52
distance
Fig. 2. Two level image of contour line
the preprocessing is to produce a black-and-white
contour line image that meets the following
requirements :
(i) Noises, e.g.•intermediate grayness, superfluous
spikes and dots should be removed.
(ii) Each contour line should be an unbroken curve,
either start and end at the edge of the image, or be
a closed curve by itself.
(iii) Each contour line should represent one
elevation value only. In other words, contour lines
are not allowed to intersect with each other.
(iv) Each contour line should be one pixel in
thickness. However, for our purpose this is not
essential.
The preprocessing consists of the following steps:
Step 1. Take the image of a blank white paper with
the vidicon camera, then substract it from the image
to be processed. This step eliminates the background
noises originated from the environment.
Step 2. Using the technique of threshold to produce
a two-level image (Fig.2). (Duda & Hart, 1973,
Rosenfeld & Kek, 1982)
Step 3. Isolated dots can be eliminated by medium
filtering(Pratt, 1978).
Step 4. Thinning of the contour line can be carried
out by the methods suggested by (Japouetti(1984).
Step 5. Spurious spikes should be removed.
Entangled curves should be separated. Some contour
lines may become broken in the foregoing 4 steps, and
thus, they have to be mended.
Step 6. Each contour line should be labeled with
the elevation value.
The steps 1-4 can be carried out automatically, but
the last two steps have to be done, at the best,
semi-automatically. An interactive processing
system, such as IDIMS (Interactive Digital Image
Manipulation System by TRW/ESL), affords great
facilities for these steps.
then Z 1
However,
Z 2 , and
at P is
where i
weighting
decreseii
1/D(P,Z)
Some c
closed cc
a terra:
and the
above f
different
simplici
same ele
or valle
the re
prepoces
resel.
applied i
5. A fast
Fig. 3. The effective distance between two points P
and Q within a resel is the minimum length of all j n a j
possible paths that connect P and Q within the resel. by a p a j
Heavy solid lines are the contour line, and dotted With th«
lines are the possible paths within the resel. The last sect
dash-dotted line has the minimum length of all
possible paths. Note that all the line segments are E(i,
either horizontal, vertical or slant with 45°.
Subscript
Dg) assc
For f c
' 0 if i-m=0 and j-n=0 method is
^(P,Q)= 1 I if either one of the (i-m) and and E's.
(j-n) is zero essentia]
, J if both (i-m) and (j-n) are not (1) Ir
zero line, lc
contour
The ratio I/J is /2 for Euclidean distance. For easy line, le
computation, we find it adequate to let J=3 and 1=2. E^=Eg=0
A "path" C consists of a series adjacent points P
(ii.ji). PzUz.jz) PkUk.Jk-). The length of
this path is defined as L(C)= JE ^(P a »Pi+i)- The
effective distance between two points P,Q within a
resel is, then defined as
D(P,Q)=Min L(C K )
k
Where C K represents all possible paths within the
resel that connects P and Q (see Fig.3).
Now, let Z denote a contour line which delineates
the resel, and P denotes any point on Z. The
effective distance between a point Q within the resel
to Z is then defined as
D(Q,Z)=Min D(Q,P)
p«z
d 4 m-
D.CI-
V'-
C* < < -
E, < 1-
E t < 1 -
3. Effective distance within a resel
A resel is a connected blank area within a contour
line image. It is always bounded by one or more
contour lines and, sometimes, by the edge of the
image.
Let's define the effective distance between two
adjacent pixels, P(i,j) and Q(m,n) with |i-m|<l,
|j-n|<1, as follows:
4. Interpolation Scheme
For a given resel, in addition to the bordering
contour lines, there may exist some closed contour
lines or isolated peaks within it. Let denote
these as Z i, Z2 and their elevation values
as Ei, E2 For each interior point P of this
resel, we choose two lines with different E's which
are the nearest ones to P in terms of the effective
Fig. 4. '
pixel. T]
for the
(5), (6)
scanning i