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Section 12.2 Model-based Vision: Registering Rigid Objects with Projection 375

FIGURE 12.5: Top, 80 images registered automatically to one another to create a
panoramic mosaic (which is what one would see if the camera had cylindrical film, and
o
a 360 field of view). Bottom, the images feathered into one another to suppress the
effects of intensity variation between different views of the same pixel. This figure was
originally published as Figure 3 M. Brown and D. Lowe, “Recognizing Panoramas,” Proc.
ICCV 2003, c IEEE, 2003.

T 3→1 by minimizing

(1) (2) 2
g(||x −T 2→1 x || )+
j j
j∈1, 2 matches
2
(1) (3)
g(||x −T 3→1 x || )+
j j
j∈1, 3 matches
2
(2) (3)
g(||T 2→1 x −T 3→1 x || )
j j
j∈2, 3 matches
(where g might be the identity if there are no outliers, and an M-estimator oth-
erwise), and then register with these transformations. Notice that, as the number
of images goes up, this strategy will yield a large and nasty optimization problem
that will most likely exhibit local minima, and so will need to be started with a
good estimate of the transformations. Registering individual pairs of images can
supply that start point. Once images have been registered to one another, we can
come up with a single panorama by overlaying images, then carefully blending pix-
els to account for spatial variations in image brightness caused by the lens system
(Figure 12.5).

12.2 MODEL-BASED VISION: REGISTERING RIGID OBJECTS WITH PROJECTION
We would now like to register rigid objects with images. Solutions to this problem
can be extremely useful in practice, because they allow us to estimate the position,