=Paper=
{{Paper
|id=Vol-2608/paper77
|storemode=property
|title=Image structural classification technologies based on statistical analysis of descriptions in the form of bit descriptor set
|pdfUrl=https://ceur-ws.org/Vol-2608/paper77.pdf
|volume=Vol-2608
|authors=Volodymyr Gorokhovatskyi,Svitlana Gadetska,Natalia Stiahlyk
|dblpUrl=https://dblp.org/rec/conf/cmis/GorokhovatskyiG20
}}
==Image structural classification technologies based on statistical analysis of descriptions in the form of bit descriptor set==
https://ceur-ws.org/Vol-2608/paper77.pdf
Image structural classification technologies based on
statistical analysis of descriptions in the form of bit
descriptor set
Volodymyr Gorokhovatskyi1[0000-0002-7839-6223], Svitlana Gadetska2[0000-0002-9125-2363],
Natalia Stiahlyk3[0000-0002-0573-3508]
1
Kharkiv National University of Radio Electronics, Nauka Avenue 14, Kharkiv, 61166,
Ukraine
gorohovatsky.vl@gmail.com
2
Kharkiv National Automobile and Highway University, Yaroslava Mudrogo str., 25, Kharkiv,
61002, Ukraine
svgadetska@ukr.net
3
Kharkiv Educational and Research Institute of the University of Banking, Peremogy Avenue
55, Kharkіv, 61174, Ukraine
natastyaglick@gmail.com
Abstract. The problem of image recognition in computer vision systems is con-
sidered. We offer technologies for classifying visual objects using a statistical
center based on a structural description of the image as a set of key point de-
scriptors. The use of statistics for the bits of the description data helps to in-
crease performance while providing sufficient classification performance. Re-
sults of experimental modeling and peculiarities of implementation of the de-
veloped approaches are discussed.
Keywords: computer vision, image classification, key point, descriptor, statis-
tical center, nonparametric statistics, performance, classification results
1 Introduction
In today's computer vision systems, the use of data processing technology has
become widespread, providing information about recognized visual objects as set of
key points (KPs) of 100-1,500 pixels [1]. At the same time, each point reflects the
properties of the image in the neighborhood of its coordinates and is described by a
vector-descriptor with dimensions in 64… 512 components [2]. Due to the large
volumes of visual data flows, there is an urgent need to use the mining apparatus to
identify the most essential regularities in the content of the description of the visual
objects in order to reduce computational costs while ensuring effective classification.
Considering the structure of the analyzed data, which contains numerous set of
identical elements, it is promising to use the apparatus of mathematical statistics. Its
tools are able to reveal the deep informational properties of descriptions, which are
necessary for effective recognition of images [2-5].
Copyright © 2020 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
The aim of the paper is to study the technologies of statistical analysis and
nonparametric methods for the formation of innovative feature space, which provides
effective classification of images by their structural description.
The tasks of the paper are the construction of mathematical models for the
transformation of descriptions and the calculation of relevance in the synthesized
space of features, the implementation of software modeling to evaluate the
effectiveness of the developed modifications.
2 Formal problem statement
Traditionally, the system of structural pattern recognition R V , T , U involves
three main components [1]: V – used method (comparison with the etalon in the
feature space), T – set of features used in training and recognition (set of descriptors
of KPs), U – set of recognized situations (set of classes given by samples). One of
the particular cases R is a "one-on-one" classification, when only one class is
identified compared to others, that is U 0,1 .
In our work, within the framework of recognition technology, effective
modifications for features T and related method V have been proposed. If it is
reliable assumption that the elements of description create the concentrated cluster
structures, then it is possible to build a classification based on the cluster
characteristics for the description data [6]. From the point of view of processing speed
the most effective situation is when only cluster is created on a dataset and its
properties are given by the statistical center [8]. The analysis and purposeful
processing of the center proposed in the paper significantly increase the rate of
performance.
The second area of research is the direct application of nonparametric statistics
methods to the set of the bit description, which together with the acceleration of
processing considers the peculiarities of the entire statistical picture of the data
description.
3 Literature review
Detecting of deep regularities in the set of numerical data is a powerful tool for the
robust distinguishing of dataset by their quantitative characteristics in the
classification process.
Recent studies in the field of image analysis and processing have developed in the
aspect of quantitative analysis regarding the structure of the analyzed data [7-11].
According to specific applications, authors of the contemporary research continue
to offer effective measures to determine the similarity of object descriptions that are
calculated and analyzed with the help of the key point descriptor sets obtained by
detectors [8-14].
Particular attention is focused on the parameters of the proposed method
performance [16-20]. Based on this, it is essential to use spatial analysis and
processing of descriptor values in the form of a block system model, which makes it
possible to statistically summarize the information and accelerate the implementation
of classification procedures [4, 8].
Powerful statistical analysis tools in the practice of computer vision are
nonparametric statistics methods that do not rely on information about type of
distribution [4-6]. It seems natural to use them to analyze the properties of a random
vector system, which in this case acts as a model for the analyzed object description.
The essence of the BRISK detector for determining the KPs of the image and the
procedures of comparison of descriptors are analyzed in [19-22]. The possible ways
of forming the description centers are discussed in [2, 3], moreover, modifications of
the space of KP descriptors are considered in [8, 25]. Studies related to the use of
structural descriptions when processing video streams are contained in the monograph
section [26].
Reference to the software used in modeling the developed methods is given in [27].
4 Analysis and construction of feature space
Let the vector space of binary vectors of dimension n defines the universe B n ,
card B n 2 n . We will identify space B n with the set of descriptors which are the
vectors constructed by the KPs detector for the image [2-3].
Consider the description of the analyzed image as a fixed finite subset Z B n
which consists of the vectors from B n . In general, we can consider Z as a multiset,
since the description elements can be repeated or similar to each other. This approach
promotes the representation of the visual object as a collection of its structural
elements, and the value of each descriptor is the result of extracting meaningful
features of the spatial fragments of the image. The set Z z v vs 1 , z v B n , is
composed of s descriptors of KPs with binary values, generated by detectors such as
ORB, BRISK, AKAZE [19-21].
Consider the set Z in a structured matrix form D d i, j s
n
i 1 j 1
for the fixed
value n and specific sequence of s descriptors of KPs. For simplicity, we consider
s to be the same for all etalons, whose finite set represents the recognized classes of
images [2-3].
Suppose that the structural description Z is characterized by the compact
placement of elements around a center in the space B n . This makes it possible for the
available data to estimate the allowable limit for the distance within the neighborhood
of the determined center and classify the description by calculating the number of its
equivalent elements and the refined center used the established threshold.
It is clear that in the aspect of multi-class classification, the effectiveness of this
method naturally depends on how well the computed centers will differ from each
other in the applied feature space.
Let's interpret the sequence of bits of each descriptor z v (it is the row of the matrix
D ) as separate case of n – dimensional discrete signal. We also construct for Z the
aggregated image hZ of the “data center” in the form
h Z h1 , , h j , , hn , h j i 1 d i , j ,
s
(1)
where h j are the sums of the elements of corresponding columns.
Let's call the vector hZ the statistical center (SC) of the description and put its
values at the basis of classification.
It is important for the practical implementation of recognition procedures that
representation hZ doesn’t depend on the order of descriptors z v in the set Z , that
is, the model hZ is invariant to mixing descriptors that corresponds to the arbitrary
arrangement of rows in the matrix. This property makes it possible to receive
descriptors in any order, taking into account the allowable geometric transformations
of objects. In fact, the vector hZ is a generalized image of an object in the n –
dimensional space C n of the vectors with integer nonnegative components since
hZ C n , h j 0 . The range of values h j in (1) is determined directly by the
calculation procedure and the number of descriptors s ; due to the bit type of data, it
can be considered as given: h j 0,1, , s 1, s .
In addition to the description, we will also refer to the normalized representation
h Z h1s , h2s , , hss , where his hi / s are obtained by normalizing values hi to
s
the descriptor number s of the description, his 0;1 . Vectors h and h s can be
considered as posteriori characteristics of the description, as they are calculated on the
basis of input information.
5 Classification based on data center
Let's carry out a statistical analysis of the data of the binary matrix D and on the
basis of the values of the vectors h or h s set a logical procedure for determining the
fact of belonging an arbitrary vector b B n to the given description Z B n .
At the pre-processing stage, we calculate a vector whose components have the
form qi h s , z i , i 1, , s , where h s , zi is a distance between vector h s and
descriptor zi Z . The range of values for h , z is known, since the space of
s
i
vectors is determined by the metric and value of the data. For example, the value of
the Manhattan distance h s , zi v 1 h s v zi v belongs to the segment 0; n .
n
Let's rank the values qi by type q1 q2 q s , then choose the median value
qs / 2 from the sorted sequence. The distance value qs / 2 halves the whole set of
descriptors and half of the descriptors will be in the neighborhood of the center h s
with distance less than qs / 2 [2].
We choose the value qs / 2 as the threshold for the distance h s , zi to
classify the query for the assignment of an arbitrary vector b to the set Z . This
choice of the value under the condition h s , z i provides equivalence with
accuracy for most vectors of description Z and its center h s .
Determining the threshold by moving the sorted sample to the left or right of its
center allows further to adapt the data content to the center value and can contribute to
a more reliable classification.
After that we define a refined SC h s * for the subset of the descriptors selected by
the threshold with the help of the averaging the values of only the descriptors for
which the condition h s , z i is satisfied:
h s*
1
s
1, h s , zi ,
z z , z (2)
s * i 1
i i i
0, h s , zi ,
where s * – the number of such descriptors, zi – characteristic function as a
result of logical analysis of distance.
We now apply the refined SC h s * to classify descriptors of the arbitrary
description. The selected concentrated portion of the description data in the form (2)
contributes to a more thorough identification of characteristics of data concentration
in terms of differences with other descriptions.
In general, the classification using the SC for the image database will be
represented by technology in the form of data processing steps:
1) analysis of the set of etalon descriptions of the image base to determine the SC
and the threshold for each etalon;
2) calculating the refined SC (2) for the set of etalons;
3) analysis of descriptor set that is the description of a recognized object for
satisfaction of inequality h s * , zi with respect to each etalon;
4) counting the number of voices of descriptors that satisfy the condition
h s * , zi for each etalon;
5) classification of the object on the basis of determining the etalon with the
highest number of received votes.
The proposed technology gives the possibility of modification, for example, in
stage 3 it can be competitively identified only one of the etalons based on the shortest
distance to the refined center. Another development of the approach may be the use of
weighting classification coefficients for single bits of the SC, which enhances the
individual characteristics of the descriptions and aims to improve the quality of
classification.
6 Application of nonparametric statistics apparatus
The vector hZ is a characteristic of a structural description of a visual object.
Another factor for distinguishing the descriptions presented by the matrix D can be
directly statistical distributions of data [2-3] or the parameters of these distributions
for individual bits or blocks D [3]. Such “indirect” approaches to performance
analysis, instead of directly data values, often make it possible to successfully solve
applied problems. The advantage is a significant reduction in the amount of
computation. The disadvantages are related to some blurring in the image space when
determining relevance.
i 1,, s
Let's imagine the value d j d i , j of the j -column bits of the matrix D as
the realization of some random variable b j , j 1,, n , which takes the binary values
b j 0,1 . We consider the column sequence as a system of independent random
variables. On the basis of sampling d j , we determine experimentally the
mathematical expectation and variance of each of the quantities b j 0,1 .
We now apply a nonparametric statistical criterion based on the experimental
values of mathematical expectation and variance to evaluate the relevance of the
distributions of the corresponding bits for the compared descriptions. A distinctive
advantage of nonparametric criteria using numerical characteristics of distributions is
their independence on the type of statistical data distribution [4, 5].
If the statistical characteristics a1 , 12 and a 2 , 22 for two random variables are
known ( a – mathematical expectation, 2 – variance), then the degree of closeness
of these variables can be estimated on the basis of statistics [1, 3]:
/ 2 a a / 2 .
2
1
2
2 1 2
22
(3)
12 22
At full coincidence of parameters a1, a2 and 12 , 22 we have 1 , and as their
differences increase, the value increases indefinitely. Based on the introduction
and application of the threshold for the criterion value , we will construct a
procedure for determining the relevance of the two descriptions and the classification.
Unlike parametric statistical criteria, the implementation of criterion (3) does not
rely on statistical tables. In this case, there is a problem of determining the lower limit
for the value j , which exceed indicates a significant difference between the
studied object descriptions.
The value of expression (3) is calculated separately for each element d j of the bit
array. At the same time it can be considered in sense of multidimensional distribution,
where the parameters a, 2 are vectors containing the characteristics of the
independent variable system. For a multidimensional situation, the criterion is
given by a vector of values.
The application of criterion (3) in the relevance analysis of the descriptions makes
it possible to significantly simplify the classification of the object in comparison with
the traditional apparatus for accepting statistical hypotheses [4, 5] and does not
depend directly on the type of probability distribution.
For example, consider the value of a single bit from a set of descriptors as a
discrete random variable, described by distributions p0 , p1 , where p0 – the
probability of 0, p1 - the probability of 1. Mathematical expectation of is defined
as M k k p k p1 . The variance of is calculated as
D k k M 2 pk p0 p1 [4].
Based on the analysis of the values b1 , b2 ,, bn from the system of independent
bits, we obtain for each etalon description its image in the form of a representation by
the vector values of the mathematical expectation M M 1 ,, M n and variance
D D1 ,, Dn . Further, on the basis of values M , D by expression (3) and by
applying the logical processing using a threshold for the value , we can decide
or reject the equivalence of the compared descriptions.
The most general model for a system of independent bits involves different
probability values of occurrence of 1 in each single bit for a given etalon class. In this
case, we have a distribution where in each bit values 1 or 0 appear independently. If
p j is the probability of occurrence of 1 in the j-th bit, then we have a system of
random variables given by the set of proper probabilities: p1 , p2 ,, pn . A specific
set of values for these probabilities will determine the etalon class. That is, the etalon
can be represented in a probabilistic way in the form p1 , p2 ,, pn .
The probability of a specific sequence of 0s and 1s is described by the product of
n probabilities p j or 1 p j depending on the value at the j-th position: 1 or 0. The
probabilities p j are directly calculated based on the normalized distribution as
p j h j / s . For example, the probability of occurrence of a sequence (0,1,0,1,1,1) is
a product P0,1,0,1,1,1 1 p1 p2 1 p3 p4 p5 p6 .
A separate theoretical case of the analyzed distribution is binomial one when
p1 p2 pn p , that is, the case of coincidence of values p j for single bits
from the list of descriptors. It means that the characteristic of the description is the
value p . It is clear that, in such an idealized model, the different descriptions must
have the different values p to distinguish them.
Then the descriptor values provide a random vector of dimension n with the
parameter p of occurrence of 1 in every single bit. The probability of occurrence of
1s in some specific sequence of 0s and 1s can be written as C nk p k 1 p n k , where
Cnk is a number of combinations. As we know, the binomial distribution is described
by the parameters of mathematical expectation M np and variance D np1 p .
Values M , D are the integral characteristics of the whole image and they can be
directly applied in expression (3).
The threshold value for logic processing can be found by the fraction of the
number of bits in the chain representation of the description, whose distributions have
significantly different mathematical expectations according to the Z-criterion [3, 4].
For example, 75% of the bits of two test objects have significantly different
mathematical expectations (i.e. 25% of them have no significant difference). We
calculate the values of statistics j , j 1,, m , rank the obtained values in ascending
order, and reject the first 25%. The first remaining value is taken as the limit. Objects
will be considered the different ones if at least 75% of the obtained statistic values
j exceed the threshold.
7 Experiments and results
We have performed a software modeling of the proposed classification
technologies based on structural data description in C # Visual Studio 2017 using
Open CV library tools [2-4, 27]. To conduct the investigation we took the images
(Fig. 1) for which the structural descriptions were calculated using the BRISK
detector (parameters s = 176, n = 512). Neighborhoods of KPs are shown in Fig. 1 as
small rings. The first two images are visually similar to each other ("angel and
demon"), which always causes difficulties in recognition even by human vision.
Fig. 1. Images with neighborhood of KPs
The calculated Manhattan distances i, k between statistical centers ( i, k -
numbers of centers) for the images of Fig. 1 have the following values: 1,2 23 ,
1,3 44 , 2,3 37 . Generally, it indicates a significant similarity between the
values of the descriptions in the investigated feature space of SCs, since all values of
distance in this example belong to the interval [0; 512]. The corresponding
normalized values are * 1, 2 0.044 , * 1,3 0.085 , * 2,3 0.072 . As we can
see, even visually similar images in Fig. 1 can be distinguished by the value of the
distance between the SCs.
Сalculating the refined centers (2) on the basis of the threshold for half of the
descriptors, we obtained: * 1, 2 0.052 , * 1,3 0.087 , * 2,3 0.076 ,
therefore, the degree of differentiation between the SCs has obviously increased. This
indicates a certain improvement in the effectiveness of classification.
The obtained number of votes for the elements of the etalons assigned to the
corresponding class (Fig. 1) by comparing the distance between them and refined
center with the boundary value is shown in Table 1.
Table 1. The number of classified elements in the description of etalons
Class
1 2 3
number
1 44 29 11
2 36 44 20
3 32 27 44
As we can see, the number of votes on the diagonal of Table 1 is sufficiently
greater than the values in the row and column, which confirms the effectiveness of the
method when classifying the descriptors. The two visually similar images in Fig. 1 are
also successfully differentiated. Thus, the formation of a concentrated subset (cluster)
of the description using the refined SC with logical processing (2) provides effective
classification.
The effectiveness of the application of nonparametric criterion (3) in the
classification of visual objects was tested experimentally in the problem of
distinguishing halftone silhouette images shown in Fig. 1. For each of the images, 500
ORB descriptors of dimension 256 have been generated. We can see that the images
used in the experiment are visually similar to each other, which makes it possible to
evaluate the sensitivity and performance of structural methods to distinguish such
signals. It is clear that for significantly dissimilar images, recognition performance
will be better.
Calculation of the criterion by the expression (3) for one-bit distributions of the
first two similar images in Fig. 1 showed results which were quite close to the
minimum value 1 . All values for each of the 256 bits of the dataset were in the
range 1.0 ̶ 1.12. Choosing the threshold value 1.006 the necessary decision
value n0 128 (half of the total number of bits) is achieved. It means the ability to
distinguish these essentially similar images in the constructed space of statistical
features, which is based solely on the values of mathematical expectation and
variance of data. Under the condition 1.006 , these images are considered
different by the proposed classification method. In Fig. 2 the curve 1 shows the
dependence of the value n0 on the threshold value .
The effect of impulse noise on the input image was also simulated: with a given
probability p, the pixels of the image were changed by a randomly generated noise
value in the range 0,…, 255 [1]. Experiments have shown that under the influence of
impulse noise for images in Fig. 1 the curve of dependence of the number of
equivalent bits n0 required for statistical decision making on the threshold shifts
to the right (Fig. 2, curve 2). Even for a significant noise value p = 0.7, each of the
distorted images are recognized successfully by this measure when setting the
threshold 1.05 .
Software modeling has also shown that when calculating the criterion as a
vector for substantially dissimilar images, a slightly higher threshold value should be
set, for example, 1.1 . It makes it possible to reliably identify each of the images
in the experiment. The dependence of the value on the threshold value has the form
shown in Fig. 2.
Fig. 2. Dependence of n0 on threshold : 1 - for similar images, 2 - for noise-affected
images, 3 - for visually different images
As we can see from the obtained experimental results, effective classification
actions of a logical plan with a threshold value for the analyzed images can only
be performed in a quite small size range 1;1.1 (when choosing n0 128 ).
Obviously that closeness of to 1 is a criterion for identifying an etalon image
among others, or when assigning a classified image to one of the etalons. In fact, the
choice of the threshold value 1.1 , as can be seen from Fig. 2, makes it possible
to reliably identify each of the images analyzed in the experiment, including visually
similar ones. The analysis of the results of the modeling showed that for an arbitrary
set of images it is possible to set a common or individual threshold for each
etalon, which gives an opportunity to classify the images to one of the etalons.
8 Conclusion
The statistic center and criterion (3) constructed in the paper are based on the
evaluation of the properties of the bit structure formed on the data description, as they
obtained by independent bitwise processing of a set of descriptors.
The formation of a concentrated subset in the form of clusters for description
elements using a refined statistical center with logical processing provides a reduction
in computational cost and effective classification by revealing significant patterns of
description of the visual objects.
The use of nonparametric methods for the statistical analysis of descriptor bits
using the mathematical expectation and variance makes it possible to classify even
visually close images.
The scientific novelty of investigation is improvement of the methods of structural
classification of images by introducing a statistical methods apparatus for a system of
bit description, which facilitates the processing and enhancement of classification
performance without reducing the efficiency.
The practical value of the paper is the developed mathematical and software
models for the implementation of image classifiers in the computer vision.
The further development of the study is the creation of applications of
multidimensional or block data structure based on set of bits.
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