of the area of the transect required for estimating the standard deviation of the volume‐weighted mean volume. By first tracing manually the outline of the periphery of the object with a cursor, on a magnetic tablet or on an image acquired into the computer with a video camera, the location of all pixels of the periphery is registered and the area of the transect is measured concurrently. The computer is informed of the coordinates of the selection point in the uniform random (UR) sampling grid by clicking the cursor. All ensuing operations are automatic. In the case of isotropic UR (IUR) sections the algorithm traces a series of uniform systematic random linear probes between the sampling point and the object profile periphery emanating from this selection point, radiating at angular intervals of 29–30° to the periphery. In the case of vertical sections, similar lines are generated at intervals where the sine of the angle changes by a value of 0·33. The volume‐weighted mean volume of the object is estimated from the average of all the products , where l represents the length of each individual random linear probe. As the periphery is traced, the algorithm can automatically determine the area of the cross‐section of the object, from which the standard deviation of the volume‐weighted mean volume can be calculated. Some elements of the above algorithm are also used for the measurement of the number‐weighted mean volume. The latter procedure is facilitated using an acoustic vertical depth monitor attached to the microscope. The impact of truncation (‘lost caps’) on the precision of the measurements is discussed. The algorithm is of particular use in light microscopy for measuring cell nuclei by direct visual inspection of the microscopic field using a side‐arm mirror assembly interfaced with a magnetic tablet.