i. In Histogram equalization, the image that is being equalized, is processed in such a way that all the grey levels present in an image get equal number of pixels and we get a flat histogram.

ii. Let us consider a continuous image

iii. Now in order to get an equalized image, the Cumulative Density Function (CDF) has to be calculated and in order to calculate the cdf, the Probability density function should be known.

iv. The continuous image occupies the complete range of intensities

v. from 0 to L-1, and as histogram is an approximation of the PDF of these intensities, when the transformation is applied to the above continuous image, it results in a perfectly equalized image as shown in figure 1(b)

vi. When we consider a digital image, it will never occupy all the intensity levels that are available.

vii. And as Histogram is an approximation to a PDF, also no new allowed intensity levels are created in the process, perfectly flat histograms i.e. a perfectly equalized image is rare in case of a digital image.

Thus Continuous image histogram can be perfectly equalized but it is practically very difficult to perfectly equalize a digital image.