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Generation of radar echo images from a contour map
COMPUTER VISION, GRAPHICS, AND IMAGE PROCESSING 24, 114-128 (1983)
NOTE Generation of Radar Echo Images from a Contour Map Yosmo YANAGmA~, MINORUTAN~J~A,SHINICmTAMU~, AND K O K I C H I TANAKA
Department of Information and Computer Sciences, Faculty of EngineeringScience, Osaka University, Toyonaka, Osaka 560, Japan Received August 27, 1982 A radar simulation system has been developed which generates radar echo images from contour line information on a map. The system generates and displays a radar echo image at any position of the imaginary radar on the map. The idea of an Echo Table is introduced to generate the echo image easily. The angular resolution of the generated radar echo images is 1 degree and the range resolution is ¢2- pixel (about 40 m). 1. I N T R O D U C T I O N
PPI radar detects and locates an object by reflection of electromagnetic wave, and displays an echo image on a CRT. It can display locations of objects in spite of darkness, fog, clouds, and so on. Radar is utilized on the sea, in the atmosphere, and on the ground. The fundamental principle of radar is that the distance t o / f r o m an object is calculated according to the echo-return time of a radiated electromagnetic wave. A conventional PPI radar utilizes the following display method: the spot moves out from the center along a radius on a CRT when an electromagnetic wave pulse is radiated, and the brightness of the spot is controlled according to the strength of the received electromagnetic wave. Thus, the radar displays locations of objects on a CRT. Since both the direction of the radiated electromagnetic wave and the direction of the spot on the CRT are rotated synchronously, a radar echo image of the whole azimuth is obtained. In this paper we propose a radar simulation system which generates and displays radar echo images of a navigation radar on a ship. We use an Echo Table to generate echo images easily. The existing methods of radar echo simulation are as follows: (1) Analog method. The system obtains an imitated radar echo image signal by an FSS (flying spot scanner), and displays it on a CRT. Thus, even if the position of the imaginary radar is moved, the system displays only a shifted copy of the same image. Though the analog method may have low cost, it lacks versatility. (2) Digital method. A digital sensor simulation system utilizing digital databases is described by Faintich [1]. One of the databases contains terrain height information and the other contains the culture, or radar reflectivity potential information over the corresponding terrain. This system, however, does not work in real time. We have implemented a new radar echo simulation system on a digital computer based on a method different from the above. It produces an Echo Table correspond114 0734-189X/83 $3.00 Copyright © 1983 by AcademicPress.'Inc. All rights of reproductionin any form reserved.
115
G E N E R A T I O N OF R A D A R ECHO I M A G E S
[cEc-5 5,, 1
( 24 KW)
V NAFAco U-300 j
(64KB)
~2
F
FACOM 30-45S
(256KB)
FPANAFACOM
I
u-l,~.00 ~ L L
2KB)
(L 1 G H T - P E ' N )
FIG. 1. Block diagram of hardware system.
ing to a radar echo image at a given position of the radar, using sequences of sample points on the contour lines, and displays the contents of the table on a CRT by applying Echo Rules. When the position of the radar is moved, the Echo Table is rewritten and a new image is displayed. Thus, the system can display a radar image at each position of a moving radar. When map information is represented by contour data, it is compressed to about one-tenth in comparison with the original mesh data. Therefore, our system utilizes digital contour data to reduce the data to be stored. The key feature of our system is that it is compact and works in real time. Our method removes hidden objects in a manner similar to perspective before displaying an echo image. However, the projection planes of our method and perspective are different. Consider a cylinder which includes the whole object world and the center of whose base is the position of an observer (or a radar). In our method objects are projected onto the base of the cylinder. On the other hand, in perspective they are projected onto the side face of the cylinder. 2. HARDWARE AND SOFTWARE SYSTEM Figure 1 illustrates the computer facilities used for the simulation system. The computer CEC555H inputs and digitizes a topographical map through an FSS. It also extracts contour lines from the map and thins them to make a contour map. The contour map is transmitted from the CEC555H to the computer FACOM230-45S through a relay computer PANAFACOM U-300. The FACOM230-45S preprocesses the contour map and generates an Echo Table and then displays radar echo images on its CRT. The position of the radar is indicated by a light-pen before the simulation starts. An additional computer PANAFACOM U-1500 and its facilities are used for making hard copy of the generated echo images. Figure 2 shows the schematic process flow of the simulation. The main part of the process is the generation of the echo image, the details of which will be described later. In the next section the other parts will be explained briefly. 3. E X T R A C T I O N A N D A R R A N G E M E N T O F C O N T O U R D A T A
3.1 Input of Topographical Map and Thinning Contour Lines The method of generating contour data from a topographical map is described in this section. A topographical map drawn on a scale of 1 to 50,000, whose contour
116
YANAGIHARA ET AL. T A
S
R T J
l IInput of Topographical Map 1 [Binarization & Thinning
1
I into Sequences of Points [Arrangement of Data
I
[Generation of Echo Image
t
I
I OJ
(E
FIG. 2. S c h e m a t i c process flow of s o f t w a r e system.
lines are enhanced by black ink, is used as input. A part of the map (an area of about 6.7 km × about 9 km in the real world) is digitized at 240 × 320 pixels, where each pixel is approximately equal to 28 m. The digital map is binarized by applying a thresholding operation. The contour lines are thinned by applying an ordinary thinning operation. A contour map used in the example is shown in Fig. 3.
3.2 Sequences of Contour Points The contour lines are converted into sequences of (X, Y) coordinates of contour points on the same contour line. Each sequence corresponds to a contour line and is expressed by ((X/l, Yn)(Xt2, Y#2).-'(Xtk, Ylk))" At the next step, the altitude information is added to each sequence, and the sequences are rearranged in order of altitude. The contour
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FIG. 3. E x a m p l e of c o n t o u r map.
GENERATION OF RADAR ECHO IMAGES
117
data are represented in the following form:
(Zl(SllSl2".. Slnl)Z2(S21...)Zm(SmlSm2... Smnm)) , where Sij is a sequence of contour points on t h e j t h sequence of the ith altitude, i.e.,
Sij = (Xijl, Yijl)(Xij2, Yij2)"" (Xijk,,, Yijl%), m is the number of different altitudes, Z i is an altitude number (the real altitude is obtained by multiplying it by 25), n~ is the number of contour lines having altitude number Zi,
kij
is the number of points in sequence S/j. 4. GENERATION OF THE ECHO IMAGE
This section gives the principle of generating echo images. Let us consider a beam starting from the radar position. The beam defines a vertical section plane of the ground (Fig. 4). That is, a half line l in the section plane starting from the position of the radar intersects some configuration lines. The nearest intersection is a point where the beam is reflected (shown by " A " in Fig. 4(b)). Let us call such a point a reflection point. A section plane has a set of reflection points, and the reflection points construct an echo image in the azimuth of a beam. A radar echo image consists of such images in every azimuth surrounding the radar position. In the simulation system, we assume that the width of the imaginary beam is 1 degree, and so the echo image is constructed by 360 radial subimages. 0m
100 m
Sea Om ~-~
Position of radar
L)
0 Imaginarybeam
Island (a) Imaginarybeam. Altitude z
'Reflection point'
--
100 ~
f
)
r
0m
(b)
Vertical
I I
I
I
I
I
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I
J
J
J
I
section
and
echo
Distance
image.
FIG. 4. Vertical section. (a) an imaginarybeam; (b) an echo image (echobeam is reflectedonly fromA).
118
YANAGIHARA ET AL. S
T
A
R
T
)
] Input of Position of Radar I
I Generation
of Basic Echo Table
Transmission
of Data
I Interpretation of (X,Y)-coordinates I ifor each i
0 Sorting of Data
I
L Generation of Echo Table for each @
Deletion of Redundant Points
Interpolation on Height-Direction
]
I
i Display on C.R.T. I E
N
D )
FIG. 5. Schematicflow of generation of echo image.
Figure 5 shows the schematic flow of generation of echo images. The generation process uses contour data obtained in the previous section and generates an echo image at a radar position given by an operator. Figure 6 shows a unit solid body used in the generation process. This figure is a fan-shaped pillar with angle of 1 degree whose height is effectively infinite. After lining up points of the contour data existing in a unit pillar according to their distance from the origin, we apply the generation principle to the points. There are, however, two problems. (1) We have a nonecho phase where the unit pillar contains no contour point because of the coarse sampling of the contour points. In such a case, the beam in the unit pillar cannot catch the contour line. (2) Since the contour data do not give the ridge of the mountain, we cannot obtain the visible side of the mountain definitely. To work out those problems, the system uses an interpolation of contour points and an estimation of the altitude of the top points. Those algorithms are explained in Section 4.1 and 4.2, respectively. We introduce a Basic Echo Table (BE Table for short) and an Echo Table (E Table for short). Both tables consist of 360 rows, respectively. The O th row corresponds to azimuth 0 , and contains triples (ri, z,., T~) of contour points at that azimuth (Fig. 10). In Section 4.1, we describe a method which converts contour data
119
G E N E R A T I O N OF R A D A R E C H O I M A G E S
Contou~ Iine. i ,, I
..... .
.
.
.
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.......
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r
!
#
t
0
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/
Position of radar
;, x
)<: Contourpoint on contour line.
FIG. 6. Process unit for generation of Echo Table.
into (r, 0, z) cylindrical coordinates, and the method which generates the BE Table. In Section 4.2, we describe the method of converting a BE Table into an E Table. The system generates and displays an echo image based on the E Table. 4.1 Generating the Basic Echo Table
First, according to (1), the rectangular coordinates (x, y, z) of a contour point are converted into cylindrical coordinates (r, 0, z) whose origin is located at the position (x 0, Y0, 0) of the radar
r = 7 ( X - X o ) 2+ ( y - y o ) 2 +,
ify -Yo --> 0
(1) +1
ify -Yo < O.
Furthermore, each point is given one of the five types illustrated in Fig. 7 according
°" Type
1'
@
0
@
@
I
1
X--@(--X) X--@ (-X)
2
3
FIG. 7. Connectivity type of contour points.
120
YANAGIHARA ET AL.
k kx X: Sample contour point.
Position of radar
FIG. 8. Case of nonecho phase.
to the connectivities of its adjacent contour points, and represented as (r, O, z, T) (T: type name). A contour point of type 0 is a point where the contour line is continuous azimuthally, and a contour point of type 1 is a starting point or an end point of the contour line azimuthally. Types 2, 3, and 4 mean that the contour line is discontinuous azimuthally. Data (r, O, z, T) are stored in row ® of the BE Table, individually. Now we describe the method for solving the nonecho phase (Fig. 8). It arises in the following case. Even if two contour points are adjacent on the x - y plane, they are occasionally nonadjacent on the r - O plane. We worked out this problem by a method of interpolating additional contour points between such points and adding them to the BE Table. The method of interpolation is as follows: let us consider two adjacent points (ri, ~)i, 7., Ti) and (i), Oj, z, Tj) where Oj = Oi + m, m > 2. Then (m - 1) additional points (r, O, z, T) are interpolated according to (2) and stored in the corresponding rows of the BE Table, respectively. r = ri + ( r j -
ri) • k
m
O=O~+k T=O (1 < _ k < _ m -
(2)
1).
Position of radar X:
Sample contour point.
0 : Interpolated point.
FIG. 9. Interpolation of additional points.
GENERATION OF RADAR ECHO IMAGES
e @+1
0+2
121
(ri, z, T.) ((ri+r~)/2 , z, 0) (r j, z, T.) J
360 FIG. 10. Example of Echo Table (case of including additional points).
An example of the interpolation for m = 2 is shown in Figs. 9 and 10. Points in a row are, then, rearranged in ascending order of distance r. Thus, we obtain a BE Table.
4.2 Generating the Echo Table In this section, we describe the method which generates an E Table from the BE Table obtained in the previous section. Some of the points with the same altitude number in the same row of the BE Table are deleted and top points for each row of the BE Table are interpolated. Then, the obtained data is stored in the corresponding row O of the E Table. The details of the method are given below. First, all points with type 4 in the BE Table are deleted because they are redundant for generating radar echo images. Then, points P~ lining up in ascending order of distance r in the same row are examined as to whether the altitude of the point P~ is the same as the next point P~+ 1. If so, some points are removed or the types of some points are rewritten. The details of the method are given by Algorithm 1, where m is the number of points in a row. In Algorithm 1, when the types of two successive points Pi and P~+ ~ with the same altitude are 2 and 3, or 3 and 2, the point P~+I is deleted because it is redundant for generating radar echo images (Fig. 11). (Algorithm 1: deleting point and rewriting connectivity type) (Step 1) i = 1. (Step 2) if i > m, then go to Step 7. (Step 3) if the altitude number z i of the point Pi is not the same as the altitude number zi+ 1 of the point Pi+ 1, then increment i and go to Step 2. (Step 4) if both the type T~ of the point P~ and the type T~+ ~ of the point P~+ 1 are 2, or if both of them are 3, then rewrite both their types to 0, add 2 to i, and go to Step 2. (Step 5) if T~is 2 and T/+ l is 3, or if T~is 3 and T/+ l is 2, then rewrite T, to 0, remove the point P~+1 from the row, add 2 to i, and go to Step 2. (Step 6) otherwise, increment i and go to Step 2. (Step 7) stop. Next, the system uses estimation and interpolation of top points (summits) of islands and mountains. After assuming the configuration of the vertical section of
122
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-)~
/ j
-)K"4
/ P o s i t i o n of radar
×
(a)
/
Before
processing.
I
f
/
P o s i t i o n of radar
x
iX
e"
/
(b) After processing.
FIG. 11. Deletion of connecting points existing in the same direction. (The mark " × " represents a sample point and the under-fight numeric of " × " represents its type.)
the contour points in a row O, the system of top points and store them in the row interpolated between successive points Pi(ri, O, then r, z', and T are calculated according
estimates the altitude and the position O. When the top point P ( r , z', T ) is z, Ti) and Pi+ i(ri+ l, z, Ti+ 1) in the row to (3) (Fig. 12):
r = (r i + ri+,)12 z'=
re+R/5 t z + 3.5
if R < 17.5 if R > 17.5
T=I
( R = ri+ l - ri).
(3)
As altitude sampling of contour points is coarser than horizontal sampling, we need to interpolate some other points. On inputting a topographical m a p the system extracts contour lines at every 100 m, while it samples contour points at a 28-m interval on the x - y plane. So, by interpolation we make the difference of the altitudes of successive points in a row O less than or equal to 25 m. The method is as follows: For successive points Pi(ri, zi, Ti) and Pi+l(ri+l, Zi+l, Zi+l), if zi+ l is
123
G E N E R A T I O N OF R A D A R ECHO I M A G E S
Altitude
Pl
R
)r Distance
Pi+l
)< : Contour point. O : Interpolated point. (a) Interpolation of a top point. He i ght Z (m) (pixel) 100
4 3.5
75
3
50
2
25
1
0
0
) R (Length) 0
5
10
15
0
140
280
420
17.5
20 560
(pixel) (m)
(b) Relation of R and Z. FIG. 12. Interpolation of a top point and estimation of its height.
greater than zi+ 1, then some points P(~', z), T/) are interpolated between them according to (4). (The unit interval in the altitude direction is 25 m.) ,
J
5 = r, + (,-,+, - r~). k 7- 1
,
J
~J = ~' + ( ~ ' + ' - ~')" k -S- 1
T;=O
124 where
YANAGIHARA ET AL. j=l
..... k i
k=
i f l < z i + I - z i<__2
if2
(4)
4.3 Generation of the Echo Image An echo image is constructed from the 360 subimages generated from the Echo Table at every ® by applying Echo Rules. We assume that a row O contains m points, (ri, zi, T/) (1 < i _< m). (Echo Rules: Generation of subimage) (Rule 1) if i =~ m and ePm(i) < zi/ri, then if T / = 1 or qa,,(i + 1) > zi+ l/ri+ 1, generate an echo on interval [Ri, R~ + otherwise generate an echo on interval (Rule 2) if i = m and ePm(i) < zi/ri, then if T~ = 1, generate an echo on interval [R~, R~ + otherwise generate an echo on interval (Rule 3) otherwise, do nothing because of no echo,
0.5]; [R~, Rz+ l]-
0.5]; [Ri, Rz + 5].
where epm(j) is given by MAX(zl/rt[1 < I < j ) , (/)re(l) has an appropriate negative value, and R i is given by ~ + z 2 . An illustration of generating a subimage is shown in Fig. 13. 5. RESULTS AND DISCUSSION Generated echo images are shown in Fig. 16. The input topographical map is a contour map drawn at 1 to 50,000 of an area in Japan (Fig. 15). The beam of the simulated radar has a width of 1 degree on the horizontal plane and its range is set at 100 pixels (about 2.8 km in the real world). Figures 16(C)-(E) show echo images of the bay at distinct positions of the radar. The echo marked by *- in Fig. 16(G) is an example of an incorrect echo subimage in the case where there is a beam between two contour lines (Fig. 14). We will cope with this problem by applying interpolation of points in the azimuth direction, or by varying the brightness on the CRT according to the inclination of the slope of the land. Finally, we mention the angular resolution and range resolution of the simulation system. Echo Table is generated at every one degree, so that the angular resolution is one degree. The echo image is displayed at every pixel, so that the range resolution is V~- pixel (about 40 m). 6. CONCLUSION We have proposed a radar echo simulation system, which translates data (x, y, z) of contour lines in rectangular coordinates into data (r, O, z) in cylindrical coordinates, and displays echo images generated from an Echo Table by applying Echo Rules. The proposed system was designed so as to be implemented by several
GENERATION OF RADAR ECHO IMAGES
125
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o t-~ u
'\\,~\O\o~°~ \ \ O
o.o
¢,
i
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126
YANAGIHARA
ET AL.
z = 0
z = 100
on contour It
I
I
I
II
I
I
I
map.
I ~
~ ' ' ~ -
on echo
image.
FIG. 14, C a u s e of e c h o i m a g e m a r k e d b y a n a r r o w .
microprocessors and evaluated on the following points: (1) reduction of input data of contour lines, (2) conciseness of process algorithm. To accomplish (1), string data of contour points defined by (x, y, z) rectangular coordinates was introduced. For (2), by introducing the idea of an Echo Table, each algorithm becomes simple and effective. There remain some points that should be improved for the system. One of them is a method which varies the brightness of the beam on the CRT according to the strength of the reflected echo. It is possible to vary the brightness of the beam on the CRT because the angle of inclination on the land can be calculated from the data of the Echo Table. The others are a simulation of the sea clutter and of reflected echos from other ships.
XD
~
oX G
C)
FIG. 15. C o n t o u r m a p s f o r e x p e r i m e n t .
G E N E R A T I O N OF R A D A R ECHO I M A G E S
FXG. 16. Echo images at each point
(A-tt) on Fig. 15.
127
128
YANAGIHARA ET AL.
FIG. 16 Continued. We mention a comparison with the use of mesh data as input. Mesh data has 76.8 K-words of data on representing the map shown in Fig. 3, while contour data (every 100 m) has about 7.3 K-words of data including altitude information. Thus, the information of the map is compressed to about one-tenth. However, since the mesh data has the altitude of every sample point, an echo image generated using the mesh data as input can be more faithful in regard to altitude information.
REFERENCES 1. M. B. Faintich, Digital sensor simulation, PhotogrammetricEng. Remote Sensing,42, 1976, 1427-1440. 2. L. N. Rindenour, Radar System Engineering, McGraw-Hill, New York/London, 1947. 3. D. P. Meyer and H. A. Mayer, Radar Target Detection, Academic Press, New York/London, 1973.
NOTE Generation of Radar Echo Images from a Contour Map Yosmo YANAGmA~, MINORUTAN~J~A,SHINICmTAMU~, AND K O K I C H I TANAKA
Department of Information and Computer Sciences, Faculty of EngineeringScience, Osaka University, Toyonaka, Osaka 560, Japan Received August 27, 1982 A radar simulation system has been developed which generates radar echo images from contour line information on a map. The system generates and displays a radar echo image at any position of the imaginary radar on the map. The idea of an Echo Table is introduced to generate the echo image easily. The angular resolution of the generated radar echo images is 1 degree and the range resolution is ¢2- pixel (about 40 m). 1. I N T R O D U C T I O N
PPI radar detects and locates an object by reflection of electromagnetic wave, and displays an echo image on a CRT. It can display locations of objects in spite of darkness, fog, clouds, and so on. Radar is utilized on the sea, in the atmosphere, and on the ground. The fundamental principle of radar is that the distance t o / f r o m an object is calculated according to the echo-return time of a radiated electromagnetic wave. A conventional PPI radar utilizes the following display method: the spot moves out from the center along a radius on a CRT when an electromagnetic wave pulse is radiated, and the brightness of the spot is controlled according to the strength of the received electromagnetic wave. Thus, the radar displays locations of objects on a CRT. Since both the direction of the radiated electromagnetic wave and the direction of the spot on the CRT are rotated synchronously, a radar echo image of the whole azimuth is obtained. In this paper we propose a radar simulation system which generates and displays radar echo images of a navigation radar on a ship. We use an Echo Table to generate echo images easily. The existing methods of radar echo simulation are as follows: (1) Analog method. The system obtains an imitated radar echo image signal by an FSS (flying spot scanner), and displays it on a CRT. Thus, even if the position of the imaginary radar is moved, the system displays only a shifted copy of the same image. Though the analog method may have low cost, it lacks versatility. (2) Digital method. A digital sensor simulation system utilizing digital databases is described by Faintich [1]. One of the databases contains terrain height information and the other contains the culture, or radar reflectivity potential information over the corresponding terrain. This system, however, does not work in real time. We have implemented a new radar echo simulation system on a digital computer based on a method different from the above. It produces an Echo Table correspond114 0734-189X/83 $3.00 Copyright © 1983 by AcademicPress.'Inc. All rights of reproductionin any form reserved.
115
G E N E R A T I O N OF R A D A R ECHO I M A G E S
[cEc-5 5,, 1
( 24 KW)
V NAFAco U-300 j
(64KB)
~2
F
FACOM 30-45S
(256KB)
FPANAFACOM
I
u-l,~.00 ~ L L
2KB)
(L 1 G H T - P E ' N )
FIG. 1. Block diagram of hardware system.
ing to a radar echo image at a given position of the radar, using sequences of sample points on the contour lines, and displays the contents of the table on a CRT by applying Echo Rules. When the position of the radar is moved, the Echo Table is rewritten and a new image is displayed. Thus, the system can display a radar image at each position of a moving radar. When map information is represented by contour data, it is compressed to about one-tenth in comparison with the original mesh data. Therefore, our system utilizes digital contour data to reduce the data to be stored. The key feature of our system is that it is compact and works in real time. Our method removes hidden objects in a manner similar to perspective before displaying an echo image. However, the projection planes of our method and perspective are different. Consider a cylinder which includes the whole object world and the center of whose base is the position of an observer (or a radar). In our method objects are projected onto the base of the cylinder. On the other hand, in perspective they are projected onto the side face of the cylinder. 2. HARDWARE AND SOFTWARE SYSTEM Figure 1 illustrates the computer facilities used for the simulation system. The computer CEC555H inputs and digitizes a topographical map through an FSS. It also extracts contour lines from the map and thins them to make a contour map. The contour map is transmitted from the CEC555H to the computer FACOM230-45S through a relay computer PANAFACOM U-300. The FACOM230-45S preprocesses the contour map and generates an Echo Table and then displays radar echo images on its CRT. The position of the radar is indicated by a light-pen before the simulation starts. An additional computer PANAFACOM U-1500 and its facilities are used for making hard copy of the generated echo images. Figure 2 shows the schematic process flow of the simulation. The main part of the process is the generation of the echo image, the details of which will be described later. In the next section the other parts will be explained briefly. 3. E X T R A C T I O N A N D A R R A N G E M E N T O F C O N T O U R D A T A
3.1 Input of Topographical Map and Thinning Contour Lines The method of generating contour data from a topographical map is described in this section. A topographical map drawn on a scale of 1 to 50,000, whose contour
116
YANAGIHARA ET AL. T A
S
R T J
l IInput of Topographical Map 1 [Binarization & Thinning
1
I into Sequences of Points [Arrangement of Data
I
[Generation of Echo Image
t
I
I OJ
(E
FIG. 2. S c h e m a t i c process flow of s o f t w a r e system.
lines are enhanced by black ink, is used as input. A part of the map (an area of about 6.7 km × about 9 km in the real world) is digitized at 240 × 320 pixels, where each pixel is approximately equal to 28 m. The digital map is binarized by applying a thresholding operation. The contour lines are thinned by applying an ordinary thinning operation. A contour map used in the example is shown in Fig. 3.
3.2 Sequences of Contour Points The contour lines are converted into sequences of (X, Y) coordinates of contour points on the same contour line. Each sequence corresponds to a contour line and is expressed by ((X/l, Yn)(Xt2, Y#2).-'(Xtk, Ylk))" At the next step, the altitude information is added to each sequence, and the sequences are rearranged in order of altitude. The contour
4"~
.,-~x) v
',, Ll o l . - t ' x ' ( , , ("-",
C/
,....
(
.....
:'.
/
t
._.
2
i
'~
( < ,, - - - j
- .....
",,
%.
'"
~
~ . -/
(
/-J
"
s",-.., j
"> ..->
'~-',,-¢~ 7'
,7)
,
":.1 (--)
"~..._,../-"
FIG. 3. E x a m p l e of c o n t o u r map.
GENERATION OF RADAR ECHO IMAGES
117
data are represented in the following form:
(Zl(SllSl2".. Slnl)Z2(S21...)Zm(SmlSm2... Smnm)) , where Sij is a sequence of contour points on t h e j t h sequence of the ith altitude, i.e.,
Sij = (Xijl, Yijl)(Xij2, Yij2)"" (Xijk,,, Yijl%), m is the number of different altitudes, Z i is an altitude number (the real altitude is obtained by multiplying it by 25), n~ is the number of contour lines having altitude number Zi,
kij
is the number of points in sequence S/j. 4. GENERATION OF THE ECHO IMAGE
This section gives the principle of generating echo images. Let us consider a beam starting from the radar position. The beam defines a vertical section plane of the ground (Fig. 4). That is, a half line l in the section plane starting from the position of the radar intersects some configuration lines. The nearest intersection is a point where the beam is reflected (shown by " A " in Fig. 4(b)). Let us call such a point a reflection point. A section plane has a set of reflection points, and the reflection points construct an echo image in the azimuth of a beam. A radar echo image consists of such images in every azimuth surrounding the radar position. In the simulation system, we assume that the width of the imaginary beam is 1 degree, and so the echo image is constructed by 360 radial subimages. 0m
100 m
Sea Om ~-~
Position of radar
L)
0 Imaginarybeam
Island (a) Imaginarybeam. Altitude z
'Reflection point'
--
100 ~
f
)
r
0m
(b)
Vertical
I I
I
I
I
I
I
I
J
J
J
I
section
and
echo
Distance
image.
FIG. 4. Vertical section. (a) an imaginarybeam; (b) an echo image (echobeam is reflectedonly fromA).
118
YANAGIHARA ET AL. S
T
A
R
T
)
] Input of Position of Radar I
I Generation
of Basic Echo Table
Transmission
of Data
I Interpretation of (X,Y)-coordinates I ifor each i
0 Sorting of Data
I
L Generation of Echo Table for each @
Deletion of Redundant Points
Interpolation on Height-Direction
]
I
i Display on C.R.T. I E
N
D )
FIG. 5. Schematicflow of generation of echo image.
Figure 5 shows the schematic flow of generation of echo images. The generation process uses contour data obtained in the previous section and generates an echo image at a radar position given by an operator. Figure 6 shows a unit solid body used in the generation process. This figure is a fan-shaped pillar with angle of 1 degree whose height is effectively infinite. After lining up points of the contour data existing in a unit pillar according to their distance from the origin, we apply the generation principle to the points. There are, however, two problems. (1) We have a nonecho phase where the unit pillar contains no contour point because of the coarse sampling of the contour points. In such a case, the beam in the unit pillar cannot catch the contour line. (2) Since the contour data do not give the ridge of the mountain, we cannot obtain the visible side of the mountain definitely. To work out those problems, the system uses an interpolation of contour points and an estimation of the altitude of the top points. Those algorithms are explained in Section 4.1 and 4.2, respectively. We introduce a Basic Echo Table (BE Table for short) and an Echo Table (E Table for short). Both tables consist of 360 rows, respectively. The O th row corresponds to azimuth 0 , and contains triples (ri, z,., T~) of contour points at that azimuth (Fig. 10). In Section 4.1, we describe a method which converts contour data
119
G E N E R A T I O N OF R A D A R E C H O I M A G E S
Contou~ Iine. i ,, I
..... .
.
.
.
.
-~ .
.......
.
r
!
#
t
0
/
/
Position of radar
;, x
)<: Contourpoint on contour line.
FIG. 6. Process unit for generation of Echo Table.
into (r, 0, z) cylindrical coordinates, and the method which generates the BE Table. In Section 4.2, we describe the method of converting a BE Table into an E Table. The system generates and displays an echo image based on the E Table. 4.1 Generating the Basic Echo Table
First, according to (1), the rectangular coordinates (x, y, z) of a contour point are converted into cylindrical coordinates (r, 0, z) whose origin is located at the position (x 0, Y0, 0) of the radar
r = 7 ( X - X o ) 2+ ( y - y o ) 2 +,
ify -Yo --> 0
(1) +1
ify -Yo < O.
Furthermore, each point is given one of the five types illustrated in Fig. 7 according
°" Type
1'
@
0
@
@
I
1
X--@(--X) X--@ (-X)
2
3
FIG. 7. Connectivity type of contour points.
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YANAGIHARA ET AL.
k kx X: Sample contour point.
Position of radar
FIG. 8. Case of nonecho phase.
to the connectivities of its adjacent contour points, and represented as (r, O, z, T) (T: type name). A contour point of type 0 is a point where the contour line is continuous azimuthally, and a contour point of type 1 is a starting point or an end point of the contour line azimuthally. Types 2, 3, and 4 mean that the contour line is discontinuous azimuthally. Data (r, O, z, T) are stored in row ® of the BE Table, individually. Now we describe the method for solving the nonecho phase (Fig. 8). It arises in the following case. Even if two contour points are adjacent on the x - y plane, they are occasionally nonadjacent on the r - O plane. We worked out this problem by a method of interpolating additional contour points between such points and adding them to the BE Table. The method of interpolation is as follows: let us consider two adjacent points (ri, ~)i, 7., Ti) and (i), Oj, z, Tj) where Oj = Oi + m, m > 2. Then (m - 1) additional points (r, O, z, T) are interpolated according to (2) and stored in the corresponding rows of the BE Table, respectively. r = ri + ( r j -
ri) • k
m
O=O~+k T=O (1 < _ k < _ m -
(2)
1).
Position of radar X:
Sample contour point.
0 : Interpolated point.
FIG. 9. Interpolation of additional points.
GENERATION OF RADAR ECHO IMAGES
e @+1
0+2
121
(ri, z, T.) ((ri+r~)/2 , z, 0) (r j, z, T.) J
360 FIG. 10. Example of Echo Table (case of including additional points).
An example of the interpolation for m = 2 is shown in Figs. 9 and 10. Points in a row are, then, rearranged in ascending order of distance r. Thus, we obtain a BE Table.
4.2 Generating the Echo Table In this section, we describe the method which generates an E Table from the BE Table obtained in the previous section. Some of the points with the same altitude number in the same row of the BE Table are deleted and top points for each row of the BE Table are interpolated. Then, the obtained data is stored in the corresponding row O of the E Table. The details of the method are given below. First, all points with type 4 in the BE Table are deleted because they are redundant for generating radar echo images. Then, points P~ lining up in ascending order of distance r in the same row are examined as to whether the altitude of the point P~ is the same as the next point P~+ 1. If so, some points are removed or the types of some points are rewritten. The details of the method are given by Algorithm 1, where m is the number of points in a row. In Algorithm 1, when the types of two successive points Pi and P~+ ~ with the same altitude are 2 and 3, or 3 and 2, the point P~+I is deleted because it is redundant for generating radar echo images (Fig. 11). (Algorithm 1: deleting point and rewriting connectivity type) (Step 1) i = 1. (Step 2) if i > m, then go to Step 7. (Step 3) if the altitude number z i of the point Pi is not the same as the altitude number zi+ 1 of the point Pi+ 1, then increment i and go to Step 2. (Step 4) if both the type T~ of the point P~ and the type T~+ ~ of the point P~+ 1 are 2, or if both of them are 3, then rewrite both their types to 0, add 2 to i, and go to Step 2. (Step 5) if T~is 2 and T/+ l is 3, or if T~is 3 and T/+ l is 2, then rewrite T, to 0, remove the point P~+1 from the row, add 2 to i, and go to Step 2. (Step 6) otherwise, increment i and go to Step 2. (Step 7) stop. Next, the system uses estimation and interpolation of top points (summits) of islands and mountains. After assuming the configuration of the vertical section of
122
YANAGIHARA ET AL. i 1 t
-)~
/ j
-)K"4
/ P o s i t i o n of radar
×
(a)
/
Before
processing.
I
f
/
P o s i t i o n of radar
x
iX
e"
/
(b) After processing.
FIG. 11. Deletion of connecting points existing in the same direction. (The mark " × " represents a sample point and the under-fight numeric of " × " represents its type.)
the contour points in a row O, the system of top points and store them in the row interpolated between successive points Pi(ri, O, then r, z', and T are calculated according
estimates the altitude and the position O. When the top point P ( r , z', T ) is z, Ti) and Pi+ i(ri+ l, z, Ti+ 1) in the row to (3) (Fig. 12):
r = (r i + ri+,)12 z'=
re+R/5 t z + 3.5
if R < 17.5 if R > 17.5
T=I
( R = ri+ l - ri).
(3)
As altitude sampling of contour points is coarser than horizontal sampling, we need to interpolate some other points. On inputting a topographical m a p the system extracts contour lines at every 100 m, while it samples contour points at a 28-m interval on the x - y plane. So, by interpolation we make the difference of the altitudes of successive points in a row O less than or equal to 25 m. The method is as follows: For successive points Pi(ri, zi, Ti) and Pi+l(ri+l, Zi+l, Zi+l), if zi+ l is
123
G E N E R A T I O N OF R A D A R ECHO I M A G E S
Altitude
Pl
R
)r Distance
Pi+l
)< : Contour point. O : Interpolated point. (a) Interpolation of a top point. He i ght Z (m) (pixel) 100
4 3.5
75
3
50
2
25
1
0
0
) R (Length) 0
5
10
15
0
140
280
420
17.5
20 560
(pixel) (m)
(b) Relation of R and Z. FIG. 12. Interpolation of a top point and estimation of its height.
greater than zi+ 1, then some points P(~', z), T/) are interpolated between them according to (4). (The unit interval in the altitude direction is 25 m.) ,
J
5 = r, + (,-,+, - r~). k 7- 1
,
J
~J = ~' + ( ~ ' + ' - ~')" k -S- 1
T;=O
124 where
YANAGIHARA ET AL. j=l
..... k i
k=
i f l < z i + I - z i<__2
if2
(4)
4.3 Generation of the Echo Image An echo image is constructed from the 360 subimages generated from the Echo Table at every ® by applying Echo Rules. We assume that a row O contains m points, (ri, zi, T/) (1 < i _< m). (Echo Rules: Generation of subimage) (Rule 1) if i =~ m and ePm(i) < zi/ri, then if T / = 1 or qa,,(i + 1) > zi+ l/ri+ 1, generate an echo on interval [Ri, R~ + otherwise generate an echo on interval (Rule 2) if i = m and ePm(i) < zi/ri, then if T~ = 1, generate an echo on interval [R~, R~ + otherwise generate an echo on interval (Rule 3) otherwise, do nothing because of no echo,
0.5]; [R~, Rz+ l]-
0.5]; [Ri, Rz + 5].
where epm(j) is given by MAX(zl/rt[1 < I < j ) , (/)re(l) has an appropriate negative value, and R i is given by ~ + z 2 . An illustration of generating a subimage is shown in Fig. 13. 5. RESULTS AND DISCUSSION Generated echo images are shown in Fig. 16. The input topographical map is a contour map drawn at 1 to 50,000 of an area in Japan (Fig. 15). The beam of the simulated radar has a width of 1 degree on the horizontal plane and its range is set at 100 pixels (about 2.8 km in the real world). Figures 16(C)-(E) show echo images of the bay at distinct positions of the radar. The echo marked by *- in Fig. 16(G) is an example of an incorrect echo subimage in the case where there is a beam between two contour lines (Fig. 14). We will cope with this problem by applying interpolation of points in the azimuth direction, or by varying the brightness on the CRT according to the inclination of the slope of the land. Finally, we mention the angular resolution and range resolution of the simulation system. Echo Table is generated at every one degree, so that the angular resolution is one degree. The echo image is displayed at every pixel, so that the range resolution is V~- pixel (about 40 m). 6. CONCLUSION We have proposed a radar echo simulation system, which translates data (x, y, z) of contour lines in rectangular coordinates into data (r, O, z) in cylindrical coordinates, and displays echo images generated from an Echo Table by applying Echo Rules. The proposed system was designed so as to be implemented by several
GENERATION OF RADAR ECHO IMAGES
125
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o t-~ u
'\\,~\O\o~°~ \ \ O
o.o
¢,
i
\ t~ ,.-1
o-~ ~ C,
O -,-q 4-1 o,-a gt~
126
YANAGIHARA
ET AL.
z = 0
z = 100
on contour It
I
I
I
II
I
I
I
map.
I ~
~ ' ' ~ -
on echo
image.
FIG. 14, C a u s e of e c h o i m a g e m a r k e d b y a n a r r o w .
microprocessors and evaluated on the following points: (1) reduction of input data of contour lines, (2) conciseness of process algorithm. To accomplish (1), string data of contour points defined by (x, y, z) rectangular coordinates was introduced. For (2), by introducing the idea of an Echo Table, each algorithm becomes simple and effective. There remain some points that should be improved for the system. One of them is a method which varies the brightness of the beam on the CRT according to the strength of the reflected echo. It is possible to vary the brightness of the beam on the CRT because the angle of inclination on the land can be calculated from the data of the Echo Table. The others are a simulation of the sea clutter and of reflected echos from other ships.
XD
~
oX G
C)
FIG. 15. C o n t o u r m a p s f o r e x p e r i m e n t .
G E N E R A T I O N OF R A D A R ECHO I M A G E S
FXG. 16. Echo images at each point
(A-tt) on Fig. 15.
127
128
YANAGIHARA ET AL.
FIG. 16 Continued. We mention a comparison with the use of mesh data as input. Mesh data has 76.8 K-words of data on representing the map shown in Fig. 3, while contour data (every 100 m) has about 7.3 K-words of data including altitude information. Thus, the information of the map is compressed to about one-tenth. However, since the mesh data has the altitude of every sample point, an echo image generated using the mesh data as input can be more faithful in regard to altitude information.
REFERENCES 1. M. B. Faintich, Digital sensor simulation, PhotogrammetricEng. Remote Sensing,42, 1976, 1427-1440. 2. L. N. Rindenour, Radar System Engineering, McGraw-Hill, New York/London, 1947. 3. D. P. Meyer and H. A. Mayer, Radar Target Detection, Academic Press, New York/London, 1973.