Projecting Edges onto the Template

To find a head or face like contour around a point p in an image, we begin by generating the appropriate template. The template is then centered at point p on the edge map. Any edges which fall into the sampling region of the template (the darkened region in Figure ) are then considered as possible contributors to a template match. The magnitude of each edge determines the extent of its contribution. Furthermore, the orientation of the edge will also vary the contribution. If an edge is parallel to the boundary of the template, it is well aligned with the template's contour and it is a component of a boundary that is part of the overall shape we are seeking. However, if an edge is perpendicular to the boundary of the template, it is probably part of an external contour that crosses through the template. Such an edge's contribution should therefore be attenuated. In other words, edges which are not perpendicular to the normals at the template's boundary are misaligned and their magnitude should be weakened to reflect this. The normals of the template in Figure  are displayed.

Observe Figure . On the left is an annular sampling region which is triggered by 4 edge segments: $\lambda_{1},\lambda_{2},\lambda_{3},$ and $\lambda_{4}$. However, the edge labelled $\lambda_{3}$ is not aligned with the shape of the template. Its normal is not pointing radially inward/outward from the center of cocircularity as is the case for the other edges. Thus, it is misaligned with the radial normals typical of this circularly shaped region. It's contribution is thus weakened by scaling down its magnitude so that it is equivalent to a weaker yet properly aligned edge. Turning our attention to the ring on the right of Figure  we can see $\lambda_{3}$ now in a lighter shade of gray, depicting the attenuation its magnitude has undergone. Its contribution to the template matching algorithm is weakened yet not totally discarded.

Equation  is used to scale the magnitude of each edge by a scaling factor s_magnitude to vary its degree of contribution to the template's overall response.

$$s_{magnitude}=\vert\cos(\varrho-\varphi)\vert^{v_{1}}$$ (2.8)

$\varrho$

angle of template normal

$\varphi$

edge orientation

v₁

degree if attenuation of misaligned edges

The value of v₁ determines the degree of attenuation for misaligned edges. A higher v₁ completely attenuates misaligned edges thereby approximating Sela's method of discarding the edges. However, when the Sobel operator is used to compute edge maps, the phase values are not reliable enough to have such a severe attenuation. Thus, a value of v₁=2 was selected in our implementation.

  

Figure 2.15: Projecting onto template normals to attenuate misaligned edges