  We propose a theoretical framework for the image source method that
generalizes to arbitrary reflecting boundaries, e.g. boundaries that are curved
or even with certain openings. Furthermore, it can seamlessly incorporate
boundary absorption, source directivity, and nonspecular reflections. This
framework is based on the notion of reflection paths that allows the
introduction of the concepts of validity and visibility of virtual sources.
These definitions facilitate the determination, for a given source and receiver
location, of the distribution of virtual sources that explain the boundary
effects of a wide range of reflecting surfaces. The structure of the set of
virtual sources is then more general than just punctual virtual sources. Due to
this more diverse configuration of image sources, we represent the room impulse
response as an integral involving the temporal excitation signal against a
measure determined by the source and receiver locations, and the original
boundary. The latter smoothly enables, in an analytically tractable manner, the
incorporation of more general boundary shapes as well as directivity of sources
and boundary absorption while, at the same time, maintaining the conceptual
benefits of the image source method.
