Image features from phase congruency

The human visual system allocates different amounts of processing resources to different portions of the visual field which provides a trade-off between resources and time. On the one hand, attention can be shifted to a new location through saccadic eye movement. On the other hand, the photoreceptor density that decreases between the fovea and the periphery induces nonuniform processing capability over the entire field. In fact, the conclusion is still more surprising: features will only be perceived if they succeed in attracting attention [3]. The important point is then what kinds of features in an image seem to draw the subject's attention and thus become conspicuous. A great deal of biological vision research has addressed such a problem. This section describes the local energy model of feature detection [5,6,7];

Developing further the concept of specialized detectors for both major types of image features, lines, and edges, in [6,7] a local-energy model of feature detection was proposed. This model postulates that features are perceived at points in an image where the Fourier components are maximally in phase, and successfully explains a number of psychophysical effects in human feature perception [7]. It is interesting to note that this model predicts the conditions under which Mach bands appear, and also predicts the contrast necessary to see them.

To detect the points of phase congruency, an energy function is defined. The energy of an image may be extracted by using the standard method of squaring the outputs of two filters that are in quadrature phase ($90^o$ out of phase) [2]. Features, both lines and edges, are then signaled by peaks in local energy functions. In fact, energy is locally maximum where the harmonic components of the stimulus come into phase--see Ref. [7] for proof.

Figure 1: Images in (B), (D) are the points of maximum phase congruency for images in (A), (C) respectively.

The implementation of the local-energy model used is presented in [5], and the calculation of phase congruency in 2D images is performed using Gabor wavelets. To detect features at all orientations, the bank of filters is designed so that they tile the frequency plane uniformly. In the frequency plane the filters appear as 2D Gaussians symmetrically or anti-symmetrically placed around the origin, depending on the spatial symmetry of the filters. The length-to-width ratio of the 2D wavelets controls their directional selectivity, and this ratio may be varied in conjunction with the number of filter orientations used in order to achieve an even coverage of the 2D spectrum.

Fig 1 shows the points of maximum phase congruency for the two original target images. Different images have distinct features.

In Fig. 2, we can see features, both lines and edges, are then signaled by peaks in the output of a pooling mechanism utilizing the 2D local energy functions. The pooling mechanism was chosen as the sum of local energies over scales and orientations.

Figure 2: For each original image with a target: Its interest points, the corresponding neighborhoods, and minima of local energy used to calculate the radius $r$ of the digitized disks.