A prominence region is an area where all the mountains "go to" the master peak of the region. The region boundaries can be determined in several ways:
1. Uniform Cell method
2. Area Balanced method
The "uniform cell" method is the simplest to carry out. One simply defines a certain "prominence threshold" for the master peaks, make a list of the peaks, and figure out the boundaries.
The area balanced method is like taking the uniform cells, then combining certain cells to balance the areas.
In order to define mountain prominence regions we first have to review the meaning of "region". The word "region" implies subdivision of area. Regions have borders that divide them from other regions. Usually dividing something into regions is an exhaustive process where all the area is accounted for. This is the main difference between "mountain regions" and "mountain ranges". See Mountain Ranges. Mountain ranges can overlap one another, and have areas between them that do not fall into any range.
The method of defining mountain regions by prominence is to select an arbitrary number of high mountains from the area to be subdivided, and then find the prominence boundaries between them. Prominence boundaries are always the prominence defining saddles of the mountains, and the rivers that flow down from these saddles. I assume you are familiar with the subject of Mountain Prominence.
Deepest Pass Method: One method of carrying out the subdivision is to mechanically subdivide according to the "deepest pass" method. Just arrange all the peaks in prominence order, then cut the area up according to each peaks key saddle. For example, in cutting up North America, the first cut would be between Mount Logan and Mount Mckinley, at Mentasta Pass (709m). The next deepest pass is between Orizaba and Logan. This process of subdivision can continue until you have the desired number of subdivisions. In summary, this is called the "deepest pass" method. The problem with the deepest pass method is that some of the areas are very small. For example, if you stop at 7 regions, the Fairweather region only covers a small prominence island west of Grand Pacific Pass, whereas Whitney region covers half the continent. You stop subdividing when you get the desired number of areas.
Prominence Threshold Method: This method is very similar to the deepest pass, except you state at the outset that you are going to divide all the peaks over a certain prominence threshold. Eg: All the peaks over 5000 feet of prominence.
Area Balanced Regions: (Balance the areas and number of peaks) The idea of the balanced areas method is to end up with a more useful set of regions by ignoring certain deep passes, because the resulting area would be too small. This is the time honored method by which everyone has been dealing with the problem of giant high prominence peaks near the coast that command very little area. (It is referred to as the "Coastal Giants" problem in other prominence literature). In the top level Bivouac subdivision of north America, we skip over the division between Logan and McKinley. The main rule is that each area must have "integrity" which means that all peaks in the area "go to" the highest. This is the reason you can't just cut off an area called Canadian Rockies from Mount Elbert at Crowsnest pass. The problem with "Canadian Rockies" is that it doesn't have integrity, because all the peaks north of Yellowhead pass go to Elbert, not to Robson.
This document only discusses three methods of subdividing an area into mountain regions based on rules of prominence. So far we are only talking about a single level. For multiple level regions, see hierarchy of mountain regions.