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194 4 Feature detection and matching

Figure 4.12 A dominant orientation estimate can be computed by creating a histogram of all the gradient orien-
tations (weighted by their magnitudes or after thresholding out small gradients) and then finding the significant
peaks in this distribution (Lowe 2004) c 2004 Springer.

Figure 4.13 Affine region detectors used to match two images taken from dramatically different viewpoints
(Mikolajczyk and Schmid 2004) c 2004 Springer.

an unreliable indicator of orientation. A more reliable technique is to look at the histogram
of orientations computed around the keypoint. Lowe (2004) computes a 36-bin histogram
of edge orientations weighted by both gradient magnitude and Gaussian distance to the cen-
ter, finds all peaks within 80% of the global maximum, and then computes a more accurate
orientation estimate using a three-bin parabolic fit (Figure 4.12).

Affine invariance

While scale and rotation invariance are highly desirable, for many applications such as wide
baseline stereo matching (Pritchett and Zisserman 1998; Schaffalitzky and Zisserman 2002)
or location recognition (Chum, Philbin, Sivic et al. 2007), full affine invariance is preferred.
Affine-invariant detectors not only respond at consistent locations after scale and orientation
changes, they also respond consistently across affine deformations such as (local) perspective
foreshortening (Figure 4.13). In fact, for a small enough patch, any continuous image warping
can be well approximated by an affine deformation.
To introduce affine invariance, several authors have proposed fitting an ellipse to the auto-
correlation or Hessian matrix (using eigenvalue analysis) and then using the principal axes
and ratios of this fit as the affine coordinate frame (Lindeberg and Garding 1997; Baumberg