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Mapping without the sun
Zhang, Jixian

point on the feature manifold. Parida et al (1998) describe a
method for general junction detection. A deformable template is
used to detect radial partitions. The minimum description length
principle determines the optimal number of partitions that best
describe the signal” (Cordelia, et al., 2000).
Contour based methods have existed for a long time. So far
numerous contour based algorithms have been developed (Beus
et al., 1987; Freeman et al., 1977; Liu et al., 1990). A number of
frequently cited approaches are discussed in the survey by Liu
and Srinath (1990), where comparative experimental results are
also given. These algorithms are Rosenfeld and Johnston (1973),
Rosenfeld and Weszka (1975), Freeman and Davis (1977), and
Beus and Tiu (1987). But these algorithms can not give accurate
comer position and usually loss many comers (Dmitry and
Zsolt, 1999). Based on these algorithms, Dmitry and Zsolt
developed a new algorithm: IPAN99 algorithm (1999). It is a
fast and efficient algorithm for detection of high curvature
points. But this algorithm has its fatal shortcoming. It can only
detect high curvature comers. For the low curvature comers,
this algorithm can not detect them and usually give many wrong
Intensity based method is the most popular interest point
extraction method. There are two different direct comer
detection approaches in the literature. They both are based on
differential geometric concepts. The first group of detectors
measure the isophote curvature weighted with the gradient
magnitude. The second group of detectors measures the
Gaussian curvature of the intensity surface (Tobias, et al., 2004).
“Moravec (1977) developed one of the first signal based interest
point detectors. His detector is based on the auto-correlation
function of the signal. It measures the greyvalue differences
between a window and windows shifted in several directions.
Four discrete shifts in directions paralle to the rows and
columns of the image are used. If the minimum of these four
differences is superior to a threshold, an interest point is
detected. The detector of Beaudet (1978) uses the second
derivatives of the signal for computing the measure l DET:
DET = / / -It where I(x,y) is the intensity surface of
** yy
the image. DET is the determinant of the Hessian matrix and is
related to the Gaussian curvature of the signal. This measure is
invariant to rotation. Points where this measure is maximal are
interest points. Kitchen and Rosenfeld (1982) present an interest
point detector which uses the curvature of planar curves. They
look for curvature maxima on isophotes of the signal. However,
due to image noise an isophote can have an important curvature
without corresponding to an interest point, for example on a
region with almost uniform greyvalues. Therefore, the curvature
is multiplied by the gradient magnitude of the image where non
maximum suppression is applied to the gradient magnitude
before multiplication. Their measure is:
I I 2 + / É
K _ XX* y * yy X
It + /;
Dreschler and Nagel (1982) first determine locations of local
extrema of the determinant of the Hessian 'DET. A location of
maximum positive DET can be matched with a location of
extreme negative DET, if the directions of the principal
curvatures which have opposite sign are approximatively
aligned. The interest point is located between these two points
at the zero crossing of DET. Nagel (1983) shows that the
Dreschler-Nagel’s approach and Kitchen-Rosenfeld’s approach
are identical.
Several interest point detectors (Forstner, 1994; Forstner and
Gulch, 1987; Harris and Stephens, 1988; Tomasi and Kanade,
1991) are based on a matrix related to the auto-correlation
function. This matrix A averages derivatives of the signal in a
window around a point (x,y)\
(XkJkW (XkSkW
(xtJtW C*fc ,ykW
Where I{x,y) is the image function and (x h y k ) are the points in
the window around (x.y).
This matrix captures the structure of the neighborhood. If this
matrix is of rank two, that is both of its eigenvalues are large, an
interest point is detected. A matrix of rank one indicates an edge
and a matrix of rank zero a homogeneous region.
Harris (1988) improves the approach of Moravec by using the
auto-correlation matrix A. The use of discrete directions and
discrete shifts is thus avoided. Instead of using a simple sum, a
Gaussian is used to weight the derivatives inside the window.
Interest points are detected if the auto-correlation matrix A has
two significant eigenvalues. Fostner and Gulch (1987) propose
a two step procedure for localizing interest points. First, points
are detected by searching for optimal windows using the auto
correlation matrix A. This detection yields systematic
localization errors, for example, in the case of L-comers. A
second step based on a differential edge intersection approach
improves the localization accuracy. Fostner (1994) uses the
auto-correlation matrix A to classify image pixels into
categories: region, contour and interest point. Interest points are
further classified into junctions or circular features by analyzing
the local gradient field. This analysis is also used to determine
the interest point location. Local statistics allow a blind estimate
of signal-dependent noise variance for automatic selection of
thresholds and image restoration. Heitger et al (1992) develop
an approach inspired by experiments on the biological visual
system. They extract ID directional characteristics by
convolving the image with orientation-selective Gabor like
filters. In order to obtain 2D characteristics, they compute the
first and second derivatives of the ID characteristics. Cooper et
al (1993) first measure the contour direction locally and then
compute image differences along the contour direction. A
knowledge of the noise characteristics is used to determine
whether the image differences along the contour direction are
sufficient to indicate an interest point.
From the above literature review, no matter the algorithm in
frequency domain or space domain, no matter it is contour
based, parametric model based, or intensity based method, they
are all essentially gradient based. These methods can extract
comers, or junctions, or high curvature gradient, or line ends.
But they can not extract gravity center points. But for
registration of different resolution images, it is gravity center
points that provide more accurate registration result, not the
interest point extracted by the famous algorithms, such as Harris
and SIFT. Therefore, what is the difference between comer and
gravity center and what is the affection to registration of
different resolution images should be figure out is urgent and
In order to figure out the difference between comer and gravity
center, and how the sampling error affect the registration