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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences 
section 3, we picture the main idea of how we find Straight 
lines and Rectangles with Hough transform. Third, in section 4, 
the formulas to calculate Curvature of color-images are outlined. 
Last, in section 5, we describe the way to recognize rooftop by 
using of fuzzy density. 
2. NOVEL EDGE DETECTION ALGORITHM OF 
COLOR-IMAGES BASED ON EMD 
As the edge detection is one of the bases of our buildings 
detection algorithm, we made much more efforts on it. After 
many tests and comparisons, we introduce Earth Mover's 
Distance to the buildings detection algorithm in remote sensing 
images. 
With few exceptions, the fundamental assumption of all step 
edge detectors is that the regions on either side of an edge are 
constant in colours or intensity. Much effort has gone into 
making them robust to noise, but the noise is assumed to have 
statistically simple properties. 
Convolution masks are ideal for realizing this assumption 
because the sign of the weight at a pixel tells us what side of the 
edge it is hypothesized to be on. We can think of a convolution 
as finding the weighted mean of each side and then computing 
the distance between the two means (Eric N. Mortensen, 2001; 
Mark A. Ruzon, 1999). 
While this assumption holds well enough for many 
applications, it does not hold in all cases. For instance, as scale 
increases, it is more likely that the weighted mean of each side 
will not be meaningful because an operator will include image 
features unrelated to the edge. This observation is even truer of 
color images. When only intensities are involved, the average 
over a large window is still perceptually meaningful because 
intensities are totally ordered. In color images, there is no such 
ordering, so the “mean color” of a large window may have little 
perceptual similarity to any of the colors in it. 
To overcome these barriers, we introduced a novel edge 
detection algorithm based on Earth Mover’s Distance to color 
remote sensing images. As reported recently, Earth Mover's 
Distance works well in edge detection of images used in other 
fields. This novel algorithm proposes an edge model that 
assumes that the two distributions of pixel values on either side 
of an edge are different. Distributions allow for more control 
over how each region is represented and how the distance 
between two regions is computed than can be achieved by using 
only the mean value. 
Besides the above, this edge model has other advantages. 
The first is a lack of false negatives compared to other models 
false negatives result from a failure to “take into account all 
possible intensity variations that might accompany a step edge 
in practice". Since we use distributions, almost all of these 
variations are modelled implicitly. In homogeneities can be 
uncorrelated (due to noise) or correlated (due to texture) 
without affecting performance. The second benefit is that using 
distributions creates a unifying framework for edge detection in 
binary, g grey-scale, color, or multi-spectral images, so long as a 
meaningful ground distance is defined. So our algorithm is a 
generalist in edge detection. 
21 A Perceptual Ground Distance 
One of the key concepts in our novel edge detection algorithm 
is the distance between two color signatures. Before defining 
the distance between two color signatures, wc must first define 
the ground distance between two colors. Because this distance 
should conform well to human perceptual distance as measured 
by psychophysicists, we use the CIE-Lab color space, in which 
617 
, Vol XXXV, Part B2. Istanbul 2004 
small Euclidean distances are perceptually accurate. If two 
colors are separated by a long distance, however, that distance 
is no longer quantitatively meaningful; the most we can say 
about the colors is that they are different. Using the Euclidean 
distance by itself presumes that an edge with a contrast of 80 
units is twice as salient as an edge with a contrast of 40 units, 
which need not be true. We desire a distance measure that 
approaches but does not exceed 1 once the colors are far enough 
apart. There are many functions that satisfy this criterion, and 
we have chosen (Mark A. Ruzon, 1999:G. Wyszecki., 1982) 
d, D) z4-expCE, Ir) (1) 
where E, is the Euclidean distance between color / and 
color  . 
lis a constant that determines the steepness of our 
function. We have empirically chosen 7 = 16.0 for 
our experiments. 
This information has more psychophysical background and 
the output based on this is more near to what of human sight. 
2.2 The Earth Mover’s Distance 
We introduce a new distance between two signatures that we 
call the Earth Mover’s Distance (EMD). This reflects the 
minimal cost that must be paid to transform one signature into 
the other. EMD is a general method for matching 
multidimensional distributions. The main idea of EMD is 
presented below (S. Cohen and L. Guibas, 1999): 
Consider a set of points L = {, pa, } with a distance 
d, j) 
distribution P(L) on L is 
function (assumed ‘to be a metric). ^ A 
a collection of non-negative 
weights (D, Sivan Pp.) for points in À such that >, P; = 
The distance between two distributions P(L) and Q(L) is 
defined to be the optimal cost of the following minimum 
transportation problem: 
min NT f s 7) 
Vi Not, =P. (2) 
j 
Above we define a somewhat restricted form of the Earth 
Mover Distance. The general definition does not assume that 
the sum of hc weights is identical for 
distributions P(L) and (JL). This is useful for example in 
matching a small image to a portion of a larger image. 
2.3 Computing Edge Information 
We detect local edge in a circle neighbour area. As depicted 
in Fig.l by dividing the circle in half, we have created two 
color signatures of equal mass, which we denote S, and 5$, 
Finding the distance between them can be seen as an instance of 
the transportation problem, in which we wish to find the 
minimum amount of physical work needed to move the masses 
of S into correspondence with those of S, in color space. 
The Earth Mover’s Distance (EMD) is based on a solution to