Inherent limitations of bitmap discretization in quantitative microstructural analysis

Quantitative microstructural analysis is an essential element of modern materials science. This is achieved through measurements of different attributes of bitmap digital images of microstructure. In view of the discrete nature of bitmap images, such measurements have an inherent error, which is a strong function of the image resolution. A systematic study of the effect of resolution on the measurement errors is presented in this report. The analysis was performed on virtual bitmap images of both straight lines having various orientations and circles of varying resolution. It is observed that some measured quantities are better in estimating the object or feature attributes than the others. For example, the measurement error is minimum if the length of a straight line is estimated by measuring the maximum feret length in the image. It is also seen that the measurement error with increasing resolution asymptotically decreases to a constant value, which is not necessarily zero in all the cases studied. Particularly, the measurement of perimeter asymptotically reaches a finite quantity of approximately 5.5% instead of approaching zero as in the case of other measurements. Inspired by this result, an analytical expression has been derived to express the error in the perimeter measurement as a function of resolution. This equation is specific to the two image analysis systems used in this work and provides a general framework which is applicable to any arbitrary isotropic 2-dimensional image. It is demonstrated that the error in the perimeter measurement is an overestimate, which asymptotically decreases with increasing resolution to a value of 82−1π−1 (∼ 5.5%) which is very close to the measured value observed in virtual images. This implies that all perimeter measurements by image analysis are always an overestimate of the real value, and this error could be reduced by correcting the measured value by this amount.