  Source confusion has been a long-standing problem in the astronomical
history. In the previous formulation, sources are assumed to be distributed
homogeneously on the sky. This fundamental assumption is not realistic in many
applications. In this work, by making use of the point field theory, we derive
general analytic formulae for the confusion problems with arbitrary
distribution and correlation functions. As a typical example, we apply these
new formulae to the source confusion of infrared galaxies. We first calculate
the confusion statistics for power-law galaxy number counts as a test case.
When the slope of differential number counts, \gamma, is steep, the confusion
limits becomes much brighter and the probability distribution function (PDF) of
the fluctuation field is strongly distorted. Then we estimate the PDF and
confusion limits based on the realistic number count model for infrared
galaxies. The gradual flattening of the slope of the source counts makes the
clustering effect rather mild. Clustering effects result in an increase of the
limiting flux density with \sim 10%. In this case, the peak probability of the
PDF decreases up to \sim 15% and its tail becomes heavier.
