Graphics Reference
In-Depth Information
These complex filters are similar to the derivatives of a Gaussian. For example, for
m
6, we obtain a descriptor of length 15. Again, this approach avoids the need
to explicitly estimate the dominant gradient orientation.
+
n
≤
4.2.5
Other Approaches
Here, we briefly mention a few notable descriptors that don't fit into any of the
previously outlined main categories.
4.2.5.1 Steerable Filters
Steerable filters
are used to efficiently apply a desired filter (for example, the
n
th
derivative of a Gaussian) with respect to a desired angle. Freeman and Adelson [
153
]
showed that many such arbitrarily angled filters could be easily computed as the sum
of responses to a small number of basis filters at canonical orientations. Mikolajczyk
and Schmid [
325
] proposed to apply a filter bank of Gaussian derivatives with respect
to the angle given by the dominant gradient orientation at a patch, using the vector
of responses as a descriptor. The response vector is rotationally invariant assuming
the estimation of the dominant gradient orientation is correct.
4.2.5.2 SURF
Bay et al. [
33
] proposed a simplified descriptor inspired by SIFT called
SURF
(for
Speeded-Up Robust Features). As in SIFT, the oriented square at a feature's detected
scale is split into a 4
4 square grid. However, instead of computing gradient orien-
tation histograms in each subregion, Haar wavelet responses at twenty-five points
in each subregion are computed. The sums of the original and absolute responses
in the
x
and
y
directions are computed in each subregion, yielding a 4
×
=
64-dimensional descriptor. Since Haar wavelets are basically box filters, the SURF
descriptor can be computed very quickly.
×
4
×
4
4.2.5.3 PCA-SIFT
The SIFT descriptor is extremely popular, and is most frequently used as Lowe origi-
nally described it, that is, a 128-dimensional vector. However, it's natural to question
whether all 128 dimensions of the descriptor are necessary and should receive equal
weight in matching. Ke and Sukthankar [
235
] partially addressed this question using
a dimensionality reduction step based on principal component analysis (PCA). The
technique is generally known as
PCA-SIFT
, but this is a misnomer; the principal
component analysis is not performed directly on SIFT descriptor vectors, but on
the raw gradients of a scale- and rotation-normalized patch. More precisely, they
collected a large number of DoG keypoints and constructed 41
41 patches at the
estimated scale and orientation of each keypoint. The
x
and
y
gradients at the interior
pixels of each patch were collected into a 39
×
3042-dimensional vector,
and PCA was applied to determine a much smaller number of basis vectors (e.g.,
twenty or thirty-six). Thus, the high-dimensional vector of gradients for a candidate
feature is represented by a low-dimensional descriptor given by its projection onto
the learned basis vectors. Nearest-neighbor matching was then carried out on these
lower-dimensional descriptor vectors.
×
39
×
2
=
