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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
this problem. It has been proven to be more robust than other
distance measures when comparing the color signatures of
entire images because it avoids many quantization. and
discretization influences.
a
Figure 1. Detect local edge in a circle neigbour area
We can now summarize the algorithm. For every (the edge's
orientation at the centre point), there is a division of S, and
S, , so the resulting of EMD can be represented as a function
fp o 0 «180. f(0) is one period of a triangular
wave. We define the orientation at the centre point to be
0 = arg max 0 f (0) , and the strength to be f(0) .While
the importance of the maximum is intuitive, the minimum is
equally important. Regardless of strength, the minimum may
still be zero if there is an orientation produces two equal color
signatures. The minimum measures the photometric symmetry
of the data; when it is high, our edge model is violated. For this
reason, the value min, (6) is called the abnormality. One
cause of high abnormality is the existence of a junction (Mark
A. Ruzon, 1999).
3. HOUGH TRANSFORM FOR STRAIGHT LINES AND
RECTANGLES DETECTION
One of the key work phases here is to find parallel lines .In
our application; first we used the standard Hough transform for
lines, and then find parallel lines with the lines orientation angle
recorded in the parameter space of HT. Since the Hough
transform (Mark C.K. Yang, Jong-Sen Lee, 1997) has been
successful in detecting lines, circles, and parabolas. We can
represent a line parametrically as follows:
p=xcos0+ ysin 0 (3)
For every non-zero pixel within the region, we can consider its
coordinate (X, V) in the parameter space (p,0) called the
Hough space. An array H is generated for representing the
Hough space, which is divided into regular lattice regions
referred to as cells. If a cell is at the intersection of many curves
in the Hough space it is said to have a large number of votes
(for a true line). From Eq. (3) it is not difficult to see that the
cell indicates, potentially, there is a line in the image domain.
The size or the resolution of the accumulator array. /7 plays an
important role in the process and must be carefully designed.
For the buildings can head in any direction, thus the range of
H is
0c00-czx (4)
€— op «s
where 5$ is the diagonal of the sub-image containing region of
interesting.
After getting the accumulator array /7 , count the number of
point in each cell. Here we have empirically chosen a minimum
threshold of 10 for our experiment, which means that any line
which has lesser than 10 points will be ignored. We do this by
simply setting the cell value to zero if its original value smaller
than 10.
Next work is a bit complex, where we will find potential
rectangles. First we defined two thresholds: the minimum of the
length and width of rectangle MIN 0 and the maximum of the
length and width of rectangle max jo. Second, in each line of
the array 77 (of the same Ó ), find cell pairs meet the condition
that the. distance (for example showed in Fig 2: Ajo] , Ap2 )
between them is larger than MIN O and smaller than Max po.
The cell pairs are the parallel lines we defined. Then we find
couples of cell pairs’ in different lines, which meet the
condition that the Ó distance ( AO , as depicted in Fig.2)
. . 3
between the lines is larger than 87° and smaller than
Oo : . + . . . . =
93" (which is given naively in this experiment). Last we find
the potential rectangle with these couples of cell pairs’. After
detecting a potential rectangle, we extract some features (height,
width, size) of it. Apl
|
|
—X
9 tM
Ap2
Lines @ Potential rectangle edge
Figure 2. Find potential rectangle in parameter space
4. USING CURVATURE AS THE IMAGE TEXTURE
MEASURE
Curvature is powerful concepts used in describing the instinct
feature of surface and it is invariant to rotation. Here we use it
to measure the texture of a patch in color-images. The curvature
and relative concepts we used here are defined as below
First, give some related differential geometry concepts
(Monge Patch, Mathworld, USA):
Definition of Patch: A patch (also called a local surface) is a
differentiable mapping X : U — » R^, where U is an open
> ^y
subset of. A^ . More generally, if 4 is any subset of R^ ,thena
map x: A->R" is a patch provided that X can be
I ; = FE n PLI
extended to a differentiable map from U into R°, where U is
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