NOTE Deformation Invariants in Object Recognition

Another source of change is various deformations of an object that do not change its identity. If a dog gains weight, We study invariance to transformations having two components. The first is an arbitrary large affine transformation. This we still want to recognize it as the same dog. An even approximates a viewpoint change. The second is a small, but more widespread example is the boundary contours of otherwise general, non-linear deformation. Such a deformation various objects. Looking at a pear, we can see a certain can arise from several sources, including change in the object boundary contour which is quite distinctive. Looking from itself. For instance, we want to recognize an apple even if a different point of view, we see a contour which is different individual apples are slightly different from each other. While from the first one. This is because it is formed by a different there are no true invariants in this case, we show that affine occluding boundary; i.e., we see different parts of the pear. invariants are quasi-invariants of these quasi-affine transformaHowever, we can still identify the distinctive pear shape. tions. This is true for both global and local invariants. The Looking at another pear, we again have a different contour method was applied to a set of real images.  1997 Academic Press but it still has a similar pear shape. These examples lead us to be interested in a class of transformations which is beyond the viewpoint change.