Code Implementation for Normalized Mutual Information Calculation in Image Registration

In the process of image registration, it is often necessary to calculate the similarity between two images. One commonly used method involves computing normalized mutual information (NMI). Normalized mutual information serves as a metric to measure the correlation between two images, helping determine their spatial correspondence. In image registration code implementation, we typically follow these steps: First, we calculate the joint histogram of the two images, which represents the probability distribution of intensity value pairs. Then, we compute the marginal histograms for each individual image. Using these histograms, we derive the mutual information using the formula: MI(A,B) = H(A) + H(B) - H(A,B), where H(A) and H(B) are the marginal entropies, and H(A,B) is the joint entropy. The normalized version is obtained by dividing mutual information by the minimum or average of the marginal entropies: NMI = MI(A,B) / min(H(A),H(B)). Key implementation considerations include handling image intensity quantization, managing histogram bin sizes for optimal precision, and implementing efficient entropy calculations. The core functions typically involve histogram computation using functions like numpy.histogram2d in Python or similar matrix operations in MATLAB, followed by entropy calculations using logarithmic operations on probability distributions. By calculating normalized mutual information between two images, we can evaluate their similarity more effectively, leading to more accurate registration results. This approach improves both the precision and reliability of image registration algorithms, particularly in medical imaging and computer vision applications where precise alignment is critical.