Prpjt,
A Squared is probably a better source on your question; he's a lot better versed in TERPS.
The approach category, and the corresponding DH, is set by several things. Volume 3, Chapter 3, Paragraph 3.7 stipulates that the minimum DH for a category 1 approach is 200'. Per TERPS, minimums may be raised due to precipitous terrain, the requirement for a remote altimeter setting source (RASS), unusual typical wind conditions in excess of 20 knots, and obstructions and climb gradients required for the missed approach. Decision altitude is also adjusted for obstacle penetration into the obstacle clearance slope (OCS).
The concept is straightforward; if obstacles are close to the final approach course, the decision altitude is raised, and often the visibility required, to permit adequate time and space to see and avoid these obstacles. In the case of missed approach criteria, the decision altitude is placed farther out and higher up in order to permit a lesser climb gradient requirement. Often aircraft that can meet a higher climb gradient criteria are issued lower minimums.
Per TERPS, numerous considerations are in effect. By example, directly prior to the runway is the Precision Obstacle Free Area, which dimensions are 200' long and 400' either side of the centerline. If this area is not clear, the minimum HAT is 250', and the minimum visibility is 3/4 mile. Various boundaries and zones exist on each approach segment, and any terrain or obstacle penetration into those areas raises that segment altitude. This has an effect on decision altitude for the final approach segment.
Aside from the physical considerations of the approach, the aircraft, the pilot and the operator must also be approved for lower than standard operations. Thus, four criteria must be met in order to use lower than standard, or lesser than Category 1 and published minimae.
The aircraft must have equipment capable of conducting the approach to lesser minimums. The pilot must be qualified and current to do so, and the operator or individual must have authorization, which comes in both the form of a straight authorization, or operations specifications for certificate holders.