Abstract: Histogram plays an important statistical role in digital
image processing. However, the existing quantum image models are
deficient to do this kind of image statistical processing because
different gray scales are not distinguishable. In this paper, a novel
quantum image representation model is proposed firstly in which the
pixels with different gray scales can be distinguished and operated
simultaneously. Based on the new model, a fast quantum algorithm of
constructing histogram for quantum image is designed. Performance
comparison reveals that the new quantum algorithm could achieve an
approximately quadratic speedup than the classical counterpart. The
proposed quantum model and algorithm have significant meanings for
the future researches of quantum image processing.