EFFECTS OF BIT DEPTH ON THE MULTIFRACTAL ANALYSIS OF GRAYSCALE IMAGES

Multifractal box counting analysis has been widely applied to study the scaling characteristics of grayscale images. Since bit depth is an important property of such images it is desirable know the impact of varying bit depths on the estimation of the generalized dimensions (D-q). We generated random geometrical multifractal grayscale fields, which were then transformed from double precision to 16, 13, and 8 bit depths. Digitized grayscale images of soil thin sections at 13 bit depth were also selected for study and transformed to 8 bit depth. The moment based box counting method was applied to evaluate the bit depth effects on D-q. The partition functions for the multifractal fields became noticeably nonlinear on a log-log scale when q << 0 as the bit depth decreased. This trend can be attributed to loss of grayscale details, changes in the local mass distribution, and the occurrence of zeros due to the bit depth transformation and data normalization processes. These effects were most pronounced for positively skewed multifractal fields, with a high proportion of extremely small mass fractions. As a result, the generalized dimensions estimated by linear regression were not always accurate, and an alternative method based on numerical derivatives was explored. The numerical method significantly improved the accuracy of the multifractal analyses; the maximum absolute difference between the analytical and numerically-derived estimates of D-q was only 9.62 x 10(-3). However, when applied to situations in which the box counting scale factor did not match the scale factor used to generate the multifractal field, the numerically-derived estimates of D-q were severely biased. In this case, the linear regression method is preferable even though some error may occur due to limited bit depths. All of the soil grayscale images exhibited multifractal scaling characteristics, although there was little effect of bit depth on the resulting D-q values. Because of random fluctuations in the partition functions, the linear regression method proved to be more robust than the numerical derivative method for estimating the generalized dimensions of natural grayscale images.