I need to find sharp local maximums of numerically defined 4D surface.
I have a surface with lots of maximums. I already know how to find them all. Some of them look like this: wide extremum, others more like this sharp peak. I need to find only sharp ones.
For now I'm calculating ratio of peak height to it's volume (calculated by numerical integration). Unfortunately I was not able to find any suitable ratio threshold. Any threshold suits only for small part of surface. What else features of peaks may be useful to research?
For now suitableness of maximums is detected manually - I'm developing some computer vision software.
Does my problem have a specific name and methods? How it should be solved? Any ideas?
If you're finding maxima (or minima) of some function then you are in the business of "optimization". There is a vast amount of software available to help with this. The best algorithm for your situation will depend on the nature of your problem. A good place to start looking for software is the NEOS site.
The sharpness of a peak can be judged by estimating the radius of curvature at the maximum point. If you have a way to calculate function derivatives, you can calculate curvature analytically; if not, use a finite-difference approximation.