Selective encryption is a concept in which the main goal is to reduce computational cost while providing confidentiality by encrypting only chosen parts of the information to be protected. Previous work on selective encryption has mainly been aimed towards multimedia applications in order to reduce the overhead induced by encryption while still making the information perceptually secure to a desired protection level. This was accomplished by utilizing the fact that different parts of the information have different impacts on our perception senses, i.e., eyes and ears. How computationally secure the information is when using selective encryption has however only briefly been mentioned or rudimentarily analyzed. In this paper, we therefore investigate the security implications of selective encryption by generalizing the work on entropy of selectively encrypted strings to several dimensions and applying it to bitmap images. The generalization is done by constructing information neighborhoods that capture and model information dependencies in several dimensions.