In this paper, we propose a novel derivative measure based on the probability of intensity difference that is defined by observed intensities and their true intensities. Because the true intensity cannot be estimated accurately only using two observed intensities, the probability is marginalized to consider an entire set of possible true values. The proposed measure not only considers intensity dependent noise effectively using a distribution of intensity difference, but also computes the relevant difference of two corresponding pixels that have different true intensities by extending the same intensity assumption in previous works. Using the proposed measure, the estimation result of image derivative for synthetic noisy signals is closer to the ground truth than most of previous measures. We apply the proposed measure for block matching and corner detection that compute intensity similarity in the temporal domain and image derivative in the spatial domain, respectively.