-A comparative analysis of efficiency of stochastic gradient identification method on the base of pattern of objects with similar shapes by their grayscale and binary images is carried out. Object identification is understood as the determination of the object image in the studied image with the estimation of its spatial parameters in relation to the reference image. Two types of objects with similar shape are investigated on the base of COIL-20 halftone images and their binary versions. The objects of the first type have a different character of the curvature of the lines describing their contour, and the objects of the second type are close to the curvature characteristics of the contour lines.
The problem of pattern recognition, both on separate
images and on video sequences, arises in a variety of areas:
from military affairs and security systems to the digitization
of analog signals. The problem of automating the solution of
this problem remains relevant both from the point of view of
theory and technical implementation [
– recognition of many predefined objects, or classes of objects in the image;
– object detection, implemented by checking the image or its part for compliance with certain conditions; – identification on the image of the object with the assessment of its parameters and decision making.
In [
For concreteness, we will assume that possible
deformations of the identified object with respect to the
pattern can be reduced to a similarity model [
In SGIM the identification parameters ˆ , on the basis of
which the decision is made, are searched recursively [
The effective working range of the estimated parameters
of the SGIM (in which the estimates for a given number of
iterations do not go beyond the required confidence interval)
is limited. If it does not cover the domain of parameters, then
to provide coverage it is required to specify several patterns
with different initial approximations of the parameters. It was
also shown in [
It was also shown in [
The studies using halftone images from the COIL-20
base have also shown the appropriateness of low-pass
filtering. In this case, the optimal size of the Gaussian filter
mask, which allows expanding the operating range of the
SGIM while maintaining identification accuracy, is from 3 %
to 10 % of the of the object size in the image. We also note
that the approximate implementation of the Gaussian filter
proposed in [
The computational complexity of the stochastic gradient
parameter estimation procedure that underlies the SGIM
was studied in [
As a characteristic of the SGIM efficiency for binary and grayscale images, we use the convergence of the standard deviation (SD) ˆ t of the brightness differences of the modified pattern and the studied image, which is calculated at each t -th iteration from a local sample of identifiable image and pattern samples, t 0 , T . Example of ˆ t convergence graphs for the left object of Fig. 1 (car) with the mismatch parameters of the pattern and the studied T object: 0 .8 5 , 3 5 0 , h h x , h y 6 , 6 T , is shown in Fig. 2, where graph (a) corresponds to a halftone image, and (b) a binary image. The studied images and corresponding patterns are shown in Fig. 3, and the convergence graphs of the estimates of individual identification parameters are shown in Fig. 4, where the solid line corresponds to the grayscale images and the dashed line corresponds to binary images. The image sizes are 128x128 elements, the local sample size is 1 5 .
It can be seen from the plots that for this object estimates ˆ T of the identification parameters ˆ t ˆ t , ˆ t , ht when processing halftone images and patterns converge slower (for about 400 iterations) than when processing their binarized versions (for about 200 iterations). This is explained by the large size of the low-pass filter during image preprocessing. Thus, both the rate of convergence of estimates and the effective working range when using grayscale and binarized images can vary. This is especially true for images of objects having a similar shape. hˆ x t III. IDENTIFICATION OF OBJECTS WITH A SIMILAR SHAPE
Using the objects of the COIL-20 images, we consider two types of objects that are similar in shape: the curvatures of the lines describing the contour of a different nature (the objects shown in Fig. 5a can serve as an example), and with similar curvature characteristics of the contour lines (an example of such objects is shown in Fig. 5b). The indicated figures also show binary versions of the images of these objects. Obviously, the studied types of objects are critical in the processing of binary images.
In the experiment, the identification method proposed in
[
The steady state of the identification process is clearly illustrated in Fig. 2. The decision on identification is made if all three criteria are fulfilled:
R R t , mˆt mtˆi , ˆi tˆi ,
t and tˆi are threshold values. The threshold
where R t , mˆi
values of the identification criteria for the used image
database were determined by the method [
The following results are obtained for the first type of objects. For the binarized images, the correlation coefficient between the image of the object and the “correct” pattern is R 0 .9 9 and exceeds the threshold value. For this pair the additional criteria are also fulfilled:
However, the correlation coefficient between the image of the object and similar patterns transformed by the SGIM also exceeds the identification threshold value ( R 0 , 9 4 ). At the same time, the numerical values of auxiliary characteristics do not reach threshold values, although they are quite close to them ( mˆt 1 1 , ˆi 7 .3 ). For grayscale images, the correlation coefficient between the image of the object and the “correct” pattern is also 0.99 and exceeds the threshold value, and the correlation coefficient with similar patterns ( R 0 .7 ) is significantly lower than the threshold. Additional criteria for the “correct” pattern are also fulfilled:
Thus, for this type of object, when binarizing their images, the decision on identification requires the use of additional criteria. For grayscale images, a decision on identification is possible using only the main criterion for the correlation coefficient, and additional ones can be used to assess the reliability of the identification.
An analysis of the usage of SGIM for binary images of objects of similar shape in the second type showed that all identification criteria are satisfied, both for the “correct” pattern and for similar ones. So, for the “correct” pattern are:
R 0 .9 9 , mˆt 1 .3 1 mtˆi , ˆi 0 .8 9 tˆi and for similar are:
R 0 , 9 7 , mˆt 7 .2 mtˆi , ˆi 1 .4 tˆi .
For grayscale images, the correlation coefficient between the image of the object and the “correct” pattern exceeds the threshold, but less than in the other cases considered ( R 0 .9 6 ). The values of the additional characteristics are significantly lower than the threshold:
m ˆ t 1.81, ˆ i 1.74.
For similar pattern, the criterion for the correlation coefficient is not satisfied ( R 0 .8 3 ) and the values of the auxiliary characteristics significantly exceed the threshold ( mˆt 2 3 .3 , ˆi 1 2 .3 ).
Thus, for objects of similar shape with similar characteristics of contour lines curvature, their identification by the pattern from binarized images is ineffective. When identifying this type of objects by their grayscale images, it is advisable to use the additional criteria used in the work.
It should be noted that the effective operating range of SGIM for images of this type is significantly reduced. So, when choosing similarity model parameters as identification parameters, for the images considered, it is: 0 .8 ... 1 .1 ; 1 0 0 ... 1 0 0 ; h 5 ... 5 pixels. This is due to the fact that such images differ mainly in texture, and the preliminary low-pass filtering procedure smooths the texture, so the size of the preprocessing filter mask does not exceed 3 % of the size of the object.
A comparative analysis showed that the extension of the SGIM to grayscale images does not impair its performance in computational complexity, but slightly reduces the effective operating range and the convergence rate of identification parameters. This is due to the fact that with the same reliability of identification of objects, grayscale images allow a smaller size of the low-pass filter during preprocessing.
A study on the basis of COIL-20 images of identifying objects of similar shape with different curvatures characterizing the lines of an object’s contour showed that with close characteristics of the curvature of contour lines, identification by binarized images is ineffective. When identifying by grayscale images, it is advisable to increase the reliability of using, in addition to correlation criteria, additional ones based on the characteristics of the process of convergence of identification parameters. For objects of similar shape with different characteristics of the contour lines curvature, when binarizing their images, the decision to identify also requires the use of additional criteria. For grayscale images, a solution is possible using only the correlation criterion, and additional ones can be used to assess the reliability of identification.
We also note that in order to solve the problem of identification of objects according to a pattern the criterion based on correlation and referred in this paper as “basic” is not significant for identification in many cases.
The reported study was funded by RFBR & Government of the Ulyanovsk region according to the research projects № 19-29-09048 and № 19-47-730004.