Symmetry Transformation

Using the detected skin contour and some simple heuristics, a window can be defined which is expected to contain the eyes. We then propose the use of the dark symmetry transform [3] [7] [9] [6]. This is an annular sampling region which detects edge configurations that enclose an object. However, unlike template matching, a perceptual measure of symmetric enclosure is computed and blob centers are detected. When applied at the appropriate scale within a window defined by the skin contour, this transform consistently detects the eyes in the face. The dark symmetry transform is computed from a phase and edge map by wave propagation (for computational efficiency). For each point in the image p, at each scale or radius r and for each symmetry orientation $\psi$ we find the set of cocircular pairs of edges $\Gamma_{r,\psi}(p)$. The magnitude of axial symmetry in the (p, r, $\psi$) space is as follows:

$$S_{r, \psi}(p) = \sum_{\lambda_{i}, \lambda_{j} \epsilon \Gam... ...\left\Vert \lambda_{j} \ \right\Vert {(\sin{\phi/2})}^{w_{1}}$$ (2)

where $\left\Vert \lambda_{i} \ \right\Vert$ and $\left\Vert \lambda_{j} \ \right\Vert$ are the edge intensities of the two co-circular edges and $\phi$ is the angle separating their normals.

Then, radial symmetry is determined from the axial symmetry map as in Equation 3 and Equation 4. Finally, the symmetry map undergoes Gaussian smoothing and local maxima are determined.

$$S_\psi(p) = \max_{r=0}^{r_{max}} S_{r, \psi}(p)$$ (3)

$$I(p) = \sum_{\psi_{i}, \psi_{j}} S_{\psi_i}(p) S_{\psi_j}(p) (\sin(\psi_{i} - \psi_{j}))^{w_{2}}$$ (4)

The strongest peaks of dark symmetry are candidates for eye positions. Simple heuristics are used to reject pairs of eyes that have insufficient intra-occular distance (w.r.t the skin blob) and that form an angle larger than 20 degrees from the horizontal. The interest map resulting from the dark symmetry transform is shown in Figure 4.

  

Figure: Symmetry Transform's Possible Candidates for Eyes

Horizontal limb extraction is performed to find the mouth from the dark axial symmetry map. The longest linked limb is selected as the mouth.

Additionally, a coarse estimate for the nose's vertical location is found by searching for the strongest vertical gradient in the intensity image that lies in a region bracketed by the eyes and the mouth.

At this stage, a variety of candidates have been detected as possible facial features. These candidates must be tested by more discriminating techniques to discard false alarms and to refine localization.