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4.5 Exercises 229

Other detectors are described by Mikolajczyk, Tuytelaars, Schmid et al. (2005); Tuytelaars
and Mikolajczyk (2007). Additional optional steps could include:

1. Compute the detections on a sub-octave pyramid and find 3D maxima.
2. Find local orientation estimates using steerable filter responses or a gradient histogram-
ming method.

3. Implement non-maximal suppression, such as the adaptive technique of Brown, Szeliski,
and Winder (2005).

4. Vary the window shape and size (pre-filter and aggregation).
To test for repeatability, download the code from http://www.robots.ox.ac.uk/ vgg/research/
∼
affine/ (Mikolajczyk, Tuytelaars, Schmid et al. 2005; Tuytelaars and Mikolajczyk 2007)or
simply rotate or shear your own test images. (Pick a domain you may want to use later, e.g.,
for outdoor stitching.)
Be sure to measure and report the stability of your scale and orientation estimates.

Ex 4.2: Interest point descriptor Implement one or more descriptors (steered to local scale
and orientation) and compare their performance (with your own or with a classmate’s detec-
tor).
Some possible descriptors include

• contrast-normalized patches (Brown, Szeliski, and Winder 2005);

• SIFT (Lowe 2004);

• GLOH (Mikolajczyk and Schmid 2005);

• DAISY (Winder and Brown 2007; Tola, Lepetit, and Fua 2010).
Other detectors are described by Mikolajczyk and Schmid (2005).

Ex 4.3: ROC curve computation Given a pair of curves (histograms) plotting the number
of matching and non-matching features as a function of Euclidean distance d as shown in
Figure 4.23b, derive an algorithm for plotting a ROC curve (Figure 4.23a). In particular, let
t(d) be the distribution of true matches and f(d) be the distribution of (false) non-matches.
Write down the equations for the ROC, i.e., TPR(FPR), and the AUC.
(Hint: Plot the cumulative distributions T(d)= t(d) and F(d)= f(d) and see if
these help you derive the TPR and FPR at a given threshold θ.)

Ex 4.4: Feature matcher After extracting features from a collection of overlapping or dis-
torted images, 10 match them up by their descriptors either using nearest neighbor matching
or a more efficient matching strategy such as a k-d tree.
See whether you can improve the accuracy of your matches using techniques such as the
nearest neighbor distance ratio.

10 http://www.robots.ox.ac.uk/ ∼ vgg/research/affine/.