Jensen-discrete information generating function with an application to image processing

In this work, we first consider the discrete version of information generating function and develop some new results for it. We then propose Jensen-discrete information generating (JDIG) function as a generalized measure, which is connected to Shannon entropy, fractional Shannon entropy, Gini–Simpson index (Gini entropy), extropy, Jensen–Shannon entropy, Jensen–Gini–Simpson index and Jensen-extropy measures. Finally, for illustrative purpose, we use a real example from image processing and provide some numerical results in terms of the Jensen-discrete information generating function and demonstrate that the JDIG measure introduced here is an useful criteria for measuring similarity between two images.