Entropy is related to the Legendre-Fenchel transform of the cumulant generating function, the 2nd derivative of which is the Variance. More precisely, entropy H(P)=C - D_{KL}(P,Q), where C is the maximum of entropy, and D_{KL}(P,Q) is the Kullback-Leibler divergence of distribution P from distribution Q, which maximizes the entropy (i.e. C= H(Q) ).  Then the Legendre-Fenchel transform of D_{KL}(P,Q), considering it as function of P, is the cumulant generating function \Gamma(t)=D*(tx,Q)=\log\int e^{tx} dQ  (here dQ is the reference measure, in finite case usually Q=1/N).  Variance is the 2nd cumulant: k_2=(d^2/dt^2)\Gamma(t)|_t=0.  What this means in practice is that large variance implies large entropy (small KL-divergence of P from Q). The opposite implication also holds if P is Gaussian, but generally the implication is only one way, if cumulants beyond variance are non-zero.  Here is a paper with some ideas: https://arxiv.org/abs/1507.08229

Entropy => based on quantized values of the intensity /amplitude

Otsu => value (again is based on probability distribution )   for automatic thresholding based on neighborhood 

Common : as I see it , is the first order stats got from distribution curves 

Thanks @Roman V. Belavkin and @Aparna Sathya Murthy 

I've read my answer, and I think some clarification is needed.  I wrote my answer assuming that your distribution has exponential form P(x)=e^{tx-\Gamma(t)}, where \Gamma(t) = \log Z(t), and Z(t)=\sum_x e^{tx} is the partition function normalizing P. Then my answer about the variance of random variable x applies directly. However, if your P has some other form, then we have to transform x into f(x) by some function, such that P becomes P(f(x)) = e^{t f(x) - \Gamma(t)}, where \Gamma(t) is now related to Z(t)=\sum_x e^{t f(x)}.  In this case, the second derivative of \Gamma(t) is not the variance of x, but rather the variance of y=f(x).