i) Histogram is not a unique representation of an image.
ii) Histogram is a graph of gray value vs frequency of occurrence of gray value.It depends on the probability or frequency of gray value.
iii) So NO matter how the gray values are distributed over the image,if the frequency of occurrence of gray value is not changed, the histogram will not change .Therefore, Histogram is not unique representation of images.
iv) That means it is possible that two or more different images can have same Histogram.
v) For Example:Consider a set of binary images having same Histogram.