All channels are correlated, why?
The proposed mixed image is quasi-Hematoxvlin and eosin (H&E).
This kind of stainning is more used to see the morphology.
I dont think is a good idea to use segmented (H&E) image to count the nucleus. And more any measurements related to (H&E) intensity is not suitable to conclude any biological fact about nucleus:
(H&E) is more related to the amount of protein, carbohydrate, lipid, and water, that filled the specific cell, stroma, epithelial and cytoplasm, for instance.
The stroma always stain pink as it have more protein, this is normal because it’s a muscle. In your image, stroma is scarce, may be the
biopsy is from a tumor, nucleus are invading the stroma …
Normally nuclei always stain blue not black, with at least a rim of dark blue at their edges.
The cytoplasm is more variable in its appearance:
Protein-rich cytoplasm stains dark pink.
Cytoplasm can stain rich purple, pink+bleu.
Cytoplasm that is mostly filled with carbohydrate, lipid,
or water will stain pale, close to white color.
On can assume that the information source is ergodic for any specific kind of cell. It implies that the information source has only one statistical structure for any specific cell. However, the data generated(image) from stained tissue is from a mixed source made up of a number of pure components that are each of homogeneous statistical structure.
This statistical structure can confuse blood with nucleus, for instance.
Most of cytoplasm will be detected as nucleus. Bias.
With my best regards.