RU61441U1 - DEVICE FILTERING FEATURES OF THE IMAGE BASED ON CONTINUOUS WAVELET TRANSFORM - Google Patents

Abstract

A device for filtering image features based on continuous wavelet transform belongs to the field of information technology and can be used in digital image processing systems for image analysis, identifying features, local heterogeneities and nonsmooth structures. The utility model is aimed at improving the quality of filtering features having anisotropic characteristics, two-dimensional signals, in particular images. The specified technical result is achieved through the use of a separable two-dimensional continuous wavelet transform and adaptive choice of the scaling factor of decomposition for each row or column of the image. For this, two blocks for calculating a one-dimensional continuous wavelet transform, two blocks for calculating scaling coefficients at which the amplitudes of the wavelets corresponding to the regions of features reach their maximum are added to the proposed device. Based on the calculated values of the scaling coefficients from the random access memory in which wavelet images of rows or columns of a two-dimensional signal are stored, the wavelet images calculated with these values of the scaling coefficients are selected and stored in inverse type buffers, of which the wavelet images corresponding to the horizontal and vertical directions of viewing the two-dimensional signal are received in the calculation unit of the wavelet transform module. The maximum values of the elements of the wavelet transform module correspond to the regions of features of the two-dimensional signal.

Description

A device for filtering image features based on continuous wavelet transform belongs to the field of information technology and can be used in digital image processing systems for image analysis, identifying features, local heterogeneities and nonsmooth structures.

The main field of application of continuous wavelet transform at present has become the analysis and processing of heterogeneous signals of various types in space, in solving problems of identifying features, periodic dependences, local inhomogeneities, nonsmooth structures, etc. [four]

Continuous wavelet transform is a decomposition of a signal into all possible shifts and contractions (stretches) of a certain function. This transformation (for a one-dimensional signal) can be defined as the scalar product of the analyzed signal ƒ (x) and the basis functions ψ _{a, b} (x) [2]:

where the bar above indicates the operation of complex pairing.

The general principle of constructing a wavelet transform basis is to use scale transformations with the compression parameter a and the shift parameter b of the generating wavelet ψ (x) [2]:

To decompose two-dimensional signals (images) in terms of the wavelet function, it is possible to use a separable wavelet transform, i.e. separately for the rows and columns of the matrix of instantaneous signal values. Since images, as a rule, are finite discrete signals, to obtain their wavelet image, it is necessary to use an analogue of the continuous wavelet transform for discrete signals. In this case, rows or columns of the image (like any other discrete signal) s = {s _j } _j∈Z can

present in the form of a continuous signal of finite length — a piecewise constant function defined on the interval [0 ... N-1]:

Then (1) taking into account (2) takes the form:

For practical purposes, only integer shifts b in the range [0, 1, ..., N-1] and rational positive integer scaling coefficients a, in the range [1, 2, ..., N] [4] are of interest.

For each pair a and b, the function W _s (a, b) determines the amplitude of the corresponding wavelet. In other words, the function W _s (a, b) measures the change in s (x) in the neighborhood of a point b whose size is proportional to a [1]. The wavelet transform is equivalent to the convolution of the signal s (x) with the filter ψ (x), therefore, when the filter passes through the signal region containing a certain feature, the amplitude of the corresponding wavelet will be maximum with comparable sizes of the feature and filter. Those. if the signal has a singularity, then the presence of this singularity is indicated by the relatively high amplitudes of the wavelet image corresponding to those wavelets whose extrema are close to the region of the singularity [3]. This approach to highlighting the features of the signals is selected as a prototype.

Image features may have different sizes and shapes, i.e. these characteristics of the features will be anisotropic. Moreover, on a single image there may be some countable set of similar features. In this case, the use of a separable wavelet transform with an arbitrary choice of the value of the scaling coefficient will allow us to take into account the anisotropic nature of the characteristics of the features.

The technical result of the utility model is to improve the filtering quality of the features (having anisotropic characteristics) of two-dimensional signals (images) through the use of a separable two-dimensional continuous wavelet transform and adaptive choice of the scaling factor of decomposition for each row or column of the image.

The original image is divided into rows and columns that are sequentially

are subjected to one-dimensional continuous wavelet transform (3) with a scaling factor belonging to the range [1, 2, ..., N]. In the wavelet image of each row or column of the image, the wavelet coefficients with the maximum amplitude are determined and the value of the scaling coefficient is determined at which the amplitude of the wavelet coefficients reaches an extremum:

The wavelet image of a row (column) with the selected value a _{opt is} included in the horizontal (vertical) wavelet decomposition of the image:

To exclude from the further consideration the elements of the wavelet spectrum that do not belong to the feature regions, the module of the wavelet transform is calculated as:

which is due to the fact that the values of the amplitudes of the elements of the wavelet image corresponding to the region of one feature will reach their extremum, regardless of the direction of viewing the image. Therefore, the maximum values of the wavelet transform module will correspond to the regions of image features.

A device that implements an approach to highlighting the features of images based on a continuous wavelet transform is shown in the figure, where:

block 1 - analog-to-digital Converter (ADC);

blocks 2, 8, 9 - random access memory (RAM);

block 3 - read-only memory (ROM);

blocks 4, 5 - blocks of the calculation of the wavelet transform (BWP);

blocks 6, 7 - blocks for calculating the scaling factor (BMC);

blocks 10, 11 - buffers reverse store type (FIFO);

block 12 - block calculation module wavelet transform (BMVP).

The principle of operation of the device is as follows. The analyzed two-dimensional signal s (t ₁ , t ₂ ) is fed to the ADC input (block 1), the output of which is discrete

a sample of s (n ₁ , n ₂ ) of size N ₁ × N ₂ samples arrives in RAM 1 (block 2). From the ROM (block 3), a discrete sample of the “mother” wavelet ψ (k) is supplied to the first inputs of the BWP 1 and 2 (blocks 4, 5), the second inputs of which from the outputs of the RAM 1 receive one-dimensional signals, which are respectively the strings s (n _i , j) and columns s (i, n _j ) of the two-dimensional signal s (n ₁ , n ₂ ). At the outputs of the BWP 1 and 2, wavelet images of rows and columns of a two-dimensional signal are formed: W _j (a, b) and W _i (a, b), respectively. From the output of the BWP 1, the wavelet image of the line of the two-dimensional signal goes to the input of the BMK 1 (block 6) and the first input of the RAM 2 (block 8), and from the output of the BWP 2, the wavelet image of the column of the two-dimensional signal goes to the input of the BMK 2 (block 7) and the first input of RAM 3 (block 9). From the outputs of BMK 1 and 2 the values of scaling factors and _ort ^j and a _opt ⁱ calculated by (4) are fed to the second inputs of RAM 2 and 3, the outputs of which wavelet images of rows and a two-dimensional signal columns at certain values of scaling factors W _j (a _opt ^j , b) and W _i (a _opt ⁱ , b) respectively arrive at the inputs of blocks FIFO 1 and 2 (blocks 10, 11). The horizontal and vertical wavelet coefficients of the two-dimensional signal W _H (a, b) and W _v (a, b) come from the outputs of the FIFO blocks 1 and 2, respectively, to the inputs of the BMIF (block 12), at the output of which discrete values of the wavelet transform module are formed W _M (a, b) of a two-dimensional signal.

Information sources:

1. Vorobiev V.I., Gribunin V.G. Theory and practice of wavelet transform. - SPb .: VUS, 1999. - 204 p.

2. Finish I. Ten lectures on wavelets. - Izhevsk: Research Center "Regular and chaotic dynamics", 2001. - 464 p.

3. Malla S. Wavelets in signal processing: Trans. from English - M .: Mir, 2005 .-- 671 p., Ill.

4. Pereberin A.V. On the systematization of wavelet transforms // Computational methods and programming. - 2001 - T.2. - S.15-40.

Claims (1)

A device for filtering image features based on a continuous wavelet transform containing an analog-to-digital converter, to the input of which the analyzed signal is fed, and a discrete sample of signal samples is generated at the output, which is fed to the input of the first random access memory, from the first output of which there is a one-dimensional signal representing is a row of a matrix of samples of a two-dimensional signal; it goes to the first input of the first device for computing a one-dimensional continuous wavelet transform the second input of which from the read-only memory the values of the wavelet filter readings are received, and the wavelet image of the signal line is generated at the output, which goes to the input of the first block for calculating the scaling coefficient, at which the wavelet amplitude corresponding to the feature reaches its maximum at the first input the second random access memory, the second input of which from the output of the first block for calculating the scaling coefficient receives the value of the scaling coefficient, and from the output the wavelet image of the signal string is received at the input of the first inverse store-type buffer at the calculated value of the scaling factor, and from the second output of the first random access memory, the one-dimensional signal, which is a column of the sample matrix of the two-dimensional signal, is fed to the first input of the second device for calculating the one-dimensional continuous wavelet transform , the second input of which from the read-only memory receives the values of the wavelet filter samples, and the output is formed the wavelet image of the signal column fed to the input of the second block for calculating the scaling coefficient and to the first input of the third random access memory, the second input of which from the second block for calculating the scaling coefficient receives the value of the scaling coefficient, and from the output to the second buffer of the inverse store type wavelet image of the signal column with the calculated value of the scaling coefficient, from the output of which the vertical wavelet coefficients of the two-dimensional signal arrive at the second input of the wavelet transform module calculation unit, the first input of which the horizontal wavelet coefficients of the two-dimensional signal come from the output of the first inverse store type buffer, and the matrix elements of the wavelet transform module are formed at the output of the block.