JP4520962B2 - Similarity calculation device and similarity calculation program - Google Patents

Description

  The present invention relates to a similarity calculation apparatus, a similarity calculation method, and a program for calculating an inner product of differential processing results of digital data and further calculating a correlation coefficient at high speed using the inner product.

  It is a very important process in signal processing to calculate the similarity of result data obtained by digitizing continuous data. Conventionally, many speed-up methods for calculating the degree of similarity between data have been proposed (for example, Non-Patent Document 1, Patent Document 1, and Patent Document 2 below). These methods are methods of speeding up purely during calculation for data digitized by some method.

  On the other hand, a method has also been proposed in which matching is performed after performing feature extraction (feature points and edge extraction) for images. These methods mainly used for stereo matching and tracking limit collation to feature points, edge points, etc. (Patent Document 3 below). That is, it is a method of reducing the amount of calculation by limiting the processing area. This method can be applied to patterns with clear edges, but is difficult to apply to general multi-value data.

Further, as a method for devising the processing of data after differentiation in an image, for example, Patent Document 4 and Patent Document 5 below are proposed. In other words, the result of the differentiation process is defined as the gradient of the pixel change, and the process is sequentially performed for each pixel while being able to be cut off. This method is a process of performing sequential processing for each corresponding pixel.
JP 2000-76444 A Patent No. 3680826 Patent No. 2981382 Japanese Patent Laid-Open No. 9-54828 JP-A-10-162143 Image analysis handbook, supervised by Mikio Takagi and Yoji Shimoda, The University of Tokyo Press, 1991, first edition, (708, 709 pages)

An object of the present invention is to show a method of performing an inner product operation without performing a differentiation process on each data when calculating an inner product calculation or a correlation coefficient after performing a differentiation process to obtain a similarity. This provides a similarity calculation device and a similarity calculation program that can reduce the calculation amount of the preprocessing and the similarity calculation process, and at the same time reduce the calculation amount according to the required accuracy.

The similarity calculation apparatus according to claim 1 for solving the above-mentioned problem is a similarity calculation apparatus for calculating similarity of digital data that can be regarded as differentiable, wherein the first continuous digital data is calculated. Differential processing means for performing differential processing, step function group generating means for storing a step function group obtained by decomposing the result obtained from the differential processing means into a total of step functions, and a second continuous function with the step function utilizing the digital data, to have the inner product calculation processing means for calculating the integral of the multiplied value of the differential value of the digital data to be continuous differential value and the second digital continuous data of the first as the inner product It is characterized by.

In the above configuration, since the step function group expressing the differential function as a rectangular stack (that is, decomposed into the sum of the step functions) is used, the differential processing is performed on the second continuous digital data. As a result, the inner product calculation is simplified and the calculation amount is greatly reduced.

The similarity calculation device according to claim 2 is the similarity calculation device for calculating the degree of similarity with respect to the digital data that can be regarded as differentiable, first to differential processing the first running digital data Differential processing means, step function group generating means for accumulating a step function group obtained by decomposing the result obtained from the differential processing means into a total of step functions, and the step function and second continuous digital data . and inner product calculation processing means for calculating the integral of the multiplied value of the differential value of the digital data to be continuous differential value and the second digital continuous data of the first utilized as the inner product value, to the second continuous a second differential processing means for differential processing of digital data, as a normalized coefficient square of the integral of the differential value of the digital data, Oyo digital data contiguous in the first The above second successive digital data, and each of the normalization coefficient calculation processing means for calculating a normalization factor after differential processing of the data, said inner product value and, said first running digital data and the second It has a correlation coefficient calculation means for calculating a correlation coefficient from the normalization coefficient after differentiation processing of each piece of digital data .

  In the above configuration, since the step function group that expresses the differential function as a stack of rectangles (that is, decomposed into the sum of the step functions) is used, the inner product calculation and correlation coefficient calculation are simplified and the amount of calculation is greatly increased. Reduced to

The similarity calculation apparatus according to claim 3 is characterized in that the digital data is digital image data.

The similarity calculation program according to claim 4, similarity calculation program for causing a computer to function as each means constituting the similarity calculation device according to any one of claims 1 to 3, as characterized Yes.

  As described above, when the correlation coefficient is calculated after performing differential processing on digital data such as time series and images, in principle, the same result is obtained compared to when differential processing and correlation count calculation are performed separately. It can be obtained with a small amount of calculation. Further, by adjusting the coefficients of the step function group, it is possible to obtain a calculation result with a predetermined arbitrary accuracy.

(1) According to the first, third, and fourth aspects of the invention, the step function group is used, and the second continuous digital data is not subjected to differentiation, so that the inner product calculation is simplified and the calculation amount is reduced. Is greatly reduced. Moreover, a calculated value can be obtained with arbitrary accuracy by adjusting the coefficients of the step function group.
(2) According to the invention described in claims 2, 3 and 4, when calculating the correlation coefficient after the differential processing, the differential correlation coefficient is calculated from the inner product value obtained using the step function group. Therefore, the calculation amount can be greatly reduced. Further, by adjusting the coefficient of the step function group, the calculated value can be obtained with an arbitrary accuracy.

Hereinafter, embodiments of the present invention will be described with reference to the drawings, but the present invention is not limited to the following embodiments. Figure 1 shows a structure of an example embodiment of the invention as set forth in claim 1, FIG. 2 shows a configuration of an example embodiment of the invention described in claim 2.

  In FIG. 1, 1-1 is data 1, 1-2 is a differential processing unit 1 as a first differential processing means of the present invention, and 1-3 is a step function group generating means of the present invention. 1 to 4 are step function groups, 1-5 is data 2, 1-6 is an inner product calculation processing unit as inner product calculation processing means of the present invention, 1 -7 is an inner product value.

  In FIG. 2, 2-1 is data 1, 2-2 is a differential processing unit 1 as a first differential processing means of the present invention, and 2-3 is a step function group generation of the present invention. A step function group generation unit as a means, 2-4 is a step function group, 2-5 is data 2, and 2-6 is an inner product calculation processing unit as an inner product calculation means of the present invention. 2-7 is an inner product value, which corresponds to FIG.

  Further, 2-8 is a first normalization coefficient calculation processing section (hereinafter referred to as normalization coefficient calculation processing 1) as normalization coefficient calculation processing means of the present invention, and 2-9 is a second for data 2. 2-10 is a differential processing unit (hereinafter referred to as differential processing unit 2), and 2-10 is a second normalization coefficient calculation processing unit (hereinafter referred to as normalization) as a normalization coefficient calculation processing unit of the present invention. 2-11 is a correlation coefficient calculation unit as correlation coefficient calculation means of the present invention, and 2-12 is a differential correlation coefficient.

  The differential processing unit 1 (1-2, 2-2), differential processing unit 2 (2-9), step function group generation unit (1-3, 2-3), inner product calculation processing unit (1-6) 2-6), normalization coefficient calculation process 1 (2-8), normalization coefficient calculation process 2 (2-10), and each process described later performed by the correlation coefficient calculation unit (2-11) is, for example, a computer. Is what you do.

  Data 1 (1-1, 2-1) and data 2 (1-5, 2-5) are input data. The origin of this data is some continuous value, for example, data that is continuous in the time direction like audio data or data that has two-dimensional continuity like image data. In general, time-series observation values, spatially obtained continuous values, or a combination thereof can be considered.

  Hereinafter, data 1 is described as f (x) and data 2 is described as g (x). Here, x may be considered to be one-dimensional in the case of audio data and two-dimensional in the case of image data.

  The differential processing unit 1 (1-2, 2-2) calculates the differential f ′ (x) of the data 1f (x). In the case of two dimensions

Calculate Actually, since the data is digital, it may be calculated using difference processing or a filter for differentiation.

  The step function group generation unit (1-3, 2-3) calculates a step function group defined below using the differential f ′ (x) of the already calculated data 1f (x). Since this function is actually digital data,

Can be written. Where k _i is a constant,

Is a step function that takes only values of 0 and 1. There are various methods for generating the step function group. Although this generation method is not specified here, an example of this generation method will be described later with reference to FIGS.

Obtained in step function set generator {k _i, x _i} is a step function group (1-4,2-4). Hereinafter, k _{i is referred} to as a coefficient, and x _i is referred to as a step function.

  Data 2 (1-5, 2-5) is the second data. As with data 1, it is assumed that a value that was originally a continuous value is digitalized.

  The inner product calculation processing units (1-6, 2-6) are processes for calculating inner product values of the differential processing results of data 1 and data 2. The step function group (1-4, 2-4) and data 2 (1-5, 2-5) are used here. In the inner product formula

Substituting and expanding

Is obtained. That is, the inner product values (1-7, 2-7) are obtained without performing differentiation on the data 2.

  This indicates that the calculation amount of the inner product value has increased in proportion to the length and area until now, but this can be avoided by converting it to the step function form. It also shows that the calculation amount can be controlled by reducing the number of steps of the step function as much as possible, and that the accuracy can be lowered while reducing the calculation amount by reducing the number of steps.

  The above inner product value (1-7) is the result of claim 1.

  Next, a method for calculating the differential correlation coefficient (2-12) for obtaining claim 2 will be described. First, in FIG. 2, the normalization coefficient is obtained by using the result of the differential processing unit 1 (2-2).

Calculate This process is the normalization coefficient calculation process 1 (2-8). For data 2, the differential processing result is obtained from the differential processing unit 2 (2-9), and further in the normalized coefficient calculation processing unit 2 (2-10).

Calculate

The correlation coefficient calculation unit (2-11) calculates the correlation coefficient using the inner product value (2-7) and the normalization coefficients of data 1 and data 2 respectively.
The correlation coefficient is

Therefore, it can be calculated by the product and division of the three values already obtained by the above equations (5), (6), and (7).

  In the process of calculating the normalization coefficient of data 1, the above equation (6) is used.

Or by applying the method shown in claim 1,

You may calculate in the form. Also,

It is also possible to perform the same processing by calculating x _i for g.

  In fact, it is clear that the same result can be obtained even if these calculations are performed on each data before the inner product operation.

  Further, it is possible to pre-process each data. For example, smoothing for cutting high-frequency components, a method of correcting the influence of contrast, for example, logarithmic conversion, etc., can be considered.

  In the above description, x has been described as one-dimensional, but actually it may be two-dimensional or more like a digital image. In the case of two dimensions like an image, the equation is as follows. First, the inner product value to be calculated is

It is. Therefore, a step function group is created for each differentiation in the x direction and the y direction. In practice, a step function group of x-direction differentiation is calculated for each y. Conversely, a step function group of y-direction differentiation is calculated for each x. This can be expressed as an expression:

x _{(y, i)} and x _{(x, i)} are step functions determined for each y and each x, respectively. The ranges in which x _{(y, i)} and x _{(x, i)} take non-zero values are [x _1i , x _2i ] and [y _1i , y _2i ], respectively. In this case, the correlation coefficient after post-differentiation processing is

It becomes.

  Furthermore, although the above is shown as processing in the x and y directions (horizontal and vertical directions), it is clear that in actuality coordinate processing can be performed to perform diagonal processing.

Next, a specific example of a method for creating a step function group will be described with reference to FIGS. Each figure illustrates the synthesis of a step function group. Both are realized by a method of approximating the curve of differentiated data 1 (f ′) with digital data. Each rectangle corresponds to each k _i x _i .

In FIG. 3, the size of all step function platforms (non-zero range) is 1. This is represented by an equation in which x _2i −x _1i = 1 holds for x _1i and x _2i corresponding to each x _i . In this case, the amount of calculation required is the same as the number of data points, and in reality, an equivalent amount of calculation is required for direct calculation.

In FIG. 4, f ′ is configured by superimposing k _i as a small value. Specifically, k _i x _i is constructed by obtaining x that f ′ exceeds a certain value and x that is less than the same value.

Figure 5 is a turn give way a large k _i. K _i x _i is configured for a predetermined large k _i , and then a smaller k _i is set for the deficient portion at the beginning and the same processing is repeated. In this figure, in the next step of k _i , the value is illustrated in half.

When this is expressed by an equation, first, a value K ₀ exceeding half of the maximum value of f ′ is set. f 'is (x) -K ₀ to set the x _i select the area to become a plus. In this case, a plurality of x _i are obtained, and k _i = K _{0 in} all of them. In this case, in f ′ (x) originally taking a positive value,

It becomes. (The sum here is in the range of k _i = K _0. ) Next, similar processing is performed on this result with K ₁ = K _0/2 . In addition, a step function group can be generated by determining whether f ′ (x) is a negative value and performing the same processing.

  In addition, there are various methods for approximating a function using a step function group. Naturally, the method of FIGS. 3 to 5 can be applied even to two-dimensional data such as an image.

  The correlation coefficient calculation unit (2-11) is an unnecessary process if the value is normalized before calculating the inner product. What is necessary is just to normalize the data by differentiating the data in advance and calculating the coefficients necessary for normalization. The process is shown by an expression:

It becomes.

The above configuration is an embodiment in which the correlation coefficient is a similarity, but also for an index (in this case, the smaller the better) that is often used other than the correlation coefficient, It is clear that the present invention can be applied from simple formula variations. The equation is (a−b) ² = a ² + b ² −2 (ab) ² , that is

Then, the sum of squares on the right side is a constant, and by applying the present invention to the last term on the right side,

Can be calculated in the same way.

  The input image data (1-1, 1-5, 2-1, 2-5) and the step function group (1-4, 2-4) can be stored in a memory and used. .

  In the present invention, a program for causing a computer to execute the similarity calculation method is constructed.

  It is also possible to supply a recording medium recording the program to a system or apparatus, and the CPU (MPU) of the system or apparatus reads and executes the program stored in the recording medium. In this case, the program itself read from the recording medium realizes the functions of the above-described embodiment, and examples of the recording medium on which the program is recorded include CD-ROM, DVD-ROM, CD-R, CD- There are RW, MO, and HDD.

The block diagram which shows one embodiment of this invention. The block diagram which shows the other embodiment of this invention. Explanatory drawing which shows an example of the specific preparation method of the step function group in the embodiment of this invention. Explanatory drawing which shows the other example of the specific production method of the step function group in the embodiment of this invention. Explanatory drawing which shows the other example of the specific production method of the step function group in the embodiment of this invention.

Explanation of symbols

1-1, 2-1 ... data 1, 1-2, 2-2 ... differentiation processing unit 1, 1-3 ... step function group generation unit, 1-4, 2-4 ... step function group, 1-5 2-5 ... data 2, 1-6, 2-6 ... inner product calculation processing unit, 1-7, 2-7 ... inner product value, 2-8 ... first normalization coefficient calculation processing unit (normalization coefficient calculation processing 1 ), 2-9 ... differentiation processing unit (differentiation processing unit 2), 2-10 ... second normalization coefficient calculation processing unit (normalization coefficient calculation processing 2), 2-11 ... correlation coefficient calculation unit, 2-12 ... differential correlation coefficient.

Claims (4)

A similarity calculator for calculating the similarity of digital data that can be considered differentiable,
Differential processing means for differential processing the first continuous digital data ;
Step function group generation means for accumulating a step function group obtained by decomposing the result obtained from the differential processing means into a total of step functions;
Using the step function and the second continuous digital data , the integral of the product of the differential value of the first continuous digital data and the differential value of the second continuous digital data is calculated as an inner product value. A similarity calculation device comprising: an inner product calculation processing means. A similarity calculator for calculating the similarity of digital data that can be considered differentiable,
First differential processing means for differentially processing the first continuous digital data ;
Step function group generation means for accumulating a step function group obtained by decomposing the result obtained from the differential processing means into a total of step functions;
Using the step function and the second continuous digital data , an integral of a product of a differential value of the first continuous digital data and a differential value of the second continuous digital data is calculated as an inner product value . Inner product calculation means;
Second differential processing means for differential processing the second continuous digital data ;
Normal that calculates a normalization coefficient after differential processing of each of the first continuous digital data and the second continuous digital data, using the square integral of the differential value of the digital data as a normalization coefficient Conversion factor calculation processing means,
Correlation coefficient calculation means for calculating a correlation coefficient from the normalized coefficient after differential processing of each of the inner product value and the first continuous digital data and the second continuous digital data. The similarity calculation apparatus characterized by the above.   The similarity calculation apparatus according to claim 1, wherein the digital data is digital image data.   The similarity calculation program for functioning a computer as each means which comprises the similarity calculation apparatus of any one of Claim 1 thru | or 3.

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