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Quick recognition of circular objects in a black-white picture
Pattern Recognition Letters 8 (1988) 277 288 North-Holland
November 1988
Quick recognition of circular objects in a black-white picture Zbigniew M. WOJCIK Department o['Computer Science, The Wichita State University, Wichita, KS 67208, USA Received 26 October 1987 Abstract." A method of circular objects recognition is presented that depends on converting input picture into binary image, next on tracing perpendicular chords along the object determining its maximum extension, and then on separation and analysis of a rectangular frame determined by the chords. This process can be performed under the assumption that neighboring objects are sufficiently distant from each other. Brightness, area and gravity center of its original gray-scale contents are calculated inside that rectangular frame. These parameters are used for specification of each separated object. Values of these parameters are used to mark arcs connected to a node into which the object is transformed. The third step of data processing is to compare the identity (automorphism) or similarity (isomorphism) of a graph obtained as the result of a recognition process with a set of reference (template) graphs stored in a memory. The nodes of the recognized image that have the greatest weights are taken into account in the first place in the identification (matching) process. Key words." Segmentation, sky objects, target recognition, detection, quantization, identification, circular objects.
1. Introduction
Star images in sky photos, microscope images of some alloys in metallography, some images used by robots contain circular shapes. The paper presents a method for automatic recognition of such circular objects. Automatic detection of all picture elements that represent the objects in question (e.g. stars in sky photos) is performed in the first step. As the result of the preprocessing, a gray-scale input picture is converted to a binary image. Each picture element p(X, Y) gets the digital value (X, Y)= 1 in case it represents an object in question and the value (X, Y) = 0 otherwise. Disturbances are discarded in the second step. The picture with circular objects is segmented during the third step. Parameters of each separated circular object are estimated automatically in the fourth step: area, coordinates, perimeter, brightness, shape factor, etc. The object is automatically removed from the input binary image after the analysis.
Each separated and estimated circular object is represented by a very simple graph (Figure 1) that consists of a single node and some non-directed arcs linked to the node. The node is marked with the name 'object'. Arcs connected to the node represent attributes (i.e. one-argument functions) of the object and are labeled with names like 'area', 'coordinates', 'perimeter', 'brightness', 'shape factor', etc., together with values of the estimated quantities. Each object gets also weight (importance) that
brightness J
0167-8655/88/$3.50 0 1988, Elsevier Science Publishers B.V. (North-Holland)
Figure 1. The graph of a single circular object. 277
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is equal to the estimated brightness of an object in question in case of a sky image. Recognition of circular objects depends on an automatic transformation of image into its quantitative and qualitative computer representation, usually into a graph or into a set of graphs [7]. Each graph represents circular objects that are present in the image under investigation and that have the greatest weights (importances): each node represents separate object and arcs represent parameters of that object. Mutual distances of the object in question are determined on the basis of the estimated object coordinates. Interrelations (e.g. two-argument relations defined on two objects) are represented in image graph as arcs linking two nodes (Figure 2). Names of these two-argument relations and measured values of their intensities are used as the labels of these arcs. The graph is subjected to the process of identification as a result of which nodes get their proper names (e.g. names of stars) and next some considerable part of the graph may get a general name (e.g. a name of a constellation of stars).
November 1988
The arcs representing absolute coordinates of object (in the picture coordinate system) as well as arcs representing weights, are removed before an indentification process (Figure 3). Comparison process of template graphs stored in a memory with the graph obtained as a recognition process will also be considered in the paper.
2. The method of automatic detection of objects Simple smoothing is carried out in the preparatory processing of input image. Each value v'(X, Y) representing brightness of a picture element p(X, Y) is replaced by a mean brightness v(X, Y) of a circular area (window) O(X, Y): N
In
Z Z w..'.,(x,, Y,) v( x . Y) - " : 1 i: 1 N
/.% n=l
/ a~ea
~cedl2 area A2
co
area A3
C°
Figure 2. G r a p h obtained as a result of a recognition process of an image consisting of three circular objects. 278
(1)
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November 1988
_¢~ V
t
area A3
~
area A2
~
Figure 3. Graph shown in Figure 2 designed for identificationof a recognizedimage. where: I, is the number of elements of the window (area) O(X, Y) having identical weights. These weights w, can be calculated from Eq. (2a) or (2b): w, = exp( - nr2),
(2a)
w, = (q + 1 - r)/(q + 1)
(2b)
where:
r = x/(Xi - )0 2 + (Yi - y)2,
(2c)
q is the radius of the window O(X, Y); q is measured in terms of picture elements (q is an integer); i is an index of element pi(X~, Y~) belonging to the window and having weight w.; n is an index of a subset of the window elements having identical weights; N is a number of various weights of the window elements. According to the formulae (2a) and (2b), the effect of brightness of element p(Xi, V~) on the value v(X, Y) (Eq. (1)) decreases while the distance r of the element p(X/, Y~) from the central element p(X, Y) increases. The usually assumed constant distribution of weights w,: w, = I w, = 0
for p(X i, Y~) e O(X, Y), for p(Xi, Yi)¢O(X, Y)
(3a) (3b)
is not well-justified and a distribution of weights similar to (2a) is observed in the reception fields of animal eye. The mean weighted value vo(X, Y) of brightness is calculated inside a greater window O(X, Y) in the next step. For instance, the five element window can be assumed for the smoothing process, and for the process of calculating the value vo(X, Y) one can accept the nine element window. Pixel p(X, Y) belongs to an object of an unknown image in case the following condition is satisfied:
v(X, Y) > Q(X, Y) = ki
[Wo Vo(X, Y) + v(/)] Wo+ 1
(4)
where: Wo is a weight of the value vo(X, Y): any increase in the value wo means increase in importance of a local brightness on the threshold value Q(X, Y). The wo may be assumed to be equal to 0 in practice (e.g. for gray-scale picture); v(j) is the value of the abscissa of a subsequent local j-minimum of the picture histogram. If the condition (4) is satisfied, the element p(X, Y) gets digital value (X, I1) = 1, and (X, Y) = 0 in the remaining cases:
(x,Y)=
1, 0,
if v(X, Y) > Q(x, Y), ifv(X,Y)
(5)
279
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Lemma 1. The k i is the following coefficient:
3. The method of automatic removal of isolated disturbances
ki = kx < 1 if vo(X, Y) > v(j),
(6a)
ki = k2 > 1 if vo(X, Y) < v(i).
(6b)
Proof. If the inverse to the (6b) inequality were assumed (i.e. k2 < 1 for vo(X, Y) < v(j), e.g. for the background of objects in question: the background is defined approximately as a subset of picture elements, for which vo(X, Y ) < v(j)), small disturbances generating slightly greater value v(X,Y) would readily result in fulfilling the inequality v(X, Y) > Q(x, Y) for some picture elements representing darker background. The incorrect values (X,Y) = 1 for some of the background elements would be obtained and therefore inequality (6b) is true. Inequality (6a) is proved analogously. [] Hence, utilization of the coefficients k I < I and k 2 > l ensures elimination of arduous, small disturbances and irregularities in shading. In case the values v(]) of abscissae of local histogram minima of picture brightnesses are arranged in the descending order, the brightest objects are detected first (formulae (4)~6)) and the darkest in the last place. If only one binary output image is required (e.g. in case of sky images), it is possible and convenient to assume weight wo (expression (4)) greater than 1 (e.g. Wo = 8 for black-white sky pictures) and the following value Vsr instead of the value v(]) [6]: Vsr =
WsVs+ WnVn+ WxVx Ws -'l'-Wn + Wx
(7)
where: vs is the mean value of brightness of all picture elements; v,, vx are the minimal and maximal values of brightness of picture elements correspondingly; ws, w., Wx are weights of quantities v~, vn and vx respectively. The detected objects are represented by the following subset Fo of the picture P:
Fo = {p(X, Y)~P:
(X, Y) = 1}.
(8a)
The background of the objects detected forms the following subset Fb:
Fb = {p(X, Y)eP: 280
(X, Y) = 0}.
November 1988
(8b)
In case there are very strong (i.e. high-amplitude) but isolated disturbances, and the area of each individual disturbance does not exceed one picture element, it is possible to investigate digital values of the nine-element window O(X, Y) of each picture element. The first step is to read the digital value (X, Y) of the central element p(X, Y) of the assumed window O(X, Y). The next step is to investigate digital values of all other elements of the O(X, Y): only in case there are no other elements in the O(X, Y) having the same digital value as the central element p(X, Y) should the digital value (X, Y) of the central element p(X, Y) be changed to the opposite value. The above method is not good for larger disturbances. Rotating neighborhood technique introduced in [4, 3, 6] is the most effective here: is very fast and does not blur edges. Variance in digital values of rotating neighborhood pixels with respect to window center is calculated. Center of the window remains unchanged, if the minimum variance is found for at least one neighborhood. Otherwise window center gets value of the neighborhood, the best of that which is the most homogenous. In case of binary image, variance in terms of logical values can be calculated very quickly [4].
4. Method of automatic separation of circular objects In order to measure parameters of an individual object (such as area, brightness, perimeter, coordinates, shape factor), the object should be separated first from the remaining part of picture, because otherwise nobody could say what was automatically estimated: a fragment of an object, some objects or no objects? A readout of the digital value (X, Y) = 1 during a linearly ordered analysis of picture elements means that the scanning line has found an object. A chord is traced perpendicularly to the scanning direction from the first picture element of digital value (2, Y) = 1 that has been found (Figure 4). A horizontal, second chord passes across the middle of the first chord (Figure 5(c)). These two chords
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November 1988
I Convertion of an input gray scale I picture into binary image; Y = N
Ix-x+ll no
t (X,Y) = 1 7> I yes
Tracing ,a chord along an object in the direction perpendicular to the scanning line; Tracing a chorizontal chord across the middle of the above perpendicular chord; Separation of a square binary image determined by the two chords; Calculation of all the required parameters (e.g. brightness, area, gravity center) of the gray scale picture inside the frame determined by the separated binary image; Clearing of the separated and already analysed binary image frame;
I
-
I yes
no
IY = Y - 11 no
I
yes
Figure 4. An algorithm of automatic analysis of circular objects.
have dimensions DX and D Y correspondingly; they have been measured in connected picture elements having digital values (X, Y) = 1. A square image frame S that contains the circular object is determined automatically. The coordinates X0 and Y0 standing for origin of the image frame S are calculated (Figures 4, 5). The length D of each side of the frame S is equal to the greater dimension of the two DX and D Y plus some pixels (Figure 5). In the case no two circular objects overlap nor the object are very close to each other, the values v(X, Y) of all input image elements that lie in the interior of the object image S can be analyzed (Figure 5) to find particular parameters as brightness, area and coordinates. After the separated image frame S has been analyzed, all pixels of the binary image, obtained as a result of the detection process, and belonging to the frame, get the digital
value 0. In this way each object will be analyzed only once.
5. The method of automatic recognition of circular objects Each circular object that has been separated is represented by a node labeled with the name 'object'. In addition, that node gets some arcs attached to it (Figure 1). The arcs are marked with the names of parameters of the object separated and with the values of the parameters. Let us note, that the frame that has been separated contains an entire object regardless of the position of the object on the picture. Thus, the result of the separation process (i.e. the object frame S) fulfills the basic condition for image representation and therefore it can stand for a feature (e.g. for zero-argument function 'object') of an 281
Volume8, N u m b e r 4
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-j
~0
November 1988
Scanning line and ..direction'of scannin~
NNNN
a
x01 XMI
x
YNIi // f f ~
I
1
nnilnlnmiii!
Y0]
iX
i i i i i i i i I i i, i lil~
\"\,~ f ///// X02
x
XM2
x
-y
1111
IYN2
1
~N'~[~s
YS
Yo %a
/
mmmqmmmmmm m~mmmmmmmmm~mm mm Nm)mmMm mmmm
S
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x
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~
_ X02
~
1
XS
iiJii~, Il lni il l| |i l in ml i i i l ggm I~p~dini
•
XM2
x
GM
Figure 5. Steps in automatic separation of a circular object in a binary image: (a) a binary image with a circular object and the first scanning line passing across the beginning of the object; (b) vertical chord of the object traced from the first element for which (X, Y) = 1; (c) horizontal chord traced through the row determined by the middle of the vertical chord; (d) the two chords fix a rectangular image of dimensions D X * D Y that separates a circular object; (e) the separated square frame of the parameters: X0 = X S - D / 2 - - D / A ; YO = Y S - D / 2 - D / A ; G N = G M = D(1 + 2/A), where D = m a x ( D X , D Y ) . The coefficient A is selected experimentally, e.g. A = 10. 282
V o l u m e 8, N u m b e r 4
PATTERN RECOGNITION
image [3-6]. The brightness J of the detected and separated circular object can be calculated from the following formula:
LETTERS
N o v e m b e r 1988
I = card{p(X, Y)eP:
K(X, I0
= ~/ I,(X, Y) = 1], i=1
J =
~
(X, Y) J(X, Y)
(9)
p(X. Y)~S
where: J(X, Y) is the intensity of illumination of picture element p(X, Y); the J(X, Y) is represented by the value v(X, Y); XO, YO are coordinates of the origin of the separated object image S; (X, Y)= 1 in case the element p(X, Y) represents an object in question and (X, Y) = 0 in the other cases (see expression (5)). The brightness J calculated from the Eq. (9) is invariant relative to possible positions of the object in question on the picture; therefore, the result of the formula (9) represents a single-argument relation of the separated object [3-7]. Coordinates (x,y) of the detected circular object are calculated as the gravity center of contents of the separated object frame S:
(13)
where: card{...}is the number of all elements of the set {..-}; Ki(X, Y) and Ii(X, Y) are logic functions as shown in Figure 7; m,n are coefficients and can be calculated by means of the least squares method. Some measurements L~, L: ..... Lk ..... Lo of the real and well known length of perimeter L' of an object are carried out in the least squares method. Each measurement k is as follows:
L k = mKk + n Ik.
(14)
The necessary and sufficient condition for the minimum of the following error Eo: D
E/, =
y' (L' - L~):
(15)
k=l
is as follows:
Y. (x, r3g(x,Y)X x = p(x,r)~s
,
(lOa)
J
= 0,
(16a)
(3n E° = 0.
(16b)
- -
c3m
E D
y. (x,Y)J(X,Y) Y Y = p(x,r)~s
(10b) J
The gravity center designates a constant, always the same point of any physical body under investigation, regardless of the position of the body, and therefore, the values (x,y) determined from Eqs. (10a, b) can serve for a one-argument relation of the body (i.e. of the object) in question (the gravity center satisfies the basic condition for image recognition [3-6]). An approximation L of the real length of perimeter of the separated object can be given as follows:
L=mK+nl
(11)
where: K = card{p(X, Y)EP: =
K(X, Y)
~/ K , ( x , y ) = 1},
i=1
(12)
The solution of the two equations (16a, b) gives the two unknown coefficients m, n to be calculated. An approximation A of a real size of the area of the separated object is as follows:
A = a K + h i + cZ
(17)
where: Z = card{p(X, IOeP:
Z(X, Y) = 1}
(18)
where: Z(X, Y) is a logic function as given in Figure 7(c); a, b, c are coefficients calculated by means of the least squares method, as in the case of the coefficients m, n. The subsets K, L Z are independent of all possible displacements of the object in question in the interior of the separated frame S, because the values of the functions K, I and Z are invariant with respect to all possible rotations of any image around 283
Volume 8, Number 4 0
PATTERN RECOGNITION LETTERS 1
2
3
4
November 1988
5
6
7
012345678901234567890123456789012345678901234567890123456789012345678901234567 1 2 3 4 5 6 7 8 9 i0 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 3 4 5 6 7 8 9 50
XXX XXX XX
XX XX
XXX XXXX XXXX
XXX XXXX XXXXX XXXX X
X XXX XXX
XX XXXX XXXX XX
1 ....
a Figure 6. (a) Result of automatic detection of sky image objects.
any pixel p(X, Y) and all picture elements are investigated. Thus, the subsets K, I and Z represent correctly one-argument relations of the object in question [3-6] since the subsets fulfill the basic condition for image representation. A shape factor can be calculated from the formula [2]: L K - -2hA 284
1.
(19)
Since the quantities L and A satisfy the basic condition for image representation processes, the shape factor K also represents a one-argument function of an object in question. The one-argument relation 'circular' results from the method of separation of circular objects presented in Section 4 of the paper and from some assumptions accepted for the method. Attribute like 'circular' is always related to an appropriate recognition algorithm.
Volume 8, Number 4
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Intuitively one can easy tell concepts of recognition and identification apart: we recognize a sky image for we see it, but usually only an astronomer is in a position to identify an observed sky image, i.e. he can say what sort of stars are to be found in the sky fragment under investigation. As a result of recognition processes a set of symbols is generated independently of displacements of the recognition system in the space of observation of the image in question [3 6]. A set of graphs produced according to the algorithms and expressions presented in the paper satisfy the basic condition of image representation processes [4~6] and therefore the set of graphs is called a recognition result of circular objects.
= 495 = ii = 13
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J XO YO
J XO YO
= = =
1078 73 ii
- XX X- XX X- - X X -
J XO YO
= 1304 = 2 = 27
--
X
X X -
- X X X X -
J XO YO
X
X
= = =
X X -
2573 72 29
-XX X-- X X X X - - X X X X X - X X X X - -
J XO YO
= = =
921 5 36
- X XX- X X X-
J XO YO
= = =
1810 55 46
-X X-- X X X X- X X XX- - X X - -
b
November 1988
6. The method of automatic identification of sky images It is assumed that there are no two groups of stars (each group consists of three or more stars) with identical mutual (relative) distances and identical brightnesses. We assume that all objects of the image in question stand for stars and that they are specified in a catalog. The catalog may refer only to a certain fragment of the whole sky, but the fragment must involve the sky portion under investigation. It is possible to work out a number of methods of comparison of brightnesses and mutual distances of sky objects with the data included in a catalog of stars. Reading from the catalog the data concerning all these stars whose brightnesses approximate those of the most important objects of the image in question seems to be the most advantageous as the first step. If the set of all catalog stars is denoted with the symbol SAO, then the subset li that corresponds to any object i of the sky image can be written as: li = IkeSAO:
C
Figure 6. (b) Result of automatic separation of sky image objects; (c) values v(X, )I) of the sky objects shown in (b).
J-AJ
I
(20)
where: k is the index of a star in the catalog SAO, and AJ is a maximal possible error of measuring brightness J of a star. The AJ is typical of each device (e.g. a set up of a telescope and a scanner). Having a subset I = (1 ..... i . . . . . A) of the most 285
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PATTERN R E C O G N I T I O N LETTERS
important stars recognized in the image in question, we obtain the corresponding subset S I of stars separated from the catalog SAO according to the formula (20):
November 1988
selected from the sets Ii and I t (formula (20)) and are passed into the subset Iij: lit = { i e l i , j ~ I t : dlj -- Ad O < Di t < dij + Ado}.
(23)
(21)
S I = U Iv iEl
The Iij consists of the catalog objects lying at a distance Dit close to the distance dij and having bright° nesses approximate to that of the sky image. The Dij is the distance between the two catalog stars i and j; however, coordinates of any star are expressed in the units of right ascension and declination (Figure 8) and therefore these astronomical units are to be reduced to numbers of picture elements of the given optic-to-electric converter. If Ox axis of a picture coordinate system is parallel to the sky equator and Oy axis is parallel to the sky meridian, then:
The set S I contains a lot of stars having mutual distances that differ from those of stars of the recognized image, and therefore, these stars are removed from the S I in the next step. In order to do that the most important object is selected from all the objects of the image in question; the object is denoted with j-index; j e I . The distance dit between the object j and an object i calculated on the basis of the sky image under investigation is: d 0 = x/(xi
- x j ) 2 -.I- (Yl - Yj) 2.
(22)
The maximal possible error of the determination of the dij is equal to Ad,7 for a given device. Stars are
-:1o1111 X
-:l
x
Di j = x/(a(o q _ aj))2 + (d(ai - aj)) 2
I,(x,Y)
(24)
= 1
0 110 1
x
2 /'2(X, Y) -- 1
0 011 1 X
x
-:I
Ka(X, Y) = 1
1
-:T
x
K4(X, Y) = 1 1
111 0 x
x
C*)
2 Ia(X,Y) = 1
:T
1 0 1 1 0
110 it x
x
:l
x
:T 1
x
~(X,Y)
= 1
z(x,Y)
i i i i
X
1
x
10 0 x
x
(b)
C¢)
Figure 7. Graphic interpretation of values I of the following functions: (a) Ki(X, Y); (b) Ii(X, Y); (c) Z(X, Y). 286
= 1
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PATTERN RECOGNITION LETTERS
where: ai, aj are right ascensions of catalog stars i and j correspondingly; ai, aj are declinations of the catalog stars i and j respectively; a is a coefficient telling how many sides of pixels of a given device are included in one unit of the right ascension; d is a coefficient telling how many sides of picture elements are comprised in one unit of the declination. The distance di. of object i from object n and the distance dr. of object j from object n are also determined; n = i and n = j . Subsets I.i and It. are formed, in the same manner as the subset llj (expression (23)). The product lij. of the subsets lij and It. is calculated:
I~. = Iijc-~lj..
(25a)
The subset lit" consists of catalog indexes of the stars that have brightnesses corresponding to the brightness of the object j that has been recognized in the sky image in question, the stars being situated at the distances Dij and Dr. from objects i and n (placed in the subsets Ii and I.) recognized in the given sky image. Subsets Ij, i and I.i j are formed in the same manner:
Ij.i = l;.~l.i,
(25b)
l.i; = l.ialij.
(25c)
In case each subset: Iij ., It. i, I.i t contains only one element, the objects i, j and n get synonymous indexes of stars from the catalog SAO, with the indexes being elements of the subsets lit., lj.i and I.ij. However, the distance dit between stars i a n d j were not taken into account when forming the subset lit" . Therefore, the subset lit. may contain more than one element. The same is true for subsets It. i and I.i t. If the subsets lit., Ij.i and I.o contain more than one element each, the elements of these subsets should substitute for elements of the corresponding subsets Ij, I., ll; then the procedures of forming the subsets lij, lj., I.i (formula (23)), as well as the subsets lij n, Ij.i, Inlj (expression (25)) are performed again. The final subsets Iq., lj.i and I.ii should contain only one element each; otherwise more than three objects of the sky image should be taken into consideration or quality of the given scanner and telescope should be improved.
November 1988
The celestial meridian / ~
~ /
The celestial equator
/
/,4 _l~b
('i.e. declination
or lon.gitude) or latitude) spring equinoctial point Figure 8. Graphic interpretation of right ascension and declination of a star in the sky; module of the right ascention equals the module of sx, and the module of the declination equals the module of ty. where s, t are weights, and x, y are gravity centers of the recognized circular object.
7. Conclusions
The method is useful only for recognition of objects which are distant more than by the greatest dimension of each of the objects. Shape of each object is assumed to be circular. Sky images are good example satisfying these requirements. For more complex shapes or when we expect other objects to occur inside an object frame, edges should be tracked and then filled to extract the entire object and only that object from input picture [3]. Brightness of a star should be calculated only for the pixels belonging to the object, i.e. for the picture elements that have been tracked and filled. It is possible to catalog automatically all small objects of the sky image that have been previously identified. Small stars that are not cataloged may be referred to those cataloged. Sky objects in motion (e.g. satellites or comets) may be automatically recognized by comparison of coordinates of objects of at least two images of the same sky fragment that has been cataloged previously. Position of a satellite can be determined on the basis of coordinates of the stars that have been recognized and identified. It is possible to take sky images (e.g. photos) automatically by a scanner-telescope device placed 287
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on board the satellite and to transmit parameters of sky objects of unusual interest to an Earth station (satellite images of sky eliminate arduous disturbances and deformations created by atmosphere and make it possible to take pictures of the sky optic spectrum ranges inaccessible from the Earth's surface).
References [1] Danielsson, P.E. and B. Kruse (1979). Distance checking algorithms. Computer Graphics and Image Processing4. [2] Malinowska, K. (1975). Ph.D. Thesis. Institute of Textile, Lodz, Poland.
288
November 1988
[3] Wojcik, Z.M. (1985). A natural approach in image processing and pattern recognition: rotating neighborhood technique, self-adapting threshold, segmentation and shape recognition. Pattern Recognition 18 (5), 29~326. [4] Wojcik, Z.M. (1976). Automatic detection of semiconductor mask defects. Microelectronics and Reliability 15, 585 593. [5] Wojcik, Z.M. (1983). Conclusiveness of natural languages and recognition of images. Cybernetics and Systems 14, 131. [6] Wojcik, Z.M. (1984). An approach to the recognition of contours and line-shaped objects. Computer Vision, Graphics and Image Processing 25, 184--204. [7] Wojcik, Z.M. (1983). Rozpoznawanie obrazow obiektow o ksztaltach owalnych (Recognition of images of oval-shaped objects). Rozprawy Elektrotechniczne (published by Polish Academy of Sciences), 29 (2) 639-662.
November 1988
Quick recognition of circular objects in a black-white picture Zbigniew M. WOJCIK Department o['Computer Science, The Wichita State University, Wichita, KS 67208, USA Received 26 October 1987 Abstract." A method of circular objects recognition is presented that depends on converting input picture into binary image, next on tracing perpendicular chords along the object determining its maximum extension, and then on separation and analysis of a rectangular frame determined by the chords. This process can be performed under the assumption that neighboring objects are sufficiently distant from each other. Brightness, area and gravity center of its original gray-scale contents are calculated inside that rectangular frame. These parameters are used for specification of each separated object. Values of these parameters are used to mark arcs connected to a node into which the object is transformed. The third step of data processing is to compare the identity (automorphism) or similarity (isomorphism) of a graph obtained as the result of a recognition process with a set of reference (template) graphs stored in a memory. The nodes of the recognized image that have the greatest weights are taken into account in the first place in the identification (matching) process. Key words." Segmentation, sky objects, target recognition, detection, quantization, identification, circular objects.
1. Introduction
Star images in sky photos, microscope images of some alloys in metallography, some images used by robots contain circular shapes. The paper presents a method for automatic recognition of such circular objects. Automatic detection of all picture elements that represent the objects in question (e.g. stars in sky photos) is performed in the first step. As the result of the preprocessing, a gray-scale input picture is converted to a binary image. Each picture element p(X, Y) gets the digital value (X, Y)= 1 in case it represents an object in question and the value (X, Y) = 0 otherwise. Disturbances are discarded in the second step. The picture with circular objects is segmented during the third step. Parameters of each separated circular object are estimated automatically in the fourth step: area, coordinates, perimeter, brightness, shape factor, etc. The object is automatically removed from the input binary image after the analysis.
Each separated and estimated circular object is represented by a very simple graph (Figure 1) that consists of a single node and some non-directed arcs linked to the node. The node is marked with the name 'object'. Arcs connected to the node represent attributes (i.e. one-argument functions) of the object and are labeled with names like 'area', 'coordinates', 'perimeter', 'brightness', 'shape factor', etc., together with values of the estimated quantities. Each object gets also weight (importance) that
brightness J
0167-8655/88/$3.50 0 1988, Elsevier Science Publishers B.V. (North-Holland)
Figure 1. The graph of a single circular object. 277
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is equal to the estimated brightness of an object in question in case of a sky image. Recognition of circular objects depends on an automatic transformation of image into its quantitative and qualitative computer representation, usually into a graph or into a set of graphs [7]. Each graph represents circular objects that are present in the image under investigation and that have the greatest weights (importances): each node represents separate object and arcs represent parameters of that object. Mutual distances of the object in question are determined on the basis of the estimated object coordinates. Interrelations (e.g. two-argument relations defined on two objects) are represented in image graph as arcs linking two nodes (Figure 2). Names of these two-argument relations and measured values of their intensities are used as the labels of these arcs. The graph is subjected to the process of identification as a result of which nodes get their proper names (e.g. names of stars) and next some considerable part of the graph may get a general name (e.g. a name of a constellation of stars).
November 1988
The arcs representing absolute coordinates of object (in the picture coordinate system) as well as arcs representing weights, are removed before an indentification process (Figure 3). Comparison process of template graphs stored in a memory with the graph obtained as a recognition process will also be considered in the paper.
2. The method of automatic detection of objects Simple smoothing is carried out in the preparatory processing of input image. Each value v'(X, Y) representing brightness of a picture element p(X, Y) is replaced by a mean brightness v(X, Y) of a circular area (window) O(X, Y): N
In
Z Z w..'.,(x,, Y,) v( x . Y) - " : 1 i: 1 N
/.% n=l
/ a~ea
~cedl2 area A2
co
area A3
C°
Figure 2. G r a p h obtained as a result of a recognition process of an image consisting of three circular objects. 278
(1)
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PATTERN RECOGNITION LETTERS
November 1988
_¢~ V
t
area A3
~
area A2
~
Figure 3. Graph shown in Figure 2 designed for identificationof a recognizedimage. where: I, is the number of elements of the window (area) O(X, Y) having identical weights. These weights w, can be calculated from Eq. (2a) or (2b): w, = exp( - nr2),
(2a)
w, = (q + 1 - r)/(q + 1)
(2b)
where:
r = x/(Xi - )0 2 + (Yi - y)2,
(2c)
q is the radius of the window O(X, Y); q is measured in terms of picture elements (q is an integer); i is an index of element pi(X~, Y~) belonging to the window and having weight w.; n is an index of a subset of the window elements having identical weights; N is a number of various weights of the window elements. According to the formulae (2a) and (2b), the effect of brightness of element p(Xi, V~) on the value v(X, Y) (Eq. (1)) decreases while the distance r of the element p(X/, Y~) from the central element p(X, Y) increases. The usually assumed constant distribution of weights w,: w, = I w, = 0
for p(X i, Y~) e O(X, Y), for p(Xi, Yi)¢O(X, Y)
(3a) (3b)
is not well-justified and a distribution of weights similar to (2a) is observed in the reception fields of animal eye. The mean weighted value vo(X, Y) of brightness is calculated inside a greater window O(X, Y) in the next step. For instance, the five element window can be assumed for the smoothing process, and for the process of calculating the value vo(X, Y) one can accept the nine element window. Pixel p(X, Y) belongs to an object of an unknown image in case the following condition is satisfied:
v(X, Y) > Q(X, Y) = ki
[Wo Vo(X, Y) + v(/)] Wo+ 1
(4)
where: Wo is a weight of the value vo(X, Y): any increase in the value wo means increase in importance of a local brightness on the threshold value Q(X, Y). The wo may be assumed to be equal to 0 in practice (e.g. for gray-scale picture); v(j) is the value of the abscissa of a subsequent local j-minimum of the picture histogram. If the condition (4) is satisfied, the element p(X, Y) gets digital value (X, I1) = 1, and (X, Y) = 0 in the remaining cases:
(x,Y)=
1, 0,
if v(X, Y) > Q(x, Y), ifv(X,Y)
(5)
279
Volume 8, Number 4
PATTERN RECOGNITION LETTERS
Lemma 1. The k i is the following coefficient:
3. The method of automatic removal of isolated disturbances
ki = kx < 1 if vo(X, Y) > v(j),
(6a)
ki = k2 > 1 if vo(X, Y) < v(i).
(6b)
Proof. If the inverse to the (6b) inequality were assumed (i.e. k2 < 1 for vo(X, Y) < v(j), e.g. for the background of objects in question: the background is defined approximately as a subset of picture elements, for which vo(X, Y ) < v(j)), small disturbances generating slightly greater value v(X,Y) would readily result in fulfilling the inequality v(X, Y) > Q(x, Y) for some picture elements representing darker background. The incorrect values (X,Y) = 1 for some of the background elements would be obtained and therefore inequality (6b) is true. Inequality (6a) is proved analogously. [] Hence, utilization of the coefficients k I < I and k 2 > l ensures elimination of arduous, small disturbances and irregularities in shading. In case the values v(]) of abscissae of local histogram minima of picture brightnesses are arranged in the descending order, the brightest objects are detected first (formulae (4)~6)) and the darkest in the last place. If only one binary output image is required (e.g. in case of sky images), it is possible and convenient to assume weight wo (expression (4)) greater than 1 (e.g. Wo = 8 for black-white sky pictures) and the following value Vsr instead of the value v(]) [6]: Vsr =
WsVs+ WnVn+ WxVx Ws -'l'-Wn + Wx
(7)
where: vs is the mean value of brightness of all picture elements; v,, vx are the minimal and maximal values of brightness of picture elements correspondingly; ws, w., Wx are weights of quantities v~, vn and vx respectively. The detected objects are represented by the following subset Fo of the picture P:
Fo = {p(X, Y)~P:
(X, Y) = 1}.
(8a)
The background of the objects detected forms the following subset Fb:
Fb = {p(X, Y)eP: 280
(X, Y) = 0}.
November 1988
(8b)
In case there are very strong (i.e. high-amplitude) but isolated disturbances, and the area of each individual disturbance does not exceed one picture element, it is possible to investigate digital values of the nine-element window O(X, Y) of each picture element. The first step is to read the digital value (X, Y) of the central element p(X, Y) of the assumed window O(X, Y). The next step is to investigate digital values of all other elements of the O(X, Y): only in case there are no other elements in the O(X, Y) having the same digital value as the central element p(X, Y) should the digital value (X, Y) of the central element p(X, Y) be changed to the opposite value. The above method is not good for larger disturbances. Rotating neighborhood technique introduced in [4, 3, 6] is the most effective here: is very fast and does not blur edges. Variance in digital values of rotating neighborhood pixels with respect to window center is calculated. Center of the window remains unchanged, if the minimum variance is found for at least one neighborhood. Otherwise window center gets value of the neighborhood, the best of that which is the most homogenous. In case of binary image, variance in terms of logical values can be calculated very quickly [4].
4. Method of automatic separation of circular objects In order to measure parameters of an individual object (such as area, brightness, perimeter, coordinates, shape factor), the object should be separated first from the remaining part of picture, because otherwise nobody could say what was automatically estimated: a fragment of an object, some objects or no objects? A readout of the digital value (X, Y) = 1 during a linearly ordered analysis of picture elements means that the scanning line has found an object. A chord is traced perpendicularly to the scanning direction from the first picture element of digital value (2, Y) = 1 that has been found (Figure 4). A horizontal, second chord passes across the middle of the first chord (Figure 5(c)). These two chords
Volume8, Number4
PATTERN RECOGNITION LETTERS
November 1988
I Convertion of an input gray scale I picture into binary image; Y = N
Ix-x+ll no
t (X,Y) = 1 7> I yes
Tracing ,a chord along an object in the direction perpendicular to the scanning line; Tracing a chorizontal chord across the middle of the above perpendicular chord; Separation of a square binary image determined by the two chords; Calculation of all the required parameters (e.g. brightness, area, gravity center) of the gray scale picture inside the frame determined by the separated binary image; Clearing of the separated and already analysed binary image frame;
I
-
I yes
no
IY = Y - 11 no
I
yes
Figure 4. An algorithm of automatic analysis of circular objects.
have dimensions DX and D Y correspondingly; they have been measured in connected picture elements having digital values (X, Y) = 1. A square image frame S that contains the circular object is determined automatically. The coordinates X0 and Y0 standing for origin of the image frame S are calculated (Figures 4, 5). The length D of each side of the frame S is equal to the greater dimension of the two DX and D Y plus some pixels (Figure 5). In the case no two circular objects overlap nor the object are very close to each other, the values v(X, Y) of all input image elements that lie in the interior of the object image S can be analyzed (Figure 5) to find particular parameters as brightness, area and coordinates. After the separated image frame S has been analyzed, all pixels of the binary image, obtained as a result of the detection process, and belonging to the frame, get the digital
value 0. In this way each object will be analyzed only once.
5. The method of automatic recognition of circular objects Each circular object that has been separated is represented by a node labeled with the name 'object'. In addition, that node gets some arcs attached to it (Figure 1). The arcs are marked with the names of parameters of the object separated and with the values of the parameters. Let us note, that the frame that has been separated contains an entire object regardless of the position of the object on the picture. Thus, the result of the separation process (i.e. the object frame S) fulfills the basic condition for image representation and therefore it can stand for a feature (e.g. for zero-argument function 'object') of an 281
Volume8, N u m b e r 4
P A T T E R N R E C O G N I T I O N LETTERS
-j
~0
November 1988
Scanning line and ..direction'of scannin~
NNNN
a
x01 XMI
x
YNIi // f f ~
I
1
nnilnlnmiii!
Y0]
iX
i i i i i i i i I i i, i lil~
\"\,~ f ///// X02
x
XM2
x
-y
1111
IYN2
1
~N'~[~s
YS
Yo %a
/
mmmqmmmmmm m~mmmmmmmmm~mm mm Nm)mmMm mmmm
S
-J
-''-_..
v ~v
x
|Y02
~"
~
_ X02
~
1
XS
iiJii~, Il lni il l| |i l in ml i i i l ggm I~p~dini
•
XM2
x
GM
Figure 5. Steps in automatic separation of a circular object in a binary image: (a) a binary image with a circular object and the first scanning line passing across the beginning of the object; (b) vertical chord of the object traced from the first element for which (X, Y) = 1; (c) horizontal chord traced through the row determined by the middle of the vertical chord; (d) the two chords fix a rectangular image of dimensions D X * D Y that separates a circular object; (e) the separated square frame of the parameters: X0 = X S - D / 2 - - D / A ; YO = Y S - D / 2 - D / A ; G N = G M = D(1 + 2/A), where D = m a x ( D X , D Y ) . The coefficient A is selected experimentally, e.g. A = 10. 282
V o l u m e 8, N u m b e r 4
PATTERN RECOGNITION
image [3-6]. The brightness J of the detected and separated circular object can be calculated from the following formula:
LETTERS
N o v e m b e r 1988
I = card{p(X, Y)eP:
K(X, I0
= ~/ I,(X, Y) = 1], i=1
J =
~
(X, Y) J(X, Y)
(9)
p(X. Y)~S
where: J(X, Y) is the intensity of illumination of picture element p(X, Y); the J(X, Y) is represented by the value v(X, Y); XO, YO are coordinates of the origin of the separated object image S; (X, Y)= 1 in case the element p(X, Y) represents an object in question and (X, Y) = 0 in the other cases (see expression (5)). The brightness J calculated from the Eq. (9) is invariant relative to possible positions of the object in question on the picture; therefore, the result of the formula (9) represents a single-argument relation of the separated object [3-7]. Coordinates (x,y) of the detected circular object are calculated as the gravity center of contents of the separated object frame S:
(13)
where: card{...}is the number of all elements of the set {..-}; Ki(X, Y) and Ii(X, Y) are logic functions as shown in Figure 7; m,n are coefficients and can be calculated by means of the least squares method. Some measurements L~, L: ..... Lk ..... Lo of the real and well known length of perimeter L' of an object are carried out in the least squares method. Each measurement k is as follows:
L k = mKk + n Ik.
(14)
The necessary and sufficient condition for the minimum of the following error Eo: D
E/, =
y' (L' - L~):
(15)
k=l
is as follows:
Y. (x, r3g(x,Y)X x = p(x,r)~s
,
(lOa)
J
= 0,
(16a)
(3n E° = 0.
(16b)
- -
c3m
E D
y. (x,Y)J(X,Y) Y Y = p(x,r)~s
(10b) J
The gravity center designates a constant, always the same point of any physical body under investigation, regardless of the position of the body, and therefore, the values (x,y) determined from Eqs. (10a, b) can serve for a one-argument relation of the body (i.e. of the object) in question (the gravity center satisfies the basic condition for image recognition [3-6]). An approximation L of the real length of perimeter of the separated object can be given as follows:
L=mK+nl
(11)
where: K = card{p(X, Y)EP: =
K(X, Y)
~/ K , ( x , y ) = 1},
i=1
(12)
The solution of the two equations (16a, b) gives the two unknown coefficients m, n to be calculated. An approximation A of a real size of the area of the separated object is as follows:
A = a K + h i + cZ
(17)
where: Z = card{p(X, IOeP:
Z(X, Y) = 1}
(18)
where: Z(X, Y) is a logic function as given in Figure 7(c); a, b, c are coefficients calculated by means of the least squares method, as in the case of the coefficients m, n. The subsets K, L Z are independent of all possible displacements of the object in question in the interior of the separated frame S, because the values of the functions K, I and Z are invariant with respect to all possible rotations of any image around 283
Volume 8, Number 4 0
PATTERN RECOGNITION LETTERS 1
2
3
4
November 1988
5
6
7
012345678901234567890123456789012345678901234567890123456789012345678901234567 1 2 3 4 5 6 7 8 9 i0 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 3 4 5 6 7 8 9 50
XXX XXX XX
XX XX
XXX XXXX XXXX
XXX XXXX XXXXX XXXX X
X XXX XXX
XX XXXX XXXX XX
1 ....
a Figure 6. (a) Result of automatic detection of sky image objects.
any pixel p(X, Y) and all picture elements are investigated. Thus, the subsets K, I and Z represent correctly one-argument relations of the object in question [3-6] since the subsets fulfill the basic condition for image representation. A shape factor can be calculated from the formula [2]: L K - -2hA 284
1.
(19)
Since the quantities L and A satisfy the basic condition for image representation processes, the shape factor K also represents a one-argument function of an object in question. The one-argument relation 'circular' results from the method of separation of circular objects presented in Section 4 of the paper and from some assumptions accepted for the method. Attribute like 'circular' is always related to an appropriate recognition algorithm.
Volume 8, Number 4
PATTERN RECOGNITION LETTERS
Intuitively one can easy tell concepts of recognition and identification apart: we recognize a sky image for we see it, but usually only an astronomer is in a position to identify an observed sky image, i.e. he can say what sort of stars are to be found in the sky fragment under investigation. As a result of recognition processes a set of symbols is generated independently of displacements of the recognition system in the space of observation of the image in question [3 6]. A set of graphs produced according to the algorithms and expressions presented in the paper satisfy the basic condition of image representation processes [4~6] and therefore the set of graphs is called a recognition result of circular objects.
= 495 = ii = 13
176
179
173
169
189
131
169
168
- X X- X X -
196
87
138
194
185
177
168
169
179
187
167
187
185
181
149
77
116
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178
148
50
91
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192
171
160
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192
189
209
192
179
176
205
202
178
1 8 9 ,177
179
203
164
171
155
180
173
172
38
51
176
175
186
196
99
104
175
181
198
179
178
188
180
190
195
197
190
185
204
214
173
198
182
151
145
173
188
185
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134
8
2 105
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123
1
0
86
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187
185
79
47
145
171
170
182
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190
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179
196
181
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182
195
178
179
189
190
116
48
138
198
193
119
87
178
184
195
190
179
200
193
197
197
183
195
194
191
207
204
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199
199
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131
6
22 1 6 2
188
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152
5
25
177
211
199
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129
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183
210
211
211
193
200
203
194
J XO YO
J XO YO
= = =
1078 73 ii
- XX X- XX X- - X X -
J XO YO
= 1304 = 2 = 27
--
X
X X -
- X X X X -
J XO YO
X
X
= = =
X X -
2573 72 29
-XX X-- X X X X - - X X X X X - X X X X - -
J XO YO
= = =
921 5 36
- X XX- X X X-
J XO YO
= = =
1810 55 46
-X X-- X X X X- X X XX- - X X - -
b
November 1988
6. The method of automatic identification of sky images It is assumed that there are no two groups of stars (each group consists of three or more stars) with identical mutual (relative) distances and identical brightnesses. We assume that all objects of the image in question stand for stars and that they are specified in a catalog. The catalog may refer only to a certain fragment of the whole sky, but the fragment must involve the sky portion under investigation. It is possible to work out a number of methods of comparison of brightnesses and mutual distances of sky objects with the data included in a catalog of stars. Reading from the catalog the data concerning all these stars whose brightnesses approximate those of the most important objects of the image in question seems to be the most advantageous as the first step. If the set of all catalog stars is denoted with the symbol SAO, then the subset li that corresponds to any object i of the sky image can be written as: li = IkeSAO:
C
Figure 6. (b) Result of automatic separation of sky image objects; (c) values v(X, )I) of the sky objects shown in (b).
J-AJ
I
(20)
where: k is the index of a star in the catalog SAO, and AJ is a maximal possible error of measuring brightness J of a star. The AJ is typical of each device (e.g. a set up of a telescope and a scanner). Having a subset I = (1 ..... i . . . . . A) of the most 285
Volume 8, Number 4
PATTERN R E C O G N I T I O N LETTERS
important stars recognized in the image in question, we obtain the corresponding subset S I of stars separated from the catalog SAO according to the formula (20):
November 1988
selected from the sets Ii and I t (formula (20)) and are passed into the subset Iij: lit = { i e l i , j ~ I t : dlj -- Ad O < Di t < dij + Ado}.
(23)
(21)
S I = U Iv iEl
The Iij consists of the catalog objects lying at a distance Dit close to the distance dij and having bright° nesses approximate to that of the sky image. The Dij is the distance between the two catalog stars i and j; however, coordinates of any star are expressed in the units of right ascension and declination (Figure 8) and therefore these astronomical units are to be reduced to numbers of picture elements of the given optic-to-electric converter. If Ox axis of a picture coordinate system is parallel to the sky equator and Oy axis is parallel to the sky meridian, then:
The set S I contains a lot of stars having mutual distances that differ from those of stars of the recognized image, and therefore, these stars are removed from the S I in the next step. In order to do that the most important object is selected from all the objects of the image in question; the object is denoted with j-index; j e I . The distance dit between the object j and an object i calculated on the basis of the sky image under investigation is: d 0 = x/(xi
- x j ) 2 -.I- (Yl - Yj) 2.
(22)
The maximal possible error of the determination of the dij is equal to Ad,7 for a given device. Stars are
-:1o1111 X
-:l
x
Di j = x/(a(o q _ aj))2 + (d(ai - aj)) 2
I,(x,Y)
(24)
= 1
0 110 1
x
2 /'2(X, Y) -- 1
0 011 1 X
x
-:I
Ka(X, Y) = 1
1
-:T
x
K4(X, Y) = 1 1
111 0 x
x
C*)
2 Ia(X,Y) = 1
:T
1 0 1 1 0
110 it x
x
:l
x
:T 1
x
~(X,Y)
= 1
z(x,Y)
i i i i
X
1
x
10 0 x
x
(b)
C¢)
Figure 7. Graphic interpretation of values I of the following functions: (a) Ki(X, Y); (b) Ii(X, Y); (c) Z(X, Y). 286
= 1
Volume 8, Number 4
PATTERN RECOGNITION LETTERS
where: ai, aj are right ascensions of catalog stars i and j correspondingly; ai, aj are declinations of the catalog stars i and j respectively; a is a coefficient telling how many sides of pixels of a given device are included in one unit of the right ascension; d is a coefficient telling how many sides of picture elements are comprised in one unit of the declination. The distance di. of object i from object n and the distance dr. of object j from object n are also determined; n = i and n = j . Subsets I.i and It. are formed, in the same manner as the subset llj (expression (23)). The product lij. of the subsets lij and It. is calculated:
I~. = Iijc-~lj..
(25a)
The subset lit" consists of catalog indexes of the stars that have brightnesses corresponding to the brightness of the object j that has been recognized in the sky image in question, the stars being situated at the distances Dij and Dr. from objects i and n (placed in the subsets Ii and I.) recognized in the given sky image. Subsets Ij, i and I.i j are formed in the same manner:
Ij.i = l;.~l.i,
(25b)
l.i; = l.ialij.
(25c)
In case each subset: Iij ., It. i, I.i t contains only one element, the objects i, j and n get synonymous indexes of stars from the catalog SAO, with the indexes being elements of the subsets lit., lj.i and I.ij. However, the distance dit between stars i a n d j were not taken into account when forming the subset lit" . Therefore, the subset lit. may contain more than one element. The same is true for subsets It. i and I.i t. If the subsets lit., Ij.i and I.o contain more than one element each, the elements of these subsets should substitute for elements of the corresponding subsets Ij, I., ll; then the procedures of forming the subsets lij, lj., I.i (formula (23)), as well as the subsets lij n, Ij.i, Inlj (expression (25)) are performed again. The final subsets Iq., lj.i and I.ii should contain only one element each; otherwise more than three objects of the sky image should be taken into consideration or quality of the given scanner and telescope should be improved.
November 1988
The celestial meridian / ~
~ /
The celestial equator
/
/,4 _l~b
('i.e. declination
or lon.gitude) or latitude) spring equinoctial point Figure 8. Graphic interpretation of right ascension and declination of a star in the sky; module of the right ascention equals the module of sx, and the module of the declination equals the module of ty. where s, t are weights, and x, y are gravity centers of the recognized circular object.
7. Conclusions
The method is useful only for recognition of objects which are distant more than by the greatest dimension of each of the objects. Shape of each object is assumed to be circular. Sky images are good example satisfying these requirements. For more complex shapes or when we expect other objects to occur inside an object frame, edges should be tracked and then filled to extract the entire object and only that object from input picture [3]. Brightness of a star should be calculated only for the pixels belonging to the object, i.e. for the picture elements that have been tracked and filled. It is possible to catalog automatically all small objects of the sky image that have been previously identified. Small stars that are not cataloged may be referred to those cataloged. Sky objects in motion (e.g. satellites or comets) may be automatically recognized by comparison of coordinates of objects of at least two images of the same sky fragment that has been cataloged previously. Position of a satellite can be determined on the basis of coordinates of the stars that have been recognized and identified. It is possible to take sky images (e.g. photos) automatically by a scanner-telescope device placed 287
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on board the satellite and to transmit parameters of sky objects of unusual interest to an Earth station (satellite images of sky eliminate arduous disturbances and deformations created by atmosphere and make it possible to take pictures of the sky optic spectrum ranges inaccessible from the Earth's surface).
References [1] Danielsson, P.E. and B. Kruse (1979). Distance checking algorithms. Computer Graphics and Image Processing4. [2] Malinowska, K. (1975). Ph.D. Thesis. Institute of Textile, Lodz, Poland.
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[3] Wojcik, Z.M. (1985). A natural approach in image processing and pattern recognition: rotating neighborhood technique, self-adapting threshold, segmentation and shape recognition. Pattern Recognition 18 (5), 29~326. [4] Wojcik, Z.M. (1976). Automatic detection of semiconductor mask defects. Microelectronics and Reliability 15, 585 593. [5] Wojcik, Z.M. (1983). Conclusiveness of natural languages and recognition of images. Cybernetics and Systems 14, 131. [6] Wojcik, Z.M. (1984). An approach to the recognition of contours and line-shaped objects. Computer Vision, Graphics and Image Processing 25, 184--204. [7] Wojcik, Z.M. (1983). Rozpoznawanie obrazow obiektow o ksztaltach owalnych (Recognition of images of oval-shaped objects). Rozprawy Elektrotechniczne (published by Polish Academy of Sciences), 29 (2) 639-662.