Maritime University of Szczecin
Akademia Morska w Szczecinie
2008, 13(85) pp. 74‐78 2008, 13(85) s. 74‐78
Extraction of characteristic points from radar image
Ekstrakcja punktów charakterystycznych z obrazu radarowego
Tomasz Praczyk
Akademia Marynarki Wojennej, Instytut Morskich Systemów Radioelektronicznych 81-103 Gdynia, ul. Śmidowicza 69, tel. 058 626 27 03, e-mail: t.praczyk@amw.gdynia.pl
Key words: radar navigation, extraction Abstract
The problem of continuous position availability is one of the most important issues connected with human activity at sea. Because the availability of the electronic navigational systems can be limited in some cases (for example during military operations) we should consider additional methods of gathering information about ship's position. In this paper, one of these methods is presented, which is based on extraction of specific features from radar images – characteristic points of the coastline.
Słowa kluczowe: nawigacja radarowa, ekstrakcja Abstrakt
Ciągła dostępność pozycji jest jednym z najważniejszych problemów związanych z ludzką działalnością na morzu. Ponieważ dostępność elektronicznych systemów nawigacyjnych może być ograniczona w niektórych przypadkach (np. podczas operacji wojskowych), powinno się rozważyć dodatkowe metody gromadzenia in-formacji o pozycji statku. Jedna z tych metod, oparta na wybieraniu konkretnych elementów z obrazów rada-rowych – punkty charakterystyczne lini brzegowej, została zaprezentowana w niniejszym artykule.
Introduction
The primary positioning system can be un-plugged, destroyed or malfunctioning. This is the reason why alternative methods of position estimat-ing should be taken into account. This is especially important for naval ships. The military auxiliary positioning system should be as autonomous as possible. It should give the possibility of ship's position fixing without information from electronic navigational systems like GPS or others. Radar navigation performed in an automatic way has such a feature. In the paper, one element of automatic radar navigation system, namely characteristic points extraction subsystem, is presented.
Functioning of the system
Hypothetical structure of the whole system is presented in figure 1.
The main task of the radar images registration subsystem is transferring radar signal to the digital
form [1]. The additional task is elimination of ech-oes coming from moving ships. In this case, the subsystem should be able to track images coming from radar in order to distinguish the constant ob-jects from the moving ones. The main task of the characteristic points extraction subsystem is prepar-ing a vector of characteristic points visible on the registered radar image. The main task of character-istic points identification subsystem is identifying the sufficient number of previously extracted points to calculate ship's position. In the final step, the system estimates ship's position using identified points and traditional navigational methods.
The method of extraction of characteristic points from radar image
When talking about the extraction of character-istic points from radar image, we should start with presenting considered images in the form of con-tour invariant. First, we should define the image
Radar Radar images registration sub-system Positioning sub-system Characteristic points extraction sub-system Characteristic points identification sub-system Radar image Radar image Points vector Coordinates of points
Fig. 1. Structure of the system Rys. 1. Struktura systemu
R O La: a → where:
Oa – a set of points Pa(x, y):
( )
{
∈ ∈< > ∈< >}
= x y R x N y M
Oa , 2: 0, , 0,
N, M ∈ N – determine the size of the image. We may determine the digital image as a func-tion Lc(n, m):
Ν :O
Lc c→
where Oc ⊂ Oa is a set of points P
ic(n, m), i = 0,1,..,N*M – 1:
( )
{
∈ ∈< > ∈< >}
= n,m Ν :n ,N ,m ,M Oc 2 0 0Let us assume that N and M which determine the
size of the image are odd, so for every image we can determine the central point Po(n
o, mo): 2 1 , 2 1 = − − = N m M no o
The analogue image as well as the digital one can be presented in polar coordinate system. For that presentation every point P(x, y) is determined by bearing NR on that point from central one and distance d = |PoP| [3]. There is a possibility to change the representation from the polar coordinate system to the Cartesian coordinate system. A mapping function from Cartesian to the polar coordination system and vice versa are presented below (for the analogue image):
( )
x y d f( )
x y f NR= NR , , = d ,(
)
a(
)
a y a x NR d y f NR d x y O f x= , , = , , , ∈As for the digital image, we should start with determination of the mapping of each point of an analogue image to the appropriate point of a digital image. c a Pc O O f : →
( )
c a O P a Pc P P P f c c∈ =argminFinally, we get the mapping function between polar and Cartesian coordinate system for the digi-tal image:
( )
n m f(
f(
NR d) (
fa NR d)
)
y a x Pc , , , , =The next step is determination of the set of points lying on the bearing NR, i.e.
a a NR O D ⊂ and c c NR O D ⊂
( )
( )
{
x y O f x y NR}
Da a NR NR = , ∈ : , =( )
( )
( )
{
a}
NR a a Pc c c NR n m O n m f P P D D = , ∈ : , = , ∈Next we define the set c NR c
W
NR D
D , ⊆ of visible points of digital image lying on the bearing NR.
( )
{
: 0}
, = c∈ cNR c c > c W NR P D L P DFinally, we can define the function on contour invariant d=ginw
( )
NR :( )
o c D P inw NR P P g c W NR c , min ∈ = (1)In order to simplify the algorithm of characteris-tic points extraction, function (1) has been replaced by function:
( )
o c D P k inw k P P g c W k NR c , min ∈ = , k=0,1,..,2(
N+M)
−1 (2) where( )
c k b NR k f PNR = , is the bearing at k coastal point of the image
(P Dc
{
( )
n m n N m M}
b c
k
b, ∈ = , : = ∨ = ) and k is an index of the coastal point in the ordered series of coastal points. The ordering function can be presented as follows:
( )
(
)
(
)
(
)
(
)
0 , 0 1 ) ( 2 ,.., 2 for , 1 1 2 ,.., for 1 , 1 ,.., for , 1 1 ,.., 1 , 0 for 1 , 0 0 , 1 , = = − + + = − − + + = − − + = + − = + = = = + m n N M N M k m n N M N M k m n N M M k m n M k m n P f P k k k k k k k k c k b b c k bFor the function determining contour invariant for the digital image we can define function gI
( )
xinw determined on the set
{
∈ ∈< + − >}
= x R:x 0,2(N M) 1 I then g( )
x gk( )
k x k inw Iinw = for = . This function defines contour invariant for the analogue image. The proposed method of characteristic points from radar image extraction is based on the analysis of the second derivative of the functiongI
( )
xinw . As an estimator of this function we may use the following [4, 5]:
a) b)
c) d)
Fig. 2. Contour invariant of the sample radar image (a) and graph of I inw
g) for σ = 0.1 (b), σ = 1 (c) and σ = 10 (d) Rys. 2. Konturowy inwariant przykładowego obrazu radarowego (a) i wykres I
inw
( )
( ) ( )
( )
, , , 2( ) 1 0 1 ) ( 2 0∑
∑
− + = − + = = N M k k M N k k k inw I inw x x k g x g σ ϕ σ ϕ σ )( )
( 2) 2 2 ,σ σ ϕ k x k x e − − = a) b) c)Fig. 3. Graph of z(k) for σ = 0.1 (a), σ = 1 (b) and σ = 10 (c) Rys. 3. Wykres z(k) dla σ = 0,1 (a), σ = 1 (b) i σ = 10 (c)
Fig. 4. Original image (a), characteristic points calculated for σ = 0.1, λ = 0.01 (b), σ = 0.1, λ = 0.5 (c), σ = 1, λ = 0.1, (d), σ = 1, λ = 0.5 (e) and for σ = 10, λ = 0.01 (f)
Rys. 4. Obraz pierwotny (a), punkty charakterystyczne obli-czone dla σ = 0,1, λ = 0,01 (b), σ = 0,1, λ = 0,5 (c), σ = 1, λ = 0,1, (d), σ = 1, λ = 0,5 (e) i dla σ = 10, λ = 0,01 (f)
The second derivative of that function is as fol-lows:
( )
2 2 d d , x g x z I inw ) = σThe algorithm should be able to fix z(k) for defi-nite σ in points k = 0,1,..,2(N+M) – 1 and then to find k, that meets the relation shown below:
( )
( ) (
) ( ) (
)
( )
(
)
(
( )
)
(
)
c b k inw k a y k inw k a x Pc f NR g k f NR g k D f k z k z k z k z k z ∉ ∧ + ≥ ∧ − > ∧ > , , , 1 1 λwhere λ allows segregation of the set of potential characteristic points in the groups: visible – z(k) > λ
and hardly visible – z(k) ≤ λ. Another parameter of the algorithm is σ. We can say that λ eliminates hardly visible points from the list of characteristic points and σ prevents generating them.
Finally points:
( )
n m f(
f(
NR g( )
k)
f(
NR gk( )
k)
)
inw k a y k inw k a x Pc , , , , =are considered as characteristic points of the given radar image.
Demonstration working results of proposed al-gorithm are presented in figures 2−4.
Conclusions
We may draw the following conclusion: it is possible to apply presented algorithm to the task of characteristic points extraction from radar image. The conducted tests have revealed that the key pa-rameters are σ and λ. If σ > 1, then algorithm brings characteristic points in one point very close to each other or moves coast line points to the wrong places. Thus, we have decided that value of that parameter should be approximately 0.1. The presented algorithm may extract characteristic points or be considered only as an auxiliary system for an operator, who finally determines the location of characteristic points, let’s say, by hand. This concerns a situation when an object has a very large echo, and the algorithm can estimate it as a large object with a greater number of characteristic points.
Another element of the system, which can eliminate additional, impropriate points generated
by extracting points subsystem, except the user, is the identification subsystem. It should be able to choose only those points as base points that have their patterns in the base of knowledge and then correct their positions on the radar image.
References
1. TADEUSIEWICZ R., FLESIŃSKI M.: Rozpoznanie obrazów. PWN, Warszawa 1991.
2. KUCHARIEW G.: Przetwarzanie i analiza obrazów cyfro-wych. Politechnika Szczecińska, Szczecin 1999
3. WĄŻ M.: Metoda wyznaczania pozycji okrętu za pomocą porównania obrazu radarowego z mapą morską. Rozprawa doktorska AMW, Gdynia 2000.
4. PRACZYK T.: Sieć GRNN w kompresji obrazów radaro-wych. Zeszyty Naukowe AMW 2003, 3.
5. STATECZNY A., PRACZYK T.: Sztuczne sieci neuronowe w rozpoznawaniu obiektów morskich. Gdańskie Towarzy-stwo Naukowe, Gdańsk 2002.
Recenzent: prof. dr hab. inż. Andrzej Stateczny Akademia Morska w Szczecinie
