  This paper proposes a method for computing efficiently the significance of a
parametric pattern inside a binary image. On the one hand, a-contrario
strategies avoid the user involvement for tuning detection thresholds, and
allow one to account fairly for different pattern sizes. On the other hand,
a-contrario criteria become intractable when the pattern complexity in terms of
parametrization increases. In this work, we introduce a strategy which relies
on the use of a cumulative space of reduced dimensionality, derived from the
coupling of a classic (Hough) cumulative space with an integral histogram
trick. This space allows us to store partial computations which are required by
the a-contrario criterion, and to evaluate the significance with a lower
computational cost than by following a straightforward approach. The method is
illustrated on synthetic examples on patterns with various parametrizations up
to five dimensions. In order to demonstrate how to apply this generic concept
in a real scenario, we consider a difficult crack detection task in still
images, which has been addressed in the literature with various local and
global detection strategies. We model cracks as bounded segments, detected by
the proposed a-contrario criterion, which allow us to introduce additional
spatial constraints based on their relative alignment. On this application, the
proposed strategy yields state-of the-art results, and underlines its potential
for handling complex pattern detection tasks.
