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|
|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