JPH09245166A - Pattern matching device - Google Patents

Abstract

(57) Abstract: The same pattern as the reference pattern on the inspection target image is calculated by performing a correlation calculation using each pixel of the reference pattern and the corresponding pixel of the inspection target image for each scanning position on the inspection target image. The processing time of pattern matching for detecting the position where is present is shortened. SOLUTION: For each pixel of a reference pattern area 11 of an input image having a reference pattern, a directional maximum edge feature amount, which is a maximum value of a difference in density between adjacent pixels in the eight directions, is detected, and the detected maximum directional edge feature amount is equal to or more than a predetermined value. A pixel having a maximum directional edge feature amount is extracted to obtain an image 401 having a noise component 4A and a reference pattern component 1A. Further, among the pixels in the components 1A and 4A, connected pixels in which the direction of the directional maximum edge feature amount is continuous and belonging to a pixel group of a predetermined number of pixels or more are extracted to remove the noise component 4A, and a matching pixel for matching is extracted. Use as a reference pixel.

Description

Detailed Description of the Invention

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention determines whether or not there is a match between a reference image (also referred to as a reference pattern) registered in advance and a grayscale image obtained by capturing an image of an inspection object, the position of the match, and the like. More specifically, the present invention relates to a pattern matching device that discriminates by a so-called pattern matching method, and particularly to a pattern matching device that can reduce the amount of calculation. In the following figures, the same reference numerals indicate the same or corresponding parts.

2. Description of the Related Art In an apparatus for pattern matching, a correlation coefficient (also called a normalized correlation value) is generally used as a measure for measuring the degree of coincidence between a grayscale image of an inspection object (referred to as an inspection object image) and a reference image. It is used for. FIG. 9 is an explanatory diagram of a pattern matching method when determining the position of the inspection object by checking the degree of coincidence of images by calculating the correlation coefficient. In the figure, 11 is a reference pattern area as a rectangular image area prepared in advance including a reference pattern, 1 is a reference pattern as a true matching target pattern in the reference pattern area 11, and 2 is an object. It is an inspection target image as a grayscale input image obtained based on imaging. In this example, the position of the reference pattern 1 (represented by the coordinates of the upper left corner of the reference pattern region 11) is sequentially set at each coordinate point (referred to as a scanning position) Qj starting from the coordinates of the upper left corner on the inspection target image 2. While moving (scanning) each pixel, all the pixels on the reference pattern area 11 are set as the target pixel, and the density of each target pixel and the pixel on the inspection target image 2 at the position corresponding to each target pixel are set. From the density, the correlation coefficient with the image of the portion overlapping the reference pattern area 11 on the inspection target image 2 is obtained, and the inspection is performed as the scanning position Qj at which the correlation coefficient is equal to or larger than a predetermined threshold value and is maximum. The position where the same image pattern as the reference pattern 1 on the target image 2 exists is detected. Here, the coordinates of Qj as the j-th scanning position on the inspection target image 2 in the reference pattern area 11 are (Xj, Yj), the density of the i-th pixel in the reference pattern area 11 is Fi, and the inspection target image 2 corresponds to Let Gi be the pixel to be defined and N be the number of pixels constituting the reference pattern region 11, then the correlation coefficient Rj = R at the scanning position Qj.
(Xj, Yj) is given by the following equation (1).

[Number 1] Rj = R (Xj, Yj) = [N · N Σ i = 0 (Fi · Gi) - (N Σ i = 0 Fi) · (N Σ i = 0 Gi)] / [{N · ^N Σ _{i = 0} Fi ² − ( ^N Σ _{i = 0} Fi) ² } × {N · ^N Σ _{i = 0} Gi ² − ( ^N Σ _{i = 0} Gi) ² }] ^1/2 ... (1) As can be seen from the equation (1), 1 at a certain scanning position Qj
In order to obtain the correlation coefficient at a point, it is necessary to perform a large amount of integration and cumulative addition. Therefore, conventionally, in order to reduce the amount of calculation, a method of reducing the amount of calculation by extracting a characteristic portion such as a thinned image or an edge image from the reference image and using only the characteristic pixels as the reference image, For example, a method is used in which the amount of calculation is further reduced by performing a certain thinning after obtaining the edge feature.

However, the above-mentioned conventional pattern matching method has the following problems. (1) In creating a reference image based on edge features, edge features are also extracted from noise components included in the background and included in the reference image. (2) When further thinning out the pixels selected by the edge feature, the simple thinning out also thins out pixels having high features, that is, pixels representing more features depending on the pattern. (3) Even in the pattern matching processing in a portion where the same pattern as the reference pattern on the inspection target image does not exist, it is necessary to calculate up to the last pixel of the reference image. Therefore, an object of the present invention is to provide a pattern matching device capable of solving such a problem.

According to a first aspect of the present invention, there is provided a pattern matching device for performing pattern matching between a registered reference image (reference pattern 1) and a grayscale image to be inspected. Of the absolute value of the density difference in each direction between each pixel forming a predetermined image area (reference pattern area 11) including the reference image in advance and the adjacent pixel in eight directions centering on the pixel, The maximum value (E (X, Y), hereinafter referred to as the maximum directional edge feature amount) of the pixel, and the pixel whose pattern maximum directional edge feature amount is equal to or greater than a predetermined threshold value (TH1) is subjected to pattern matching. Means to extract as target pixel (direction component
The edge feature quantity extraction unit 108) is provided. A pattern matching device according to claim 2 is the device according to claim 1, further comprising: from the extracted target pixel,
Predetermined number of pixels (threshold value TH2 of noise level pixel number)
Means for extracting as effective target pixels only pixels that belong to the connected pixel group and that are composed of the above connected pixels and in which the directions of the maximum directional edge features of adjacent pixels match or are adjacent to each other (direction component / edge Feature quantity extraction unit 10
8). A pattern matching device according to claim 3 is the device according to claim 1 or 2, wherein
From the finally extracted target pixel, a predetermined number of pixels (threshold value TH4) with respect to the total number of target pixels are arranged in order from the one having the largest directional maximum edge feature amount (the shape of the reference pixel data 601). Reference pixel selecting means (histogram creating section 11) for selecting an effective target pixel
8). A pattern matching device according to a fourth aspect is the device according to the third aspect, in which a predetermined ratio (threshold value TH from the target pixels selected through the reference pixel selection means to the total number of the target pixels is used).
5) the correlation coefficient (R) obtained by using the target pixels selected in order from the largest directional maximum edge feature amount
When j) is equal to or smaller than a predetermined value (threshold value TH6), a unit (correlation calculation unit 115) that terminates the pattern matching process at the scanning position is provided. The operation of the present invention is as follows. That is, the reference image is registered,
An apparatus for performing pattern matching on a grayscale image to be inspected, 1) In the invention according to claim 1, an image region (reference pattern region 11) including a reference image (reference pattern 1)
The target pixel used for the pattern matching is extracted from a limited amount to reduce the calculation amount. As an extraction method of this pixel, an edge feature amount (difference in pixel density) in eight directions is obtained for each pixel of the reference pattern region 11, and Among the edge feature amounts for each direction, only pixels whose maximum edge feature amount (directional maximum edge feature amount) is equal to or greater than a certain threshold value are extracted and set as candidates for a pixel to be subjected to pattern matching. 2) In the invention according to claim 2, in order to further eliminate noise components from the extracted pixels, the extracted pixels are adjacent to each other with the directions of the maximum directional edge features being the same or close to each other. Pixels that are present are grouped, only those in which the number of pixels in each group is equal to or greater than a predetermined value are extracted, and these extracted pixels are set as target pixels for pattern matching. 3) In the invention according to claim 3, the number of pixels for each size of the directional maximum edge feature amount of the pixel group extracted as in the above 1) or 2) is calculated, and the directional maximum edge feature amount of In addition to creating a histogram in which the number of pixels is arranged in order of size, a predetermined threshold value for the total number of extracted pixels is set, and pixels from this pixel with the largest directional maximum edge feature amount to the threshold value And extract these extracted pixels as new target pixels (also called reference pixels)
As pattern matching. 4) In the invention according to claim 4, when pattern matching is performed using the pixel group extracted as in 3) above as a new reference pixel, the pixels are sequentially arranged from the pixel having the highest edge feature amount of the new reference pixel. One by one up to the number of pixels of a predetermined ratio to the total number of extracted pixels, and each time the degree of coincidence (correlation coefficient) is obtained (therefore, the number of reference pixels when calculating the correlation coefficient is Increase by one). When the degree of matching up to the predetermined number of pixels is smaller than the predetermined threshold value, the pattern matching process is terminated at that point, and the pattern matching at the next scanning position Qj is started.

BEST MODE FOR CARRYING OUT THE INVENTION

(Embodiment 1) First, an embodiment of the invention relating to claims 1 and 2 will be described. FIG. 1 is a block diagram showing a configuration of a pattern matching device as an embodiment of the invention relating to all claims, and FIG. 2 is an input image diagram including a reference pattern. Next, the configuration and operation of this embodiment shown in FIG. 1 will be described with reference to FIGS. An image 201 including the reference pattern 1 shown in FIG. 2 is input by the image input unit 101, and the input analog image signal is converted by the A / D conversion unit 102 into a digital grayscale image. The converted digital image is used as a work frame memory 103 and a display-only display memory 1
11 is stored. In addition, this image is displayed on the D / A conversion unit 10.
4 is also displayed on the monitor 105 via the display memory 111.
The above image can also be displayed on the monitor 105. Monitor 10
An input image 201 is displayed on the screen 5, and the area 11 of the reference pattern 1 is designated by the setting means 106 such as a mouse. As a result, the CPU 107 sets the designated reference pattern region 11 and the designated edge feature amount (that is, the target pixel as described later and the eight directions centering on the target pixel (see FIG. 5B)). The threshold value TH1 of the difference in density value between adjacent pixels) and the noise level pixel number TH2 are
The direction component / edge feature amount extraction unit 108 is instructed. CP
U107 also has a main memory 119. The direction component / edge feature amount extraction unit 108 applies an operator represented by the following equation (2) to each pixel in the designated reference pattern area 11.

## EQU00002 ## max (| P0-P1 |, | P0-P2 |, ..., | P0-P8 |) (2) Here, P0 is the density value of the pixel of interest, as shown in FIG. , P
1 to P8 are density values of eight adjacent pixels centered on the pixel of interest in each direction. Therefore, | P0-P in equation (2)
Eight absolute values from 1 | to | P0-P8 | are absolute values of differences in density values for each direction with respect to the pixel of interest P0 (that is, edge feature amounts), and equation (2) is the eight absolute difference values. It means to find the largest one of them (referred to as the directional maximum edge feature amount). In this way, the direction component / edge feature quantity extraction unit 108 determines the maximum directional edge feature quantity (E (X, Y)) for each pixel (coordinates are (X, Y)) of the designated reference pattern area 11. And a value indicating the direction (referred to as a direction component and represented by θ (X, Y)). The value of the direction component θ for each of the eight directions is shown in FIG.
It shall be defined as in (B). Further, the direction component / edge feature amount extraction unit 108 selects the set threshold value TH1 of the edge feature amount from the directionality maximum edge feature amount E (X, Y) for each pixel thus obtained. Used,
Only pixels satisfying the following expression (3) are extracted and stored in the work memory 109.

## EQU00003 ## E (X, Y) .gtoreq.TH1 (3) 401 in FIG. 4 is an image (corresponding to the input image 201) consisting of only the pixels extracted by the equation (3). This image 4
01 includes a reference pattern component 1A and a noise component 4A as shown in FIG. Further, the direction component / edge feature amount extraction unit 108 performs labeling processing on the image 401 of FIG. 4 based on the extracted direction component θ (X, Y) of each pixel. FIG. 5A shows an example of the extracted direction component θ (X, Y) for each pixel. The numerical value in each pixel indicated by a square represents the value of the direction component (defined for each of the eight directions as shown in FIG. 7B) for the pixel. In order to perform the labeling, as shown in FIG. 5A, in the three pixels adjacent to each other in the pixel group extracted by the directional maximum edge feature amount, the direction components are the same or close (adjacent to each other) as in the extracted pixel group 501. If they are in the same direction, they are labeled as the same group. However, even if they are adjacent to each other like the pixel group 502, if the directions do not match, they are not included in the same group. Of the pixel groups grouped in this way,
Only the groups having the noise level pixel number threshold value TH2 or more are extracted. As a result, the noise component 4A (of the reference pattern area 11) of the image 401 of FIG. 4 is removed. In this embodiment, the directional component continuity detection range is three pixels, but it can be changed by setting. By increasing the number of pixels, it becomes possible to remove a larger noise component. The direction component / edge feature amount extraction unit 108 is a diagram of the X and Y coordinate values of each pixel (referred to as a reference pixel) obtained as a result of the above processing and the density value D of that pixel in the original input image 201. List-format data 601 (referred to as reference pixel data) 601 is created in the memory 110. In FIG. 6, the coordinate value of the reference pixel is generally represented by (Xmi, Ymi), and the density value is represented by Di. However, i is a subscript indicating the number of n reference pixels.
The reference pixel data 601 of FIG. 6 is stored in the auxiliary storage unit 112 by the CPU 107. Inspection of an inspection target image using each reference pixel of the reference pixel data 601 of FIG.
When execution of measurement is instructed using the monitor 105 and the setting means 106, the CPU 107 transfers the reference pixel data 601 stored in the auxiliary storage unit 112 to the reference pixel memory 113 for correlation calculation, while The image to be inspected is transferred to the inspection image memory 114 for correlation calculation via the image input unit 101, the A / D conversion unit 102, and the work frame memory 103. Therefore, the correlation calculator 115 performs the above-described correlation calculation on the image in the inspection image memory 114 by using each reference pixel of the reference pixel data 601 in the reference pixel memory 113 as a target pixel, and each scanning position Qj of the inspection target image. The correlation coefficient (coincidence) Rj = R (Xj, Yj) obtained for each (coordinates are (Xj, Yj)) is stored in the correlation coefficient memory 116 capable of storing real number data. Note that j
Is a subscript indicating the number of the scanning position. In this correlation coefficient memory 116, the scanning position Qj in the inspection target image having the maximum correlation coefficient and the degree of coincidence equal to or greater than the threshold value TH3 is the position where the same pattern as the reference pattern 1 is detected. Is obtained. The correlation calculation unit 115 scans all of the specified correlation coefficient thresholds TH3 or more in the inspection region of the inspection target image instructed using the monitor 105 and the setting unit 106 (all regions unless otherwise specified). With respect to the position Qj, the coordinate value (Xj, Yj) and the correlation coefficient Rj are output as the scanning position-based correlation coefficient 701 in FIG. Based on this information, the CPU 107 can display the inspection / measurement result on the monitor 105 or output it from the I / O input / output unit 117 to notify the outside.
Further, in the above, after detecting and calculating the directional maximum edge feature amount E (X, Y) and its direction component θ (X, Y), processing such as expansion / contraction is performed in order to correct blurring of the edge feature. May be given. (Embodiment 2) Next, an embodiment of the invention according to claim 3 will be described. In the present invention, the histogram creation unit 118 is provided in the apparatus of FIG. 1 described in the first embodiment. As shown in FIG. 8, the histogram creation unit 118 uses the maximum directional edge feature amount E (Xm for the reference pixel data 601 in the memory 110 created by the direction component / edge feature amount extraction unit 108 as shown in FIG.
i, Ymi) in order of size, a histogram 80 in which the numbers of pixels N1 to Nn corresponding to the size are compared and arranged.
Create 1. At the same time, the histogram 801
Direction maximum edge feature amount E (Xmi, Y
coordinates (Xmi, Ymi) of each reference pixel corresponding to (mi)
And the density value Di are also registered. Further, when the CPU 107 sets the threshold value TH4 of the maximum directional edge feature amount in the histogram creation unit 118, the histogram creation unit 118 extracts only the pixels having the threshold value TH4 or more from the created histogram 801. Then, the reference pixel data 601 is arranged and updated in order from the highest directional maximum edge feature amount E. This threshold value TH4 not only specifies the maximum directional edge feature amount, but also the reference pixel data 60.
The percentage may be designated such that, for example, 10% of the total number of pixels is a valid reference pixel. In this case, a selection flag for selecting whether the threshold TH4 is the directional maximum edge feature amount or a percentage with respect to the total number of pixels is provided, and this is set as a percentage designation. Further, the threshold value of the directional maximum edge feature amount and the threshold value of the above percentage are provided independently at the same time, and only the reference pixels satisfying both of these two threshold values are selected to direct the reference pixel data 601. It may be arranged and updated in descending order of the maximum feature edge feature amount. Since the histogram creation unit 118 holds the histogram 801 inside, once the histogram 801 is created, if the threshold TH4 is changed, the reference pixel data 60 is automatically created.
1 can be updated instantly. This function is used when performing test inspections and measurements at the setting stage. C
The PU 107 stores the reference pixel data 601 in the auxiliary storage unit 112, and at the same time, the histogram creation unit 118.
The histogram 801 stored inside the
Saved to 12. The subsequent pattern matching processing is the same as in the first embodiment. (Embodiment 3) Next, an embodiment of the invention according to claim 4 will be described. The correlation calculator 115 described in the first and second embodiments is
Reference pixel data 60 for each scanning position Qj of the inspection target image
The correlation coefficient Rj obtained by using all the points of the reference pixel designated by 1 is stored in the correlation coefficient memory 116. In the present embodiment, the correlation calculation unit 115 has an interruption processing function.
That is, in the present embodiment, the correlation calculation unit 115 counts the pixels of the reference pixel data 601 created by arranging the reference pixels in the descending order of the maximum directional maximum edge feature amount as described in the second embodiment, from the one with the largest edge feature amount. , The ratio of that number to the total number of pixels of the reference pixel data 601 is the threshold value TH5.
For each reference pixel group up to [%], the correlation coefficient Rj obtained using this reference pixel group is output to the correlation coefficient memory 116, and the correlation coefficient Rj at that time and the threshold value TH6 are compared. To do. The reference pixel data 601 are arranged in descending order of the maximum directional edge feature amount E, and if the correlation coefficient Rj does not reach the threshold value TH6 at this point, there is no pattern identical to the reference pattern 1 at that position. Can be determined. Further, if the threshold value TH7 that defines the hold state is used, if all the correlation pixels Rj = R (Xj, Yj) are in a range that satisfies the following expression (4), all the pixels in the reference pixel data 601 are further calculated. The pattern matching using the threshold value TH5 [%] (therefore, the total number of the reference pixels used for the pattern matching at this point is (TH5 × 2) [%]). Then, the same processing is performed. This makes it possible to prevent detection omission.

TH6> R (Xj, Yj) ≧ TH7 (4) where the correlation coefficient Rj is the threshold value TH6 (threshold value TH7
Is less than TH7), or if the correlation coefficient Rj is less than the threshold value TH6 even when using reference pixels exceeding 50% of the total number of reference pixels,
The pattern matching process at the scanning position Qj is forcibly stopped, the process moves to the next scanning position Qj in the inspection region of the inspected image to be inspected, and the same pattern matching process is executed. At this time, "-1.0" is stored as the value of the correlation coefficient memory 116 at the scanning position Qj in which the pattern matching process is terminated, and it is possible to retrieve at which point the abort process was performed later. is there. When the pattern matching processing is completed at all the scanning positions within the inspection area, the processing for obtaining the position where the same pattern as the reference pattern is present is performed by mutual comparison with the magnitude of the correlation coefficient obtained as in the first embodiment.

【The invention's effect】

1) According to the inventions according to claims 1 and 2, the maximum value of the density difference in each of the eight directions for all the pixels of the reference pattern area, and the directional maximum edge feature amount equal to or more than a predetermined value and the direction component thereof are set. A reference pixel located at the edge portion of the reference pattern from which the noise component has been removed is extracted by detecting and extracting more than a predetermined number of pixels from the connected pixel group in which the direction component is continuous, and this reference pixel is used. Since the pattern matching with the image to be inspected is performed, the processing time of the correlation calculation can be shortened and the erroneous detection of the reference pattern can be prevented. 2) According to the invention according to claim 3, a histogram in which the number of pixels for each size is arranged in order of the size of the directional maximum edge feature amount of each reference pixel extracted as in the above 1) By using a predetermined threshold value such as the size of the maximum directional edge feature amount or the ratio to the total number of pixels, the group of reference pixels on the side with the maximum directional maximum edge feature amount is effective on this histogram. Since the effective reference pixel is used as the target pixel and the pattern matching process is performed with the effective reference pixel as the target pixel, it is possible to reduce the number of reference pixels and reduce the processing time without degrading the detection accuracy. Further, by holding the histogram inside, it becomes possible to instantly update the reference pixel by changing the threshold value (setting value). 3) According to the invention according to claim 4, a reference pixel selected from the one having a larger directional maximum edge feature amount in a predetermined ratio to the total number of reference pixels extracted as effective in 2) above. If the correlation coefficient based on the pattern matching process using is equal to or less than a predetermined value, the pattern matching process at the scanning position is terminated, so that the same pattern as the reference pattern does not exist, and overwhelmingly many scans are performed. The processing required for pattern matching at the position can be largely omitted, and the processing time can be greatly shortened.

[Brief description of drawings]

FIG. 1 is a block diagram showing the configuration of a pattern matching device as an embodiment of the present invention.

FIG. 2 is a diagram showing an example of an input image including a reference pattern.

FIG. 3 is an explanatory diagram of a target pixel area when obtaining the directional maximum edge feature amount of a pixel of interest based on the present invention.

FIG. 4 is a diagram showing an image after performing pixel extraction by the maximum directional edge feature amount on the input image of FIG. 2 according to the present invention.

FIG. 5 is an explanatory diagram of continuity of direction data of connected pixels according to the present invention.

FIG. 6 is a diagram showing reference pixel data according to the present invention.

FIG. 7 is an explanatory diagram of a correlation calculation for each scanning position based on the present invention.

FIG. 8 is an explanatory diagram of a histogram for each directional maximum edge feature amount based on the present invention.

FIG. 9 is an explanatory diagram of conventional pattern matching.

[Explanation of symbols]

1 Reference Pattern 1A Reference Pattern Component 2 Inspection Image 4 Noise 4A Noise Component 11 Reference Pattern Area 101 Image Input Unit 102 A / D Converter 103 Work Frame Memory 104 D / A Converter 105 Monitor 106 Setting Means 107 CPU 108 Direction Component / edge feature amount extraction unit 109 work memory 110 memory 111 display memory 112 auxiliary storage unit 113 reference image memory 114 inspection image memory 115 correlation calculation unit 116 correlation coefficient memory 117 I / O input / output unit 118 histogram creation unit 119 main storage Memory 201 Input image P0 Pixel of interest, its density value P1 to P8 Adjacent pixels in directions 1 to 8 and its density value 401 Image composed of pixels extracted by directional maximum edge feature amount 501,502 Extraction by directional maximum edge feature amount Picture Group 601 Reference pixel data 701 Scan position correlation coefficient Qj, Q (Xj, Yj) Scan position (Xj, Yj) Scan position coordinate value Rj, R (Xj, Yj) Correlation coefficient (Xmi, Ymi) Reference pixel Coordinate value Di, D (X, Y) density value E (X, Y), E (Xmi, Ymi) directional maximum edge feature amount TH1 edge feature amount threshold TH2 noise level pixel number threshold TH3 Threshold of correlation coefficient TH4 Threshold of directional maximum edge feature amount, threshold of% to all reference pixels TH5 Threshold of% to all reference pixels TH6, TH7 Threshold of correlation coefficient

Claims (4)

[Claims] 1. A device for performing pattern matching between a registered reference image and a grayscale image to be inspected, with respect to each pixel forming a predetermined image area including the reference image, the pixel and the pixel are centered. The maximum value (hereinafter referred to as the directional maximum edge feature amount) of the absolute value of the density difference for each direction with the adjacent pixels in the eight directions is obtained, and if this maximum directional edge feature amount is greater than or equal to a predetermined threshold value. A pattern matching apparatus comprising means for extracting a certain pixel as a target pixel for pattern matching. 2. The apparatus according to claim 1, wherein the extracted target pixel is further composed of connected pixels of a predetermined number or more, and the directions of the maximum directional edge features of adjacent pixels are the same or adjacent to each other. A pattern matching device comprising means for extracting only pixels belonging to a connected pixel group having such a relationship as valid target pixels. 3. The apparatus according to claim 1 or 2, wherein a number of pixels of a predetermined ratio to the total number of target pixels finally extracted are larger in directional maximum edge feature amount. A pattern matching device comprising a reference pixel selection means for selecting valid target pixels in order from the one. 4. The apparatus according to claim 3, wherein the maximum number of directional edge features of the target pixels selected through the reference pixel selection unit is a predetermined ratio to the total number of target pixels. A pattern matching apparatus comprising means for terminating pattern matching processing at a scanning position when a correlation coefficient obtained by using target pixels selected in order from the largest one is less than a predetermined value.