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Section 12.3 Registering Deformable Objects 378

to a verification score only if their orientation is similar to the orientation of the
silhouette edge to which they are being compared. The principle here is that the
more detailed the description of the edge point, the more likely one is to know
whether it came from the object.
It is a bad idea to include invisible silhouette components in the score, so
the rendering should be capable of removing hidden lines. The silhouette is used
because edges internal to a silhouette may have low contrast under a bad choice of
illumination. This means that their absence may be evidence about the illumination
rather than the presence or absence of the object.
Edge proximity tests can be quite unreliable. Even orientation information
doesn’t really overcome these difficulties. When we project a set of model bound-
aries into an image, the absence of edges lying near these boundaries could well be
a quite reliable sign that the model isn’t there, but the presence of edges lying near
the boundaries is not a particularly reliable sign that the object is there. For exam-
ple, in textured regions, there are many edge points grouped together. This means
that, in highly textured regions, it is possible to get high verification scores for
almost any model at almost any pose (e.g., see Figure 12.7). Notice that counting
similarity in edge orientation in the verification score hasn’t made any difference
here.
We can tune the edge detector to smooth texture heavily, in the hope that
textured regions will disappear. This is a dodge, and a dangerous one, because it
usually affects the contrast sensitivity so that the objects disappear, too. However,
it can be made to work acceptably and is widely used.

12.3 REGISTERING DEFORMABLE OBJECTS
There are many applications that require registering deformable objects. For ex-
ample, one might wish to register a neutral view of a face to a view displaying
some emotion; in this case, the deformation of the face might reveal the emotion
(Section 12.3.1). As another example, one might wish to register a medical image
of an organ to another image of the same organ (Section 12.3.3). As yet another
example, one might encode a family of shapes as one model shape and a family of
deformations. Notoriously, D’Arcy Thompson argued that side views of different
fish should be seen as deformations of one another (Thompson 1992).
Generally, we have registered objects by a search process that looks for a
minimum of a cost function. This applies in rather a general way to deformable
objects, but we usually cannot use RANSAC, because we cannot estimate the
parameters with a subset of tokens. As a result, registration is usually much slower.

12.3.1 Deforming Texture with Active Appearance Models
An important case is matching face images to one another, despite deformations
of the face, changes in head angle, and so on. In this case, the texture on the face
is an important cue driving the match. Cootes et al. (2001) model the face as a
plane mesh of triangles, as in Figure 12.8. Now assume that this mesh is placed
over an image of a face. If we knew their configuration in a neutral frontal view
of the face, we could generate the intensity field for that view. Call the original
image I o . For the moment, we will assume there is just one triangle in the mesh.