Image Statistics Image Statistics Brightness Mean grey level

Image Statistics

Image Statistics Brightness Mean grey level Contrast Variance, Standard deviation Image Energy Root Mean Squared Energy (RMSE) Information Content Entropy

Image Statistics Brightness mean grey level = 1 MN M-1 N-1 i[m, n] m=0 n=0 Contrast - relates to the variation of image intensity about the mean - image contrast is low when the image is uniformly grey - image contrast is high when the image lacks intermediate shades of grey

Image Statistics Contrast variance = (alternative equation) variance = std dev = M-1 N-1 1 MN m=0 n=0 (i[m, n] - average) M-1 N-1 i[m, n] m=0 n=0 variance 2 - 2 average 2

Image Energy rmse = 1 MN M-1 N-1 2 i [m, n] m=0 n=0 (root mean square image energy) rmse 2 = contrast 2 + average 2

Average 118. 7 Contrast 62. 3 RMS Energy 134. 08 Average 119. 7 Contrast 53. 2 RMS Energy 131. 1

Grey level distribution For an image with G possible intensity values (grey levels) the grey level distribution is defined as: c[g] = the number of pixels with grey level g (for each g=0, 1, . . G-1) p[g] = the relative frequency of grey level g c[g] p[g] = MN

Grey level Distribution plotted as a Histogram

Alternative Equations for Image Statistics G-1 g p[g] average = g=0 G-1 std dev = 2 (g - average) p[g] g=0 G-1 RMSE = 2 g p[g] g=0

Image Statistics entropy = G-1 p[g] log (p[g]) g=0 2 (for all p[g] > 0) Entropy is sometimes is used to characterize information content in an image. For example an image which is uniformly grey has entropy = 0. The maximum possible entropy occurs when all grey levels are present with equal probability.

Cumulative Grey Level Distribution P[g] = p[0] + p[1] +. . . + p[g] P[g] is the proportion of pixels with grey level value less than or equal to g.

camera image histogram cumulative histogram