Determination of Object Location by Analyzing the Image Blur

Contemporary Engineering Sciences, Vol. 8, 2015, no. 11, 467 - 475
HIKARI Ltd, www.m-hikari.com
http://dx.doi.org/10.12988/ces.2015.52198
Determination of Object Location by
Analyzing the Image Blur
Daniil A. Loktev
Department of Information Systems and Telecommunications
Bauman Moscow State Technical University
Moscow, Russia
Alexey A. Loktev
Moscow Technical University of Communications and Informatics (MTUCI)
8a, Aviamotornaya str., 111024, Moscow, 129337, Russian Federation
Copyright © 2015 Daniil A. Loktev and Alexey A. Loktev. This article is distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
Abstract
Problems of automation of individual modules and entire segments of integrated
monitoring and surveillance systems for the transport infrastructure in areas with
large concentrations of people and everywhere where it necessary to recognize
certain objectives and their parameters are very relevant and timely. In this paper,
the idea of determining the parameters of an object by its blurring is developed. It
is assumed that a blurring is different for different colors, which decomposes a
single image. It is offered as separate element of the study to consider the object
boundary, which determines the sharpness. Placing objects according to the flat
reference scale of blur changes, it can determine the distance from the observer to
each of them.
Keywords: image blur, object parameters, distance to the object
1 Introduction
Nowadays an increasing role in various information systems, automated
control systems and integrated monitoring systems begin to play algorithms and
modules of the determining of static and non-static object’s various characteristics:
its distance from the observer, speed, position coordinates in space [1-3], etc. To
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Daniil A. Loktev and Alexey A. Loktev
solve such problems active systems that emit electromagnetic waves of certain
frequencies: radars, infrared sources, motion sensors are often used, but overall
complication algorithms for registration, processing, transmission and storage of
data, developers are forced to simplify some elements of technical support to
reduce the final cost of the system and to simplify the procedure for obtaining
some basic information on the investigated (recognizable) object [4-10]. One of
the directions of such simplifications is the refusal to use, in addition to cameras,
coupled with them detection devices (radar, various sensors). If this is an attempt
to create such algorithms that would help to get all necessary information about
the object only by its image or series of images [11-13].
To obtain the images using conventional video detectors, video cameras, which
can generate a graphic image of a high-definition view of all available on a photo
or video colors. The main characteristics of the objects included in the image, are
the coordinates and velocity at any given time. Form of an object of interest in the
works of most authors is constant, although this fact depends significantly on the
path of movement of the object and the angle of its playback by the video detector.
Therefore, in general, cannot be considered permanent form of the object, as well
as its geometrical dimensions, so in this paper, along with the image of the object
the concept the image of its boundary on which can be easier to identify such
image parameters as sharpness and blur of individual fragments is introduced. The
feature of the proposed algorithms and techniques is the transition from the image
parameters to the parameters of the moving object.
There are several approaches to determine the characteristics of objects that
can move: stereo vision, i.e. the presence of several photo detectors; definition for
a given motion blur of a video camera; focus adjustment of the detector; definition
of the blur for different colors within the image of the object. Each method has its
advantages and disadvantages associated with the technical and programmatic
possibilities of the implementation of individual procedures.
In this paper we develop a method of determining the parameters of static or moving
object, it is based on an algorithm to process one or a series of images obtained with a
certain time interval. Firstly, the degree of blur in several ways, in order to evaluate
their accuracy and to verify algorithm is measured, then distance to the object,
depending on its degree of blur is calibrated and the calibration can be performed both
in manual and automatic mode, according to the methods of processing and object type.
2 Problem Statement
From a variety of colors in the image to identify main colors that would cover the
entire available spectrum is offered. Since each of them corresponds to a specific
wavelength, and, respectively, the frequency which varies according to the
subject's movement Doppler equation:
w=w0(1±u/c)
(1)
where w0 - frequency with which the source emits waves; с - velocity of wave
propagation in the environment; u - speed of the receiver relative to the environment.
Determination of object location by analyzing the image blur
469
Fig. 1: Light spectrum.
Light spectrum is decomposed into the following colors, which correspond to
different wavelengths: 380 - 470 nm - purple, blue; 500 - 560 nm – green; 560 590 nm – yellow, orange; 590 - 760 nm - red (Fig. 1).
For "null" (minimum) blur to take blur of pixels of green "middle" color is
offered, with blue and red colors blur will be closer to the maximum (Fig.2).
Fig. 2: Focusing RGB-rays.
The eye sees the image as a set of three colors: red, green and blue (Fig.3).
3 Object Distance Determination
Distance to the object represented in the image is proposed to determine, taking
into account the blur diameter, the diameter and focal length of the lens for
medium and extreme colors of the considered range, green and red, respectively,
when receiving images in normal lighting conditions.
In the general case, without using of a difference of blur diameters for different
colors, the distance from the detector to the object is provided, if the distance to
the object in focus is known, and will be determined by the following equation:
d=
Dpf
,
(D + s ) f - s Чp
(2)
where d - the distance from the detector to the object, f - focal length, p - the
distance to the object located at the focal point, D - diameter of the lens, σ diameter of the spot blur (it is considered that the point blur occurs equally in all
directions).
Boundaries of the blur depend on the number of aperture f / D of the used
camera: the higher the aperture, the less light reaches the camera's sensor and the
area of a circle varies as the square of its radius [1]. To the upper limit of the blur
did not go to infinity long-focus lenses should be used.
Blur softens noise on those fragments of the figure, in which there are abrupt
changes of color, i.e. softens color transitions by averaging the values of sharp
boundaries with neighboring pixels.
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Daniil A. Loktev and Alexey A. Loktev
To find the accuracy of determining the distance to an object by its blurring it
need to know the value of the diffraction blur of the entire image, which depends
on the pixel size on this camera. Calculation of the difference of colors can
eliminate the impact of general blurring of the resulting technical reasons (quality
of the camera or weather conditions).
In general, for two colors (Fig. 3) will be:
1
1
1
+
=
d V 1 F1
(3)
1
1
1
+
=
d V 2 F2
(4)
s 2 V 2- R
=
D
V2
(5)
s 1 V 1- R
=
D
V1
(6)
where σ1 and σ2 - blur diameters of the first and second colors, respectively; F1
and F2 - focal length of a lens used for the first and second colors, respectively, D
- diameter of the camera lens.
V1
V2
d
R
D
σ2
L
σ1
S
Fig. 3. The general case for any two colors.
For a moving object the decomposition of the image blur by color is shown in Fig. 4.
Solving this system of equations (3, 4, 5, 6) we obtain an expression for
determining the distance to the selected object:
d
( 1   2 )  F1 F 2
,
( 1  F1   2  F 2)  ( F 2  F1)  D
(7)
For red and green colors (Fig. 5) and the fact that green blur as zero, the
expression for determining the distance from (7) to the selected object will look
like:
Determination of object location by analyzing the image blur
d
471
 r  F r F g
,
( r  F r ( F 
g F)r D
(8)
where σr - blur diameter of the object for red color, Fr and Fg - focal length lens of the
camera for red and green colors, respectively, D - diameter of the lens of the camera.
Fig. 4. Decomposition of an image on RGB-colors.
Vr
d
R
σr
D
L
S
Fig. 5. Focusing green, and red colors.
Focal lengths of the used lens for the different colors can be found by
experience: for example, Nagata found experimentally focal lengths eye
"jumping" spiders for the red and green colors [2].
The main problem is finding of image blur estimation.
Object boundaries blur diameter in mm [3] is equal to:
σr=∆xr∙Sx,
(9)
where Δxr – the blur diameter of the object, measured in pixels, Sx - pixel size
of CCD camera used [4].
Blur usually take as Gaussian distribution or uniform distribution [5]. There are
several ways to calculate the blur estimation. The most popular are: the method
proposed J.H. Elder and S.W. Zucker, and the method proposed by H. Hu and G.
de Haan.
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Daniil A. Loktev and Alexey A. Loktev
In the method proposed by Elder and Zucker [6], boundaries of blurring detect
technically with a scaling of the local area and reliable scale are used to calculate
correctly the boundaries suitable for evaluation of the blur. Center of the boundary
is the point where the gradient is the largest. We find this point, using a
controllable Gaussian filter of the first derivative, and this signal in the direction
of the first derivative reaches its maximum where its derivative is zero. To find
the size of the blur, we can take the distance between the highest and lowest
gradients of the first derivative. To reduce noise thresholds on the amplitude of
the first and the second derivative with values equal to standard deviations of
Gaussian filter derivative are applied. The process is repeated several times with
different values for Gaussian filters of derivatives because our images often have
multiple meanings of blur. Thus, the size of the blur is calculated when there is a
motion in the direction along the boundary of the first derivative of the gradient,
while the first derivative becomes equal to zero. Blurring parameter [7] may be
represented in graphical form, depending on the constituent color, i.e. on the
wavelength. It can also plot the dependence between the blur and boundaries of
color transition of the object, which is an independent element of the study, after
which the resulting points describing the blurring of different colors can be built
according to a certain the blur law [8] and determine the distance to an object on
the proposed "reference" curve.
In approach of H. Hu и G. de Haan [9], they used twice the blur of the signal
that will determine with known Gaussian kernels σa and σb to determine the local
blur σ of the signal. For this signal the convolution with a Gaussian kernel with
different standard deviations σa and σb, which leads to two signals ba(x) and bb(x),
is used. To make the blur is independent from the amplitude and the offset ratio
r(x) is calculated:
r(x)=(b(x)-ba(x))/(ba(x)-bb(x))
(10)
The ratio of the difference reaches its maximum when the difference between
b(x) function and reblurred function is big. It will happen at the points where the
signal amplitude changes significantly, i.e. points, where the blur had the greatest
influence. In this local signal at a point where r(x) reaches the maximum, will be
defined by σ of the entire region. As it happens, because we assume that the local
spot is the same for this area. Therefore, we will apply the filter with the
maximum specified window, and we obtain rmax(x). If σa∙σb> σ, then, using the
values of σa, σb and rmax(x) we can rewrite the equation for our evaluation of the
blur σ:
s≈sasb/((sb-sa)rmax(x)+sb)
(11)
The failure of the condition σa∙σb>σ leads to an incorrect estimate of blur σ
[10].
The perfect boundary corresponds to a modified Heaviside function, which
shows the presence of an object abruptly (Fig. 6).
Determination of object location by analyzing the image blur
color
color
object
object
backgr
backgr
ound
o
x,pix
xраз
473
xраз x,pix
Fig. 6. An ideal edge and washed with Gaussianм1distribution of м2
the border.
In this connection, it is sufficient to say that in the real world is not practically
observed, and on the microlevel there is always a boundary layer whose thickness
depends on the purity of the object of surface treatment and the conditions of
reflection and refraction of light waves on the interfaces. For the simulation of
object boundaries in real conditions to use a Gaussian distribution with a double
convex-concave and an inflection point (point of the equality to zero of the second
derivative of the color function on the coordinate) is proposed [11, 12]; depending
on the definition, the width of the interval between two horizontal tangents will vary
in various ranges [13]. Presenting this value in the form of a flat scale, you can
calculate the distance from the observer to the object. The proposed scale has
reference points for objects of a certain color and a certain distance to these points.
4 Conclusion
The developed method of definition the distance to the object can be used for
determining of their parameters using active and passive measurements and
algorithms for predicting their behavior and following 3D modeling of objects.
The proposed in this paper method, after additional testing will be integrated into
a developed complex system of video monitoring, including control blocks,
recognition and identification, tracking of selected targets, as well as determining
of the parameters of their status and movement, which should allow to reduce the
influence of a operator on processes of production, transmission, processing and
storage of information which is difficult to formalization.
Acknowledgements. The reported study was supported by Russian Science
Foundation (research project No. 14-49-00079).
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Received: March 20, 2015; Published: April 27, 2015