JP2009296515A - Two-dimensional digital filter system, two-dimensional digital filtering method and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a two-dimensional digital filter extracting directional characteristics by an efficient and simple configuration of a combination of one-dimensional digital filters. <P>SOLUTION: The two-dimensional digital filter includes: a first computation means, having a first one-dimensional filtering means performing X-directional one-dimensional convolution computation on two-dimensional digital data and a second one-dimensional filtering means for performing Y-directional one-dimensional convolution computation on the computation result of the first one-dimensional filtering means; a second computation means having a third one-dimensional filtering means performing X-directional one dimensional convolution computation on the two-dimensional digital data and a fourth one-dimensional filtering means performing Y-directional one-dimensional convolution computation on an computation result of the third one-dimensional filtering means; and an adding/subtracting means for obtaining a sum of the computation result of the first computation means, and the computation result of the second computation means or a difference between them. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a two-dimensional digital filter system, a two-dimensional digital filtering method and program, and more particularly to a two-dimensional digital filter or digital signal processing apparatus for detecting a directional characteristic.

  In general, a signal processing apparatus requires a filter capable of high-speed processing when performing various processes. If the signal is digitized, this is realized by a digital filter. A digital filter (FIR digital filter) that performs one-dimensional convolution calculation processing is realized by a configuration as shown in FIG.

  In the filter of FIG. 4, a plurality of delay elements (11-a to 1m-a) are connected in series between the input terminal and the output terminal, and a predetermined filter coefficient is obtained from the tap provided at each connection point. Multipliers (11-b to 1m-b) for multiplying are connected. The outputs of the multipliers are added by adders (11-c, 12-c,...) And output to the output terminal. When a one-dimensional input signal is sequentially input from the input terminal, filter outputs are sequentially output from the output terminal after a fixed delay cycle determined by the number of delay elements. In this filter, the following convolution operation is executed.

Here, I ₁ represents an input signal, h ₁ represents a filter coefficient, and O ₁ represents an output signal. Patent Document 1 describes a method that can reduce the calculation step amount of such a one-dimensional digital filter.

On the other hand, when the signal is a two-dimensional digital signal such as an image, a two-dimensional digital filter is required for the filtering process. In general, the two-dimensional digital filter is configured as compared with the one-dimensional case. Becomes much more complicated. Therefore, when the filter coefficient is “separable”, a method of realizing this by performing the one-dimensional filter processing twice is widely adopted. When the filter coefficient h (x, y) of a two-dimensional digital filter is expressed as a product of h (x, y) = h ₁ (x) * h ₂ (y), it is “separable” (separable) That is. At this time, the two-dimensional convolution operation can be efficiently calculated by one-dimensional convolution operation twice (X direction and once in the Y direction) as shown in the following equation.

  Here, I represents an input signal, h represents a filter coefficient, and O represents an output signal. Assuming that the input signal I is an image and the size of the two-dimensional filter coefficient h (x, y) is mxm, in order to perform a two-dimensional convolution operation using this, mxm times for each pixel of the image. Multiplication of is required. On the other hand, if this can be done with two one-dimensional convolution operations, the required multiplication is only 2 × m times for each pixel (if m is large), it becomes very efficient. Such a filter can be implemented with a simple configuration. For example, Patent Document 2 describes a separable two-dimensional digital filter having a configuration in which one-dimensional filter processing is performed twice as shown in FIG.

In the filter of Figure 5 first filter X (2-1) performs a one-dimensional convolution of the X direction using the filter coefficients h _1, and stores the result in a buffer (2-2). Then perform a one-dimensional convolution operation in the Y direction by using the filter coefficients h ₂ with respect to the filter Y (2-3) is output of the filter X stored in the buffer. In this way, a two-dimensional convolution operation using h (x, y) = h ₁ (x) * h ₂ (y) as a filter coefficient is realized by a combination of one-dimensional filters. Patent Document 2 describes a method for efficiently configuring a plurality of separable two-dimensional digital filters.

  On the other hand, it is well known that the direction feature can be extracted from the image by the two-dimensional convolution calculation processing using the filter coefficient having the directionality, but the filter coefficient having the inclined directionality is not separable in general. A two-dimensional digital filter having a complicated configuration is mounted, or a parallel image processing processor is used to calculate this at high speed. For example, Non-Patent Document 1 describes a SIMD (Single Instruction Multiple Data) type image processor.

Japanese Patent Laid-Open No. 06-013845 JP 05-258054 A S. Kyo, T. Koga, K. Sakurai, and S. Okazaki, A Robust Vehicle Detecting and Tracking System for Wet Weather Conditions using the IMAP-VISION Image Processing Board, IEEE / IEEJ / JSAI International Conference on Intelligent Transportation Systems (ITSC '99), pp.423--428, Oct., 1999, Tokyo, Japan.

  The problem with the prior art in two-dimensional digital filters is that a filter that can extract tilted directional features cannot be realized by a combination of one-dimensional filters having an efficient and simple configuration. The reason is that a two-dimensional filter coefficient having an inclined directionality is not separable, and therefore a normal method of mounting a separable filter cannot be applied.

  In view of the above circumstances, an object of the present invention is to provide a two-dimensional digital filter that can extract a directional characteristic with an efficient and simple configuration by a combination of one-dimensional digital filters.

  In order to achieve the above object, the present invention has the following features.

  The two-dimensional digital filter system according to the present invention includes a first one-dimensional filter unit that performs a one-dimensional convolution operation in the X direction on two-dimensional digital data, and an operation result of the first one-dimensional filter unit. A second one-dimensional filter means for performing a one-dimensional convolution operation in the Y direction, a third one-dimensional filter means for performing a one-dimensional convolution operation in the X direction, and the third 4th one-dimensional filter means for performing one-dimensional convolution calculation in the Y direction on the calculation result of the one-dimensional filter means, the calculation result of the first calculation means, and the second And an addition / subtraction means for obtaining a sum or difference from the calculation result of the calculation means.

  The two-dimensional digital filtering method according to the present invention includes a first one-dimensional filter process for performing a one-dimensional convolution operation in the X direction on two-dimensional digital data, and an operation result of the first one-dimensional filter process. And a second one-dimensional filter step for performing a one-dimensional convolution operation in the Y direction, a third one-dimensional filter step for performing a one-dimensional convolution operation in the X direction, and the third A fourth one-dimensional filter step for performing a one-dimensional convolution operation in the Y direction on the calculation result of the one-dimensional filter step, a calculation result of the first calculation step, and the second And an addition / subtraction step for obtaining a sum or difference from the calculation result of the calculation step.

  The program according to the present invention includes a first one-dimensional filter unit that performs a one-dimensional convolution operation in the X direction on two-dimensional digital data, and a calculation result of the first one-dimensional filter unit. A first one-dimensional filter means for performing a one-dimensional convolution operation in the Y direction, a third one-dimensional filter means for performing a one-dimensional convolution operation in the X direction, 4th one-dimensional filter means for performing one-dimensional convolution computation in the Y direction on the computation result of three one-dimensional filter means, the computation result of the first computation means, It is made to function as a two-dimensional digital filter system having addition / subtraction means for obtaining a sum or difference with the calculation result of the second calculation means.

  ADVANTAGE OF THE INVENTION According to this invention, it becomes possible to provide the two-dimensional digital filter which can extract a directional characteristic with the efficient and simple structure by the combination of a one-dimensional digital filter.

  Next, the present invention will be described in detail by embodiments.

  An object of the configuration of the present embodiment described below is to provide a two-dimensional digital filter that can extract a directional characteristic with an efficient and simple configuration using a combination of one-dimensional digital filters. In order to achieve the object, the two-dimensional digital filter according to the present embodiment has a tilted directionality and a separable filter coefficient can be configured when the filter coefficient h (x, y) is expanded to a complex number range. Pay attention and use this to perform convolution calculations that can extract directional features by combining one-dimensional filters. For this reason, in the present embodiment, the first two-dimensional convolution calculation execution means composed of two one-dimensional digital filters in the X direction and the Y direction and the second two-dimensional digital filter composed of two one-dimensional digital filters in the X direction and the Y direction are used. It comprises a two-dimensional convolution calculation execution means and an adder or subtracter that calculates the output by adding or subtracting the two-dimensional convolution calculation results obtained by these.

  Due to the above-described configuration, this embodiment can extract a directional feature with a simple configuration in which one-dimensional filtering is performed four times. The reason is that a complex filter coefficient having a filter coefficient for extracting a directional characteristic in the real part (or imaginary part) is formed, and the first and second two-dimensional convolution calculation execution means depend on the complex filter coefficient. This is because a convolution operation using a complex filter coefficient having a tilted directionality and a separable direction is executed by sharing the real part and the imaginary part of the convolution operation. The configuration and operation of this embodiment will be described below with reference to the drawings.

  Referring to FIG. 1, the present embodiment is different from the first two-dimensional convolution operation executing means (3-a) for receiving a two-dimensional digital signal and performing a convolution operation on the input, and for the same input. A second two-dimensional convolution operation execution means (3-b) that performs a convolution operation using a filter coefficient, and an adder / subtracter (3) that calculates an output by adding or subtracting the operation results obtained by these. -c). The first and second two-dimensional convolution operation executing means store a one-dimensional digital filter (3-a-1, 3-b-1) that performs one-dimensional convolution operation in the X direction and the output thereof. It includes a buffer (3-a-2, 3-b-2) and a one-dimensional digital filter (3-a-3, 3-b-3) that performs a one-dimensional convolution operation in the Y direction.

  Next, the operation of this embodiment will be described in detail with reference to FIG.

First, the filter X1 (3-a-1) filter coefficients h ₁₁ for two-dimensional digital signal is inputted to configure the first two-dimensional convolution operation execution means (3-a) (3- a-4) Is used to perform a one-dimensional convolution operation in the X direction, and the output is stored in buffer 1 (3-a-2). Next, the filter Y1 (3-a-3) performs a one-dimensional convolution operation in the Y direction on the output data of the filter X1 stored in the buffer 1, using the filter coefficient h ₂₁ (3-a-5). Simultaneously with the above operation, the second two-dimensional convolution operation execution means (3-b) also includes the filter X2 (3-b-1), buffer 2 (3-b-2), and filter Y2 (3-b). The same processing is executed according to -3). However, this performs a convolution operation process using filter coefficients h ₁₂ and h ₂₂ (3-b-4, 3-b-5) different from 3-a. Here, the filter coefficients h ₁₁ , h ₂₁ , h ₁₂ , and h ₂₂ are determined by the method described below, but these are programmable and can be replaced according to the contents of the processing.

  Next, the adder / subtracter (3-c) subtracts the output of the second two-dimensional convolution calculation execution means (3-b) from the output of the first two-dimensional convolution calculation execution means (3-a), and the result Is output. The operation of the adder / subtracter can be switched to the adder by an external signal, and processing is performed by switching to either the adder or the subtracter according to the contents of the processing.

Next, filter coefficients of each filter (3-a-1,3-a-3, 3-b-1,3-b-3) will be described. This is not separable when the two-dimensional filter coefficient h (x, y) is a pattern having an inclined directionality as shown in FIG. 2, for example. That is, it cannot be decomposed into products as h (x, y) = h ₁ (x) * h ₂ (y).

Here, a supplementary explanation will be given for the “pattern having an inclined direction”. First, a pattern that changes gently when viewed along a specific direction but has a dramatic change along a direction orthogonal thereto will be referred to as a “directional pattern” below (see FIG. 2). In Figure 2, the value is constant along the direction of the white bar, but there is a drastic change along the direction perpendicular to it (at the boundary of the white bar). When the pattern h (x, y) having such directionality is inclined (that is, when the pattern direction does not match the x-axis direction and the y-axis direction), this is expressed as h (x, y) = h ₁ (x ) * h ₂ (y) cannot be broken down into products.

However, if h (x, y) is allowed to be a complex number, it can be decomposed into products as h (x, y) = h ₁ (x) * h ₂ (y), and h (x, y) H (x, y) can be set so that the real part (or imaginary part) has a pattern with a tilted directionality. In particular

(I represents an imaginary unit), this is separable regardless of the function of f ₁ , f ₂ , g ₁ , and g ₂ . Ie

  Holds. At this time, the real part of h (x, y) is

Therefore (Re represents the real part), it can be made a pattern with an inclined directionality by appropriately selecting the functions g ₁ (x) and g ₂ (y). For example, if k1 and k2 are constants and g ₁ (x) = k1 * x and g ₂ (y) = k2 * y are set, the real part of h (x, y) is orthogonal to the vector (k1, k2) It becomes a pattern with directionality. For example, if you set f ₁ (x) = − (xm / 2) ² / (2σ ² ), f ₂ (y) = − (ym / 2) ² / (2σ ² ), h (x, y) Is a function known as a Gabor function, and its real part is a pattern having directionality as shown in FIG. 3 (m is the size of the filter, and σ is a predetermined parameter). On the other hand, equation (5) is also the real part of h ₁ (x) * h ₂ (y)

  (Re represents the real part and Im represents the imaginary part) and is represented by the difference between the two separable filter coefficients. Therefore, a two-dimensional digital filter having the real part of h (x, y) as a filter coefficient can be composed of two separable filters. Specifically, the filter coefficient of each one-dimensional filter in FIG.

By subtracting the output of the second two-dimensional convolution calculation execution means (3-b) from the output of the first two-dimensional convolution calculation execution means (3-a), the actual value of h (x, y) is obtained. An arithmetic process equivalent to a convolution operation using a two-dimensional digital filter having a filter part as a filter coefficient can be realized. That is, a two-dimensional digital filter that can extract a directional characteristic can be configured by a combination of four one-dimensional digital filters. Repeatedly, h ₁₁ (x), h ₂₁ (y), h ₁₂ (x), and h ₂₂ (y) are respectively set as shown in equation (7), and g ₁ (x) and g in equation (7) are set. _{If 2} (y) is selected appropriately, for example, g ₁ (x) = k1 * x, g ₂ (y) = k2 * y, h ₁₁ (x) * h ₂₁ (y)-h ₁₂ (x) * h ₂₂ (y) can be made into a pattern with an inclined directionality, but a two-dimensional digital filter having this as a filter coefficient has two separable two-dimensional digital filters (h ₁₁ (x ) * h ₂₁ (y) and h ₁₂ (x) * h ₂₂ (y) as a filter coefficient).

The method of making h ₁₁ (x) * h ₂₁ (y)-h ₁₂ (x) * h ₂₂ (y) into a pattern having an inclined direction is not limited to the above. More generally, the curve, g ₁ (x) + g ₂ (y) = constant, has a substantially constant slope in the region, 1 ≦ x ≦ m, 1 ≦ y ≦ m, where m is the size of the filter. It is only necessary to set g ₁ (x) and g ₂ (y) in the equation (7) so as to have them. For example, g ₁ (x) = k1 * (xm / 2) ³ and g ₂ (y) = k2 * (ym / 2) ³ may be determined.

The functions f ₁ , f ₂ , g ₁ , and g ₂ that specifically determine the filter coefficients of these filters can be changed according to the application application.

  If you also want to obtain the output of a two-dimensional filter that uses the imaginary part of h (x, y) (note that this can also be a pattern with directionality) as a filter coefficient according to the application purpose.

Therefore, after the above calculation processing (two-dimensional convolution calculation processing using the real part of h (x, y) as a filter coefficient) is finished, h ₂₁ and h ₂₂ of the filter coefficients are

  The one-dimensional filter corresponding to this is processed with the one-dimensional filter (3-a-3, 3-b-3), and the adder / subtracter (3-c) is switched to the adder. You can calculate by adding the outputs.

  The preferred embodiment of the present invention has been described above, but the present invention is not limited to this, and various modifications can be made without departing from the scope of the invention.

It is a figure which shows the two-dimensional digital filter of embodiment by this invention. It is a figure which shows the example of the filter coefficient with a tilted direction in embodiment by this invention (white represents 1 and black represents 0). It is a figure which shows the example of the filter coefficient represented by the real part of the Gabor function in embodiment by this invention (The value of a filter coefficient is shown by the brightness). It is a figure which shows the digital filter which performs the one-dimensional convolution operation of a prior art. It is a figure which shows the digital filter which performs the separable two-dimensional convolution operation of a prior art.

Explanation of symbols

11-a ~ 1m-a delay element
11-b to 1m-b multiplier
11-c, 12-c, ... adder
2-1 One-dimensional filter
2-2 Buffer
2-3 One-dimensional filter
2-4 to 2-5 Filter coefficient
3-a / 3-b 2D convolution calculation execution means
3-a-1 / 3-a-3 / 3-b-1 / 3-b-3 one-dimensional filter
3-a-2 / 3-b-2 buffer
3-a-4 / 3-a-5 / 3-b-4 / 3-b-5 filter coefficient
3-c Adder / Subtracter

Claims (7)

For 2D digital data,
A first one-dimensional filter means for performing a one-dimensional convolution operation in the X direction; a second one-dimensional filter means for performing a one-dimensional convolution operation in the Y direction on the operation result of the first one-dimensional filter means; First computing means comprising:
A third one-dimensional filter means for performing a one-dimensional convolution operation in the X direction; a fourth one-dimensional filter means for performing a one-dimensional convolution operation in the Y direction on the operation result of the third one-dimensional filter means; Second computing means having
Addition / subtraction means for obtaining a sum or difference between the calculation result of the first calculation means and the calculation result of the second calculation means;
A two-dimensional digital filter system characterized by comprising: The first filter coefficient used by the first one-dimensional filter means during calculation is different from the third filter coefficient used by the third one-dimensional filter means during calculation,
2. The second filter coefficient used by the second one-dimensional filter means during calculation and the fourth filter coefficient used by the fourth one-dimensional filter means during calculation are different from each other. 2D digital filter system. The first filter coefficient h ₁₁ , the second filter coefficient h ₂₁ , the third filter coefficient h ₁₂ , and the fourth filter coefficient h ₂₂ are represented by h ₁₁ (x) * h ₂₁ (y) − h ₁₂ (x) * h ₂₂ (y) or h ₁₁ (x) * h ₂₁ (y) + h ₁₂ (x) * h ₂₂ (y) is a pattern with a directionality inclined on the xy plane The two-dimensional digital filter system according to claim 1, wherein the two-dimensional digital filter system is set. The first filter coefficient h ₁₁ , the second filter coefficient h ₂₁ , the third filter coefficient h ₁₂ , and the fourth filter coefficient h ₂₂ are obtained by the following equations: The two-dimensional digital filter system according to any one of 1 to 3.

[However, Re represents the real part, and Im represents the imaginary part. ] In the above formula,
The curve g ₁ (x) + g ₂ (y) = constant has a substantially constant slope in the region 1 ≦ x ≦ m, 1 ≦ y ≦ m, where m is the size of the filter. 4. The two-dimensional digital filter system according to 4. For 2D digital data,
A first one-dimensional filter step that performs a one-dimensional convolution operation in the X direction; a second one-dimensional filter step that performs a one-dimensional convolution operation in the Y direction on the calculation result of the first one-dimensional filter step; A first calculation step including:
A third one-dimensional filter step for performing a one-dimensional convolution operation in the X direction; a fourth one-dimensional filter step for performing a one-dimensional convolution operation in the Y direction on the operation result of the third one-dimensional filter step; A second calculation step including:
An addition / subtraction step for obtaining a sum or difference between the calculation result of the first calculation step and the calculation result of the second calculation step;
A two-dimensional digital filtering method comprising: Digital signal processing equipment,
For 2D digital data,
A first one-dimensional filter means for performing a one-dimensional convolution operation in the X direction; a second one-dimensional filter means for performing a one-dimensional convolution operation in the Y direction on the operation result of the first one-dimensional filter means; First computing means comprising:
A third one-dimensional filter means for performing a one-dimensional convolution operation in the X direction; a fourth one-dimensional filter means for performing a one-dimensional convolution operation in the Y direction on the operation result of the third one-dimensional filter means; Second computing means having
Addition / subtraction means for obtaining a sum or difference between the calculation result of the first calculation means and the calculation result of the second calculation means;
A program characterized by functioning as a two-dimensional digital filter system.

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