Let's assume we have two objects, A and B. What we know about them is their center points' coords (x, y which are floats) and a map (a string of one-zeros - objects' heights are always equal to its width), that tell us which areas of an object can collide with other objects.
I already have all the side tools, e.g. to check whether a given point is lying inside an object, and in which area (and whether it's marked as solid, or not).
Since I want to implement it in the HTML5 game that I'm working on, I need this algorithm to be working really fast. The first thing I've done, I'm obviously excluding all the objects, that are basically out of reach. But when two objects do interfere - I'm stuck. Of course I could just loop through all the map pieces of both objects, but that would be way too slow, since in practice, my object's actual maps are usually 15x15 (400 fields) or even 25x25. Combining only two objects like this would take ~400 000 loop iterations.
EDIT: As mentioned before, I already implemented bounding boxes, and since my objects are not simple shapes, the standard solutions do not seem to apply here.
Do you have any ideas, how should I solve this problem?