Fully automated intensity compensation for confocal microscopic images

One well-recognized problem in three-dimensional (3D) confocal microscopic images is that the intensities in deeper slices are generally weaker than those in shallower slices. The loss of intensity with depth hampers both qualitative observation and quantitative measurement of specimens. Two major types of methods exist to compensate for this intensity loss: the first is based on the geometrical optics inside the specimen, and the second applies an empirical parametric intensity decay function (IDF) of depth. A common feature shared by both methods is that they are parameter-dependent. However, for the optics-based method there are as yet no fully automated parameter-setting approaches; and for the IDF method the traditional profile-fitting approach cannot provide proper parameters if the presumed IDF model does not match the experimental intensity-depth profile of the 3D image. In this paper, we propose a novel maximum-entropy (ME) approach to fully automated parameter-setting. In principle the ME approach is suitable for any compensation method as long as it is parameter-dependent. The basic assumption is that without intensity loss an ideal 3D image should be generally homogeneous with respect to depth and this axial homogeneity can be represented by the entropy of a normalized intensity-depth profile. Experiments on real confocal images showed that such a profile was consistent with visual evaluation of axial intensity homogeneity and that the ME approach could provide proper parameters for both compensation methods mentioned above. Moreover, for the IDF method, experiments on both real and simulated data showed that the ME approach could provide more precise parameters than with traditional profile-fitting. The Appendix provides a proof that under certain conditions the global maximization of the profile-entropy is guaranteed.