RU2440608C1 - Object recognition method based on fractal-wavelet analysis - Google Patents

Abstract

FIELD: physics. ^ SUBSTANCE: classification of objects according to their images using fractal dimensions is a measure of signal self-similarity based on converting the image scale, calculating decomposition matrices, measuring the image fractal signature and calculating the fractal dimensions of the images for subsequent classification of the objects. By applying wavelet-transformation to an image, an approximation array-image (A) of a larger scale and four detailed array-images for horizontal, vertical and diagonal (H, V, D) details are obtained. This transformation is applied iteratively to matrix A for each image level and multilevel decomposition of the image on scales is obtained, which enables to analyse and recognise an object regardless of the aspect angle and the effect of noise. ^ EFFECT: broader functionalities owing to classification of objects according to their images using fractal dimensions. ^ 12 dwg

Description

The invention relates to electronic systems and can be used in various fields of technology, in particular in the development and creation of recognition devices in the design of fractal radio systems based on fractal information processing methods.

The formation of fractal theory is a vivid example of the development of a new direction of science, based equally on achievements in very abstract areas of mathematics, and on a new look at the long-known empirical material, which before creating adequate theoretical models could not be scientifically described and interpreted.

The new geometric and topological representations of fractal analysis in the future will be the same indispensable part of the analysis of signals and waves, which became the Fourier analysis (The latest methods of image processing. / Ed. By A.A. Potapov. - M .: FIZMATLIT, 2008).

Also known are methods of analyzing the image structure based on segmentation methods, which subdivide the image into its constituent regions or objects. One of the possible methods of segmentation is based on the selection of contours in the image. Contours, in turn, are such curves in the image along which there is a sharp change in brightness (brightness gap) or its derivatives with respect to spatial variables. In many situations, it is the contours that are the most informative components of the image. There are three main reasons for the appearance of contours in the image:

- violation of the continuity of surface orientation;

- changes in surface reflectivity;

- effects associated with lighting, such as, for example, shadows.

Contouring is a key initial step in optical location. This task includes the problem of the dependent use of various two-dimensional derivatives. In many cases, this is similar to highlighting areas corresponding to the characteristic points of the derivative, for example, such as its maxima or zeros. In certain cases, the previous algorithms based on binary signs, namely, on the presence or absence of contours, completely coincide or are similar to algorithms in which continuous values of derivatives are directly used. From this point of view, the task, usually called contouring, is to choose a differential operator suitable for further processing of images (Maar D. Vision. Information approach to the study of the representation and processing of visual images. - M .: Radio and communication, 1987).

The simplest model of the contour in the image is a straight line dividing two regions with constant brightness B ₁ and B ₂ , as shown in FIG. For this model, it is necessary to determine the unit step function u (z) in the form

This function is an integral of a one-dimensional unit momentum

A sharp change in brightness leads to a peak or trough of the first derivative, which is equivalent to the intersection of the zero level with the second derivative, as shown in Fig.2-4.

Thus, as a result, a quantity is calculated (first, second derivative, contrast), which can take a wide range of values. However, the result of the contour selection must be binary, i.e. the points at which the contour is identified are taken equal to unity, and all other points are equal to zero. The use of operators using the first derivative should be followed by a search for extreme values of the result. The easiest way is to enter a threshold. If the value of the operator is greater than a certain threshold value, then this point is a contour point, otherwise it is assumed that no contour is detected at this point.

Therefore, it becomes difficult to develop computational schemes for isolating loops (a loop is missing or a false loop).

The purpose of the invention is the classification of objects according to their images using a fractal dimension, which is a measure of signal self-similarity, i.e. to calculate it, it is necessary to determine the fractal signature S on several scales.

The goal is achieved by the fact that the image scale is converted, the decomposition matrices are calculated, the fractal signature of the image is measured, and the fractal dimension of the images is calculated for the subsequent classification of objects.

A model for measuring a fractal signature is a two-dimensional scene with a relief, the heights of which are the brightness values of the image elements (pixels). Figure 5 shows the simplest Sierpinski triangle and its representation in the form of a relief.

Measure S can be the area of the resulting relief. We will calculate the area by the triangulation method. In this case, four neighboring nodes of the image array are divided into two triples, and then the area of the triangle “forward” - S _f and the triangle “backward” - S _b are measured. The total area is S ₁ = S _f + S _b . To calculate the area of the entire image, it is necessary to sort through all four nodes.

Thus, we obtain the value of the fractal signature on one scale. To calculate the fractal dimension, these values are required at least on two scales. And for confident recognition on several (up to 6-7).

Undoubtedly, the wavelet transform is the most powerful tool for analyzing images at various scales. Applying this transformation to the image, we get an approximating image-array (A) of a larger scale and four detailed image-arrays for horizontal, vertical and diagonal details (H, V, D). Further, this transformation is applied iteratively to matrix A for each image level. Thus, we obtain a multi-level decomposition of the image in scale, multiplicity 2. Figure 6 shows a diagram of a multi-level wavelet decomposition, and Fig. 7 shows an example of a first level wavelet decomposition.

Thus, there is an image at scales that are multiples of 2. The fractal dimension is calculated by the following formula (The latest image processing methods. / Ed. By A.A. Potapov. - M.: FIZMATLIT, 2008):

where S is the fractal signature;

δ is the scale;

Δ is the sampling step in scale;

This fractal dimension is calculated for several levels of wavelet decomposition and a graph is constructed.

On Fig, as an example, we present an image of the satellite and graphs of its fractal dimensions D at different scales A, H, V, D, respectively. As you can see, the image is non-fractal (D is different from 2).

In the classical approach, the task of detecting an object against the background of the starry sky is very non-trivial. Border detectors, various correlation methods are used, however, all these methods are suitable for special cases and require constant adjustment to a new problem. The proposed method of fractal-wavelet recognition solves this problem with ease. The fact is that the starry sky is a fractal structure, and the satellite - the creation of man, on the contrary, is not fractal. Thus, if the satellite is not in the image, the fractal dimension is close to two. As soon as a satellite appears in the image, the fractal dimension changes dramatically. Also, in addition to the starry sky, fractal structures are natural landscapes, against which various objects created by man can be successfully recognized.

Figure 9 shows the Sierpinski triangle and satellite on its background and graphs of their fractal dimensions. The Sierpinski Triangle is one example of classic fractal images. As can be seen from the graphs, the spectral dimension of the image on which the satellite is present is very different. Thus, image analysis using a fractal detector is possible.

For recognition, first of all, it is necessary to take into account the fractal dimensions for the image matrix A, which is shown in the upper left graph.

Figure 10 shows satellite images at different angles and graphs of their fractal dimensions. As can be seen from the graphs, and especially from the graph of the fractal dimension for A, the fractal dimensions of the images are close.

Now we calculate the fractal dimensions for the images of different satellites.

Figure 11 shows images of different satellites and graphs of their fractal dimensions. As can be seen from the graphs, and especially from the graph of the fractal dimension for A, the fractal dimensions of the images differ. Thus, it is possible to construct a fractal classifier that will not depend on the rotation of the satellite in the image.

A check was made of the application of the method when exposed to noise. Figure 12 shows the images of the Mir space station - the original and noisy Gaussian blur and noise, and graphs of their fractal dimensions. As can be seen from the graphs, and especially from the graph of the fractal dimension for A, the fractal dimensions of the images are close. Therefore, we can conclude that the method of fractal-wavelet recognition is resistant to interference.

Information sources

1. The latest image processing methods. / Ed. A.A. Potapova. - M .: FIZMATLIT, 2008.

2. Issues of prospective radar. Collective monograph. / Ed. A.V.Sokolova. - M.: Radio Engineering, 2003.

3. Maar D. Vision. An informational approach to the study of the representation and processing of visual images. - M.: Radio and Communications, 1987.

4. Zotov R.V., Tormosin A.S. Shevanev D.N. Some approaches to the formation of reference features in the recognition system of space objects based on fractal analysis. - M: RAS collection of scientific papers "Selected Works of the Russian School on the Problems of Science and Technology", 2010.

5. Zotov R.V., Luchin A.A. A method for generating reflection charts from spacecraft design elements. - M .: Collection of scientific and methodological materials. Military unit 03425.2001.

Claims (1)

A method for recognizing objects based on fractal-wavelet analysis, based on transforming the image scale, calculating decomposition matrices, measuring the fractal signature of the image and calculating the fractal dimension of the images for the subsequent classification of the object, which consists in
applying the wavelet transform to the image, we obtain an approximating image-array (A) of a larger scale and four detailed image-arrays for horizontal, vertical and diagonal details (H, V, D), then this transformation is applied iteratively to the matrix A for each image level Thus, we obtain a multi-level decomposition of the image in scales of 2 multiplicity, which allows analyzing and recognizing an object based on the fractal dimension, regardless of the observation angle and interference interference.

Images