![](https://csdnimg.cn/release/download_crawler_static/3863929/bg5.jpg)
degradation present in this type of data). They applied
elastic contour extraction. The comparison of different
operators for the feature edge detection and the ridge
detection in multimodal medical images is presented by
Maintz et al. [121,122].
Point features. The point features group consists of
methods working with line intersections [175,198], road
crossings [79,161], centroids of water regions, oil and gas
pads [190], high variance points [45], local curvature
discontinuities detected using the Gabor wavelets [125,
219], inflection points of curves [3,11], local extrema of
wavelet transform [58,90], the most distinctive points with
respect to a specified measure of similarity [115], and
corners [20,92,204].
The core algorithms of feature detectors in most cases
follow the definitions of the ‘point’ as line intersection,
centroid of closed-boundary region or local modulus
maxima of the wavelet transform. Corners form specific
class of features, because ‘to-be-a-corner’ property is hard
to define mathematically (intuitively, corners are under-
stood as points of high curvature on the region boundaries).
Much effort has been spent in developing precise, robust,
and fast method for corner detection. A survey of corner
detectors can be found in Refs. [155,172,220] and the most
up-to-date and exhaustive in Ref. [156]. The latter also
analyzes localization properties of the detectors. Corners are
widely used as CPs mainly because of their invariance to
imaging geometry and because they are well perceived by a
human observer.
Kitchen and Rosenfeld [101] proposed to exploit the
second-order partial derivatives of the image function for
corner detection. Dreschler and Nagel [43] searched for the
local extrema of the Gaussian curvature. However, corner
detectors based on the second-order derivatives of the image
function are sensitive to noise. Thus Fo
¨
rstner [62] developed
a more robust, although time consuming, corner detector,
which is based on the first-order derivatives only. The
reputable Harris detector (also referred to as the Plessey
detector) [135] is in fact its inverse. The application of the
Fo
¨
rstner detector is described in Ref. [107], where it is used
for the registration of dental implants images.
More intuitive approach was chosen by Smith and Brady
[173] in their robust SUSAN method. As the criterion they
used the size of the area of the same color as that of the
central pixel. Trajkovic and Hedley [192] designed their
operator using the idea that the change of the image
intensity at the corners should be high in all directions.
Recently, Zitova
´
et al. [224] proposed a parametric corner
detector, which does not employ any derivatives and which
was designed to handle blurred and noisy data. Rohr et al.
designed corner detectors, even for 3D data, allowing user
interaction [158].
The number of detected points can be very high, which
increases the computational time necessary for the regis-
tration. Several authors proposed methods for an efficient
selection of a subset of points (better than random) which
does not degrade the quality of the resulting registration.
Goshtasby [71] used only points belonging to a convex hull
of the whole set. Lavine [104] proposed to use points
forming the minimum spanning trees of sets. Ehlers [45]
merged points into ‘clumps’—large dense clusters.
3.3. Summary
To summarize, the use of feature-based methods is
recommended if the images contain enough distinctive and
easily detectable objects. This is usually the case of
applications in remote sensing and computer vision. The
typical images contain a lot of details (towns, rivers, roads,
forests, room facilities, etc). On the other hand, medical
images are not so rich in such details and thus area-based
methods are usually employed here. Sometimes, the lack of
distinctive objects in medical images is solved by the
interactive selection done by an expert or by introducing
extrinsic features, rigidly positioned with respect to the
patient (skin markers, screw markers, dental adapters, etc.)
[123]. The applicability of area-based and feature-based
methods for images with various contrast and sharpness is
analyzed in Ref. [151]. Recently, registration methods using
simultaneously both area-based and feature-based
approaches have started to appear [85].
4. Feature matching
The detected features in the reference and sensed images
can be matched by means of the image intensity values in
their close neighborhoods, the feature spatial distribution, or
the feature symbolic description. Some methods, while
looking for the feature correspondence, simultaneously
estimate the parameters of mapping functions and thus
merge the second and third registration steps.
In the following paragraphs, the two major categories
(area-based and feature-based methods, respectively), are
retained and further classified into subcategories according
to the basic ideas of the matching methods.
4.1. Area-based methods
Area-based methods, sometimes called correlation-like
methods or template matching [59] merge the feature
detection step with the matching part. These methods deal
with the images without attempting to detect salient objects.
Windows of predefined size or even entire images are used
for the correspondence estimation during the second
registration step, [4,12,145].
The limitations of the area-based methods originate in
their basic idea. Firstly, the rectangular window, which is
most often used, suits the registration of images which
locally differ only by a translation. If images are deformed
by more complex transformations, this type of the window
is not able to cover the same parts of the scene in
B. Zitova
´
, J. Flusser / Image and Vision Computing 21 (2003) 977–1000 981