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THE METHOD OF ASSOCIATED SOLID IMAGE IN THE THEORY OF
GROUP POINT OBJECTS IMAGE RECOGNITION1
A.V. Krevetskiy 2
2
Mari State Technical University,
424000, Yoshkar-Ola, Lenin Sq, 3, (8362)455412, [email protected]
The analysis of spectral and statistical characteristics of group point objects image has
been made. The optimal algorithm of group point objects recognition by agreed spatial
filtration of the observed defocused images was produced. The ways of redundant
reduction for the observed image description which are based on the references partial
sampling passed through whitewashed section of the pointed scene and their special
encoding are suggested.
Introduction
The artificial origin objects which in their size
are close to the sensor resolution cell as well
as their groups are often of great interest for
acoustic radar imaging of orientation,
navigation and aircraft control,
remote
sensing and for other fields. Such objects we
will term point object(PO) and group point
objects (GPO) respectively. The lack of PO
images form and the impossibility of
brightness image noises spatial smoothing
should be considered size-dependant factors
which prevent their detection, recognition and
data estimate. The additional preventing
factors in the group point objects processing
are point mark coordinate noise from the aim,
impulse noise as false marks and missing
signals as well as a priori uncertainty in regard
to geometrical transformation parameters.
The current situation of these factors
overcoming in processing location signals and
PO and GPO images can be briefly described as
follows. The most considerable results were
obtained in the field of distributed large-size
objects (for example geographical) analysis,
detached low-sized and point objects detection,
as well as in the field of navigational problem
solving (recognition and overlapping of
images) according to the stationary GPO which
is represented by a set of separate point marks
with a fixed relative position geometry and high
contrast range against background while
reprocessing the optoradioelectronic system
location signals Whereas, the problem analysis
of radar GPO with nonstationary configuration
which can be of different models and have
different problem range (detection and
recognition) and are of great practical interest
still remain underworked.
Besides, up-to-date radio systems allow to
obtain not only 2D but also 3D images of the
observed objects including GPO. New 3D
representations, in theory, are more
informative, however to obtain this additional
information it is necessary to work out new
adequate mathematical models of the signals
and to produce optimal and quasi-optimal
algorithms of their processing.
The detection and recognition tasks of such
GPO are often conclusive in the scene
processing range, formed by radar, thermal
imaging and visual sensors. So, in this
situation GPO processing automatization
based on more reliable methods in case of
complicated interference can be an urgent
scientific problem. This work is devoted to its
solution.
_______________________________________________________________________
1
This work was supported by the Russian Foundation for Basic Research (Project no. 07-01-00058-а)
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Problem definition
The result of detached point objects detection
in the observed image frame can be
represented by the following model:
K(x,y)  SC(x,y)  S N (x,y)  Sэт x, y   Sш x, y  ,
where
S C ( x, y )   J Cj ( x  x j  x j , y  y j  y j ) –
j
PO field, J Cj – registered brightness of the
corresponding object , possessing noise
component with normally centered probability
distribution law;
S N ( x, y )   J Nj ( x  x j , y  y j )
j
– random uniform field of the false marks
K
with the density   CP
(here K CP X Y
average PO on the image of X  Y elements
size) and brightness J N , distributed according
to the uniform law ; j – the number of PO in
the frame, x, y  – coordinate noise,
S эт x, y  – standard component of the point
scene, S ш x, y  – image noise component,
distinguishing it from the standard.
The task is to produce GPO detection,
recognition and data estimate algorithms,
aimed at decision making in real and close to it
time scale in case of a priori uncertainty in
regard to observation conditions.
Task solution
The spectral analysis of the observed point
scenes showed that the image noise component
S ш x, y  is not white noise. As there are no
zero references in the amplitude spectrum of
the image noise component then the optimal
recognition device based on the Bayesian
estimate should contain whitewashing filter, a
number of spatial filters agreed with standard
reference points images passed through
whitewashing filters, the solver selecting a
filter with the weighted peak response.
In this work the scheme of the device which
performs the quasi-optimal processing of the
point scene is presented taking into account
the variance of the described device working
algorithm to the image rotation and its high
work content. In this device the empirical
impulse response is approximated by potential
function and only a small part of the image
references is used for decision making.
When using the terminology of the potential
function method the work of the quasi
whitewashing filter is reduced to cumulative
potential field formation (potential image)
N
N x    J n  h pf x  xn , y  y n |   ,
n 1
where
h pf x |  
–
potential
function,
x  ( x, y ) . The form of the cumulative field in
the vicinity of a point is known to be
connected with relative position of its
neighbors i.e. with GPO form [1-3].
All data set of the cumulative field in the
analyzed frame turns out to be redundant from
the view point of GPO unique form
description [3]. Thats why to increase
calculating efficiency of the similarity
criterion estimation of the GPO images it is
reasonable to use restricted set of references
–
cumulative
field
N  v0 , v1 ,..., vk 1 
sections N (x) . Cylindrical cross sections (field
N (x) data in circle of the set radius r with the
center in the initial point q n of the field

 N x , при x  arg  x  x n 2   y  y n 2  r 2
N x   
0, if not.


and for spatially compact GPO with the
nonstationary configuration - the references
located on the equipotential line are offered to
use for image rotation invariance
To retain coordinate data every l -th reference
N x l  of the cumulative field section is set by
the complex number (vector) vl , where the
module corresponds to cumulative field value
N x l  , and the argument  l – towards the
center of the secant circle:
vl  N x l expil ,
 l  arctg( y  y l / x  xl ) , l  0,1,...k  1 .
In case of equipotential line usage the level
line is approximated by the polygon the faces
of which are encoded by the complex number.
The module is characterized by the face
length, and the argument by its angular
attitude.
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The complex character of potential field
references encoding allows to consider its
sections as associated solid image (АSI),
which is specified by a number of elementary
vectors, i.e. vector- contour. As a result of the
observed point scene reflecting into a set of
ASI N m x 1, M the set of observed vector-
contours N m 1,M , N m   m0 ,  m1 ,...,  L1  is
formed.
The pulse noise in the form of some essential
marks omission, false mark availability and
coordinate noise distort field N (x) shape, and
respectively references of the field  mi – of the
elementary vectors of the contour N m . The
distortions of the vector- contours shape are
represented by the additive model of the
contour noises:
N n  Г n d n ,  n 0   Ε n   nl 0,k 1   nl   nl 0,k 1 ,
where Ε n – a noise vector-contour,  0 –
angular deviation of the standard and observed
images, d n – circular shift of the contour
initial point , Гd ,  0    l  d  exp i 0 l 0,k 1 .
The rule of the recognition for contours
represented in this way which is optimal
according to the minimum-distance criterion in
the feature space is well known [2] and comes
to the module calculation of the scalar product
of the standard and observed vector-contours:


N, Г n d  
H  arg max max
 , n  1,..., N ,
Гn
n
 d

L 1
where N, Г n     j  nj ,
*
–
complex
j 0
conjugation symbol. The argument of the
scalar product simultaneously gives the
angular attitude estimate of the GPO.
This algorithm is invariant to the image shift
and turn, that together with vector-contour
small size provides for their high efficiency in
case of a priori invalidity in regard to
observation angle.
The device, implementing the received quasioptimal GPO recognition algorithm has the
structure
including
common
quasiwhitewashing section, reference selector, the
set of the agreed contour filters with module
formers and maximum choice device, a solver,
which decides what filter with the weighted
peak response to chose.
The main results of the received algorithms
analysis were the GPO recognition validity
estimate for different coordinate and impulse
noises, as well as different similarity criterion
of the reference point shape.
In addition there are characteristics for the
most well known noise-eliminating algorithms
of the GPO recognition.
Conclusion
As it follows from the obtained characteristics,
the best algorithm according to the GPO
recognition validity estimate criterion is the
one based on the spatial agreed filtration, and
in the class of the algorithms with real
operation speed for complete a priori invalidity
in regard to observation angle – quasi-optimal
algorithm based on the ASI form recognition.
The algorithm of the GPO recognition by ASI
form is three times as better as the calculating
efficiency of the optimal algorithm for
insignificant loss in identification reliability.
This defines the utility of its usage in the
complete a priori invalidity in regard to GPO
angular attitude.
The ASI formation based on the equipotential
lines together with the recognition task
provides for the solution of the spatial
localization and GPO resolution task.
The ASI recognition based on the cylindrical
section can be considered as GPO separate
point objects identification.
The considerable decrease of the tested
hypotheses number by the optimal algorithm
for the well-known image orientation defines
its utility usage when the GPO recognition
system works in the tracing mode.
References
1. A.V. Krevetskiy. The recognition of the image set
by the multitude of the typical points on the image plane
/ Avtometriya, 1999, №2. – p.28-36.
2. Introduction to the contour analysis and its
application in image and signal processing/ Ya.A.
Furman, A.V. Krevetskiy, A.K. Peredreev, and others.;
Edited by Ya.A. Furman . – М.: Fizmatlit, 2002.–592 p.
3. A.V. Krevetskiy., Chesnokov S.Е. The encoding and
recognition of the multitude point object image based on
the physical field models//Avtometriya,2002.–№3.–
p.80–89.