150 
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 
comers. 
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 
2W„ 
It + /; 
(1) 
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)\ 
Axy)= 
(XkJkW (XkSkW 
(xtJtW C*fc ,ykW 
(2) 
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 
meaningful. 
2. COMPARISON OF CORNER AND GRAVITY 
CENTER 
In order to figure out the difference between comer and gravity 
center, and how the sampling error affect the registration