Graphics Reference
In-Depth Information
x 10
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1
0.2
0
0
0
50
100
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70
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i
i
(a)
(b)
(c)
Figure 4.15.
(a) The area of the dark extremal region at the location of the dot in Figure
4.14
a
as a function of increasing intensity threshold. (b) The measure in Equation (
4.33
) as a function
of intensity threshold for this extremal region. The function is minimized at intensity level 99,
roughly corresponding to the center of the nonzero plateau in (a). (c) The corresponding dark
MSER.
illustrate the area of
i
and value of Equation (
4.33
) as a function of intensity thresh-
old
i
for the component centered at the dot in Figure
4.14
a. Figure
4.15
c illustrates
the maximally stable extremal region corresponding to the minimizer of
M
(
)
;we
can see that the region corresponds to a dark, irregularly shaped blob in the original
image that has high contrast with the lighter background.
All the extremal regions in an image can be quickly generated using an efficient
algorithm for computing
watersheds
[
514
], and the test for extracting the maximally
stable extremal regions is fast. The overall algorithmcan extractMSERs at video frame
rates. Matas et al. [
314
] also showed that MSERs are also affine-covariant, as well as
invariant to affine changes in the overall image intensity.
i
4.2
FEATURE DESCRIPTORS
Once a feature's location (and perhaps some additional information such as its scale
or support region) has been determined, the next step is to describe the feature with
a vector of numbers called a
descriptor
. To enable high-quality feature matching —
especially among images taken fromwidely separated cameras—the descriptormust
be designed so that features arising from the same 3D location in different views
of the same scene result in very similar descriptor vectors. That is, we desire that
D
, where
D
is an algorithm to create a descriptor, and
f
and
f
are detected
features in twodifferent images, such that
f
(
f
(
f
)
≈
D
)
Tf
for some geometric andphotometric
transformation
T
of the first image. Thus, while we want feature detection to be
covariant
to geometric transformations, we want feature description to be
invariant
to them. We must also specify a criterion for
matching
two descriptor vectors from
different images to form
correspondences
.
The easiest descriptor is simply a vector containing the intensity values from a
fixed-size block of pixels centered at the feature's location. Two such vectors can
be compared simply by computing the sum of squared differences (SSD) between
corresponding elements. When the change between two images is small (with respect
=
