=Paper=
{{Paper
|id=Vol-2534/47_poster_paper
|storemode=property
|title=Small Objects Detection in Two-Color Images with Spatially Non-Stationary Background
|pdfUrl=https://ceur-ws.org/Vol-2534/47_poster_paper.pdf
|volume=Vol-2534
|authors=Valery P. Kosykh,Gennady I. Gromilin,Nikolay S. Yakovenko
}}
==Small Objects Detection in Two-Color Images with Spatially Non-Stationary Background==
https://ceur-ws.org/Vol-2534/47_poster_paper.pdf
Small Objects Detection in Two-Color Images with
Spatially Non-Stationary Background
Valery P. Kosykh1,2, Gennady I. Gromilin1; Nikolay S. Yakovenko1
1
Institute of Automation and Electrometry SB RAS, Novosibirsk, Russia, kosych@iae.nsk.su
2
Novosibirsk State University, Novosibirsk, Russia
Abstract. A method for improving the reliability of detecting low-contrast small-sized
objects in two-color images is considered by pre-suppressing their spatial-non-stationary
background. Suppression is carried out by constructing a locally stationary background
model using an optimal linear prediction. It is shown how the joint processing of images
pair obtained in different spectral ranges affects the detection probability for a given false
alarm probability
Keywords: low-contrast small-sized objects detection; spatially non-stationary
background; two-color images; optimal linear prediction.
1 Introduction
One of the frequently formulated requirements in the problem of early potentially dangerous objects detection and
processes on the Earth's surface from images obtained by equipment placed on various media is the need to highlight
weak anomalies in the recorded parameter (brightness, color intensity, wavelength, etc.) comparable in size to the size
of the recording optical system the point scattering function (PSF). If the image background component is spatially
stationary, the problem of finding such anomalies can be solved by matched image filtering, taking into account the
background correlation properties and the shape of the optical system scattering spot. However, if the image
background component does not obey the spatially stationary model, matched filtering will not provide an efficient
anomaly identification. In this case, when small-sized, low-contrast anomalies are detected, preliminary the spatially
unsteady background component suppression is applied. Let the analyzed image be represented in the form
π·(π, π) = πΉ(π, π) + π΄ Β· π(π β π0 , π β π0 ) + π(π, π), (1)
where πΉ(π, π) is an image background component, π(π β π0 , π β π0 ) β object image with amplitude π΄ centered in point
(π0 , π0 ), π(π, π) β random uncorrelated recording noise. Then, knowing the background component model πΉΜ (π, π), it is
advisable to search for objects in the modified image
Μ (π, π) = πΉ(π, π) + π΄ Β· π(π β π0 , π β π0 ) + π(π, π) β πΉΜ (π, π) = π΄ Β· π(π β π0 , π β π0 ) + π(π, π).
π· (2)
Here π(π, π) = πΉ(π, π) β πΉΜ (π, π) + π(π, π) is the disturbance, consisting the residual part of the background, the
spatial correlation of which is significantly weakened if the model is chosen successfully, and the original image
noise component.
Very effective means of suppression is inter-frame processing, when the model of the background component of
the analyzed frame is estimated from previously obtained images of the same area [1-3]. If the previous image is
unavailable, the suppression is based on background model prediction on the current image fragment in the
neighborhood suspected anomalies. This work is devoted to the study the possibility of constructing a model using
the optimal linear prediction (OLP) [4] and the application of this approach when analyzing images pair of the same
scene obtained in different spectral ranges.
2 Building a background model using OLP
Based on the optimal linear prediction, a locally stationary background model at the point (π, π) is a linear
combination of image samples in the this point neighborhood π
πΉ(π β² , π β² ) = βπ,πβπ π·(π β π β² , π β π β² ) β(π, π) . (3)
Copyright Β© 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0
International (CC BY 4.0).
Here β(π, π) is the set of weighting coefficients, which are defined as
Μ = ππππππ {βπβ²,πβ²βΞ©[π·(πβ², πβ²)βπ‘π ππβ²,πβ² ]2 },
π‘ (4)
ππβ²,πβ² is the vector consisting of lexicographically ordered samples of the point (πβ², πβ²) neighborhood π, π‘ is similarly
ordered weighting coefficients vector, and Ξ© is the background stationarity region. To exclude the influence of the
object, which may appear at the point (πβ², πβ²), this point itself and its nearest neighbors are not included in the
neighborhood π. It is quite obvious that the worst background suppression will be in the image areas where the
background spatial stationarity is violated, in particular, in the region of the brightness sharp changes. Therefore, the
stationary region Ξ© cannot be too large.
3 Joint image processing
The proposed method for detecting small objects in two-color images consists in a images joint analysis of two
spectral ranges pre-modified according to expression (2). It is assumed that the object spectral range overlaps both
analyzed ranges. The basic structural image features suppression of the in each channel with its local models leads to
decreasing interchannel correlation of the background component, while maintaining the correlation between the
images of objects. With joint processing, due to this, we can expect a decrease in the false alarm probability, or, with
a given false alarm probability, an increase in the detection probability. The most effective way of joint processing
would be to build a common locally stationary background model similar to (4), in which ππβ²,πβ² contains appropriately
ordered points of two images. The problem is that with a twofold increasing weight coefficients vector π‘, the
computational cost of its estimating increases many times. Therefore, for each color, its own background model was
built independently, local maxima were selected that exceeded the threshold providing a given false alarm
probability, and then these maxima were combined. The upper limit of the false alarm probability with this processing
method will be equal to
πππ = π1ππ + π2ππ β 2π1ππ π2ππ β π1ππ + π2ππ , (5)
(this approximate equality is true for π1ππ , π2ππ βͺ 1, which is usually satisfied) and it will be achieved in the
absence of correlation between the background components of the images. Otherwise, the false alarm probability will
be lower.
4 Numerical experiment
The increase in detection reliability is confirmed by a numerical experiment performed with multispectral images
(size 1024 Γ 1024, spectral ranges: 1 ΜΆ 0.45 Γ· 0.515, 2 ΜΆ 0.525 Γ· 0.605, 3 ΜΆ 0.63 Γ· 0.69, 4 ΜΆ 0.775 Γ· 0.90 and 5 ΜΆ 1.55 Γ·
1.75 ΞΌm) obtained by the Landsat 7 satellite [5]. In accordance with expression (1), small-sized objects with an
average amplitude equal to 1.5 standard deviations (StD) of the background and uncorrelated noise with StD of 0.1
StD were additionally applied to the images pair of different spectral ranges. Object detection was carried out after
filtering the images by adaptive filters, implemented according to (3) and (4), by thresholding, which provides a given
false alarm probability πππ . The first detection option consisted of selecting a threshold separately for each image and
combining points that exceeded the threshold into one image. The second was to select a threshold and detect points
that exceeded the threshold in the sum of the filtered images. Next, the detection probabilities in each image (P1 and
P2), in the summarized image PΞ£, and the detecting probability Por obtained as a result of combining the points
selected in each image were estimated.
The processing results for a given false alarm probability πππ = 0.005 are illustrated in the table below. The
column R of the table shows the correlation coefficients between the images in the selected channels, and the
columns Kn show the ratio of the standard deviation of residual noise (background + noise after filtering) to the
standard deviation of noise in the original image. These numbers show that the use of a locally stationary model can
reduce the average background level to a value comparable to the noise level in the original images. In parentheses in
columns P1 and P2 are given the detection probabilities for π1ππ = π2ππ = πππ /2, which, when combined according
to (5), provides an upper limit of the false alarm probability equal to πππ .
It follows from the table, first, that image filtering, based on the formation of a local background model, reduces
the background component standard deviation to a value comparable to the noise standard deviation. Secondly, the
images joint processing of different spectral ranges reduces the false alarm probability. Thirdly, the smaller the cross-
correlation between the background component of the images, the less likely the false alarm.. Fourth, with a fixed
false alarm probability, joint processing increases the detecting probability objects. Figures 1,2 illustrate the process
and of a two-color image joint processing result at πππ = 0.005 (fragments of images with a size of 256 Γ 256 pixels
are shown).
Table. Joint processing of different spectral ranges image pairs results
Channels R Pfa P1 Kn1 P2 Kn2 Por PΞ£ KnΞ£
1-2 0.91 0.005 0.95(0.88) 1.69 0.89(0.80) 1.81 0.95 0.96 1.48
1-3 0.92 0.005 0.95(0.88) 1.69 0.92(0.85) 1.76 0.95 0.98 1.48
1-4 -0.49 0.005 0.95(0.88) 1.69 0.99(0.97) 1.56 1.00 1.00 1.05
1-5 0.45 0.005 0.95(0.88) 1.69 1.00(0.99) 1.46 1.00 0.99 1.28
2-3 0.85 0.005 0.89(0.80) 1.81 0.92(0.85) 1.76 0.93 0.94 1.51
2-4 -0.22 0.005 0.89(0.80) 1.81 0.99(0.97) 1.56 1.00 1.00 1.16
2-5 0.47 0.005 0.89(0.80) 1.81 1.00(0.99) 1.46 0.99 0.99 1.33
3-4 -0.42 0.005 0.92(0.85) 1.76 0.99(0.97) 1.56 1.00 1.00 1.06
3-5 0.65 0.005 0.92(0.85) 1.76 1.00(0.99) 1.46 0.99 0.99 1.32
4-5 0.25 0.005 0.99(0.97) 1.56 1.00(0.99) 1.46 1.00 1.00 1.04
In Figures 1,2 images with indexes a are fragments of 3-rd (0.63 Γ· 0.69 ΞΌm) and 4-th (0.775 Γ· 0.90 ΞΌm) channels
of source multispectral image with added small objects (figure 1,d). Objects size is determined by recording device
point spread function and approximately equal to 1.5 Γ· 2 pixels. Images with indexes b in both figures are obtained
after adaptive filtering images a, implemented according to (3) and (4), and with indexes c β after thresholding with
level, determined by πππ = 0.005. Figure 2, d shows objects, detected after conjunction marks of figures 1, c and 2, c.
a b c d
Figure 1. Two-color images joint processing (a-c: channel 3).
a b c d
Figure 2. Two-color image joint processing (a-c: channel 4)
4 Conclusion
The proposed method for approximating a spatially unsteady background by a locally stationary model based on
an optimal linear prediction reduces the background level in images containing small sized low-contrast objects to a
value comparable to the noise level. Subsequent detected signals joint processing in different channels of a two-color
image allows, with a fixed false alarm probability, to increase the objects detection probability.
Acknowledgements. This research is supported by the Ministry of Science and Higher Education of the Russian
Federation (State Registration No ΠΠΠΠ-Π18-118051190053-8).
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