So far we have kept our discussion to one-dimensional image features, that is, events in the image signal that represent one-dimensional information. But higher order features are also very important in image understanding. For example, it is well known that by placing simple light pointer markers on a subject at strategic places, and then getting the subject to walk around in the dark with only the pointers visible, there is still enough information for a viewer to interpret the scene. Since there are also many less corner or junction points than there are edge points, two-dimensional features are often used in stereo and motion understanding. Corresponding corners are tracked between or across images so that depth or motion can be inferred.
There has been much research into the detection of corner and junction points in images [3,14,15]. There are generally two approaches taken: either the grey level distributions around a junction are analysed and searched for directly, or edges are first detected and then junctions are found at edge terminations and edge intersections. Both approaches suffer from certain problems, the most notable being that certain types of two-dimensional features fail to be detected by either method.
The approach to detecting two-dimensional features under the local energy model is quite different. Again, we search for order amongst the phase components in the Fourier domain, but now it must be two-dimensional order.
The local energy approach to the detection of one-dimensional features is intrinsically one-dimensional: the filters are designed with an imposed orientation, and features are found with respect to that orientation. Moreover, it has been noted that local energy is an idempotent operation [11], in the sense that if the local energy operator is applied to its own output (the marked peaks of the phase congruency map) then those same features will be found again at the same locations. However, if the local energy operator is applied in the orthogonal direction, it will now find the one-dimensional features of the one-dimensional features, that is, the two-dimensional features (the edges of a line edge are its termination points, for example). This is precisely the idea that has been developed by Ben Robbins [13] in his Ph.D. thesis. The results of the local energy corner detector are shown below in figure 13 for a simple test image.
This approach to higher-order feature detection can be extended into higher dimensions, for example to the detection of one-dimensional features (or higher order features) in three-dimensional images such as those produced by a confocal microscope [12], or to higher order features that appear in motion sequences.
