IPT adapthisteq() does linear interpolation between the results from neighboring tiles. It's been a few years since I wrote an implementation, so I can't exactly describe it in detail from memory. If you're getting the eq for the tiles, then you're probably off to a good start.
FWIW, adapthisteq() itself has a fair amount of descriptive comments, though if I recall correctly, one of the relevant interpolation steps is obfuscated in MEX.
The version I implemented is all done in m-code, so the transform and weighting interpolation steps should be more clear. That can be found on the File Exchange here as part of MIMT.
There are also other implementations on the FEX, though I don't know if there are good ones.
