thresholding the maximum entropy

Maximum entropy thresholding is based on the maximization of the information measure between object and background.

let C1 and C2 two classes for the object and the background respectively; the maximum entropy measure can be calculated :

hC1(t)= - sum (pi/pC1)*log(pi/pC1) for i<=t
hC2(t)= - sum (pi/pC2)*log(pi/pC2) for i>t

pC1=sum pi i<=t and pC2=sum pi i>t

pC1+pC2=1 because the histogram is normalized

pi estimate the probability of the gray-level value "i"
pi=ni/N
where ni is the occurrence of the gray level "i" in the image.
ni is the histogram h(i)