  We present a novel approach to the detection and characterization of edges,
ridges, and blobs in two-dimensional images which exploits the symmetry
properties of directionally sensitive analyzing functions in multiscale systems
that are constructed in the framework of alpha-molecules. The proposed feature
detectors are inspired by the notion of phase congruency, stable in the
presence of noise, and by definition invariant to changes in contrast. We also
show how the behavior of coefficients corresponding to differently scaled and
oriented analyzing functions can be used to obtain a comprehensive
characterization of the geometry of features in terms of local tangent
directions, widths, and heights. The accuracy and robustness of the proposed
measures are validated and compared to various state-of-the-art algorithms in
extensive numerical experiments in which we consider sets of clean and
distorted synthetic images that are associated with reliable ground truths. To
further demonstrate the applicability, we show how the proposed ridge measure
can be used to detect and characterize blood vessels in digital retinal images
and how the proposed blob measure can be applied to automatically count the
number of cell colonies in a Petri dish.
