JP2925707B2 - Edge feature measurement method - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for measuring an edge feature in a digital image, and is used for recognizing and measuring an object using image processing.

(Prior Art) When an image of a portion where the brightness of an object changes or the direction of a surface changes, that is, a boundary portion of an object is captured, the boundary portion of the object becomes a portion where the density changes stepwise in the image. In other words, a portion where the density in the image changes due to a change in the property of the object surface (reflectance and orientation of the surface) is an edge. The extraction of the edge feature is the most basic processing among various types of image processing. Information about edge features
It is indispensable when measuring the position of an object in an image or recognizing the object.

An edge is characterized using its position and orientation as shown in FIG. In FIG. 1, the center position of the pixel, that is, the position of the sample point is taken as the origin O, and the horizontal line passing through the origin O is taken as the x-axis and the vertical line is taken as the y-axis. Edge e from origin O
And a point of intersection with the edge e is defined as P. Assuming that the length of the perpendicular OP is ρ (edge position) and the direction between the perpendicular OP and the x axis is θ (edge direction), a step edge is represented by ρ = xcos θ + ysin θ (1). Each area divided by the step edge is represented by a density f ₁ and f ₂ , and f ₁ <f ₂ . The portion shown by the broken line in FIG. 1 is the boundary between pixels.

Many algorithms have been proposed for the edge feature measurement method. Here, as a conventional technique, a model fitting type edge feature measuring method proposed by Hueckel and an edge feature measuring method by referring to a table are taken from among them.

Hueckel's method is a model fitting type representative edge feature measurement method that belongs to the same category as the present invention, and the edge feature measurement method by referring to a table creates a correction table in advance by experiment in order to remove the effect at the time of image input It is to keep.

First, the method of inputting digital pixels and the effect on the image at this time will be described, and then the above-described two conventional techniques and their interim points will be described.

(Problems to be Solved by the Invention) When an object is imaged, reflected light from the object is imaged on a photoelectric conversion element by a lens of a camera, and here, one-dimensional video signals arranged in a time series while repeating horizontal scanning. Is converted to Then, this video signal output from the camera is digitized by an A / D converter, that is, sampled and quantized, and input to a computer memory as a two-dimensional image. When an image is input to the calculator in this way,
The image deteriorates due to various causes at the time of a lens system or photoelectric conversion.

The main causes are the blur added when forming an image with a lens, the afterimage that does not occur in the vertical scanning direction but occurs in the horizontal scanning direction when digitizing, and in a solid-state imaging device camera that has been frequently used recently, the horizontal This is a sensitivity difference due to a direction caused by a difference in shape and pitch of the photoelectric conversion element between the direction and the vertical direction. For these reasons, the image input to the computer does not become an ideal step edge even if the boundary portion of the object is imaged.

The edge model when Hueckel's idea is applied to the step edge is shown by the broken line in Fig. 2 (Shunji Mori, Tsugako Itakura: "Image recognition board (II)", p.
p.127-134, Ohmsha, 1990). As shown in FIG. 2, the edge model used by Hueckel is an ideal step edge model em. Let D be the calculation area used for calculating the edge feature, and let g (x, y) be the density of the input image at coordinates (x, y) when the center O of D is the origin. Here, an edge model in which the density there is m (x, y, ρ) is considered. Here, ρ is a parameter indicating the edge position, direction, and contrast, that is, an edge feature. As the difference between them _{wherein, [∫ D {g (x} , y) -m (x, y, ρ)} 2 dxdy] 1/2 ...... consider (2), nine orthonormal shown in Figure 3 Function H _i (i = 0 to
The edge feature that minimizes the equation (2) is calculated analytically using 8). That is, the edge direction θ is determined from the condition that minimizes the evaluation function E = (e ₂ cos θ + e ₃ sin θ) ² + e ₄ cos θ + e ₅ sin θ, and the edge position ρ and the like are determined using the result. However, e ₁ = (1/3) ^1/2 a ₁ ... (4) e ₂ = (1/3) ^1/2 a ₄ ... (5) e ₃ = (2/3) ^1/2 a _{5 ...... (6) e 4 =} 2e 1 e 2 + {a 2 2 + a 6 2 (a 3 2 + a 7 2)} / 2 ...... (7) e 5 = 2e 1 e 3 + e 2 e 3 + e 6 e ₇ is a ... (8), is _{a i = ∫ D H i (} x, y) g (x, y) dxdy, i = 0~8 ...... (9).

However, the edge density pattern of the input image does not become the ideal step edge model em as shown by the broken line in FIG. 2, and the real edge of the smooth density pattern as shown by the solid line due to the image deterioration described above. Model em 'is shown. As a result, the density pattern of the pixels near the edge is applied to an edge model that does not match the edge density pattern of the actual input image. Also, when calculating equation (9), _Hi
In order to realize (x, y), the calculation area D is 8 to 9 in diameter.
It is difficult to measure a local edge feature because a circular area of about a pixel, that is, 50 to 60 pixels is used.

On the other hand, as a table reference type, there is Japanese Patent Application No. 2-47247 (Ide et al .: "Method for Measuring Edge Direction of Digital Image"). In this method, a large number of images having different edge positions and edge directions are input at intervals that provide desired accuracy, and the edge positions and edge directions obtained from the images, and the actual edge positions and edge directions used for input are determined. Is determined in advance as a correction value. A correction table for obtaining a true edge position and an edge direction from the edge position and the edge direction thus measured is created. FIG. 4 shows an example of this correction table.

In FIG. 4, the horizontal axis and the vertical axis represent the measured edge position and edge direction, respectively, and the correction values are displayed as contour lines. In this method, for example, in order to obtain an edge direction table with an accuracy of 1 °, 360 accurate measurements of angles must be performed in advance.

Further, since it is necessary to obtain correction tables for various edge positions for each edge direction, it is difficult to efficiently create a reference correction table. Further, since all of the conventional methods are algorithms that are difficult to perform in parallel processing, a process of obtaining an edge feature by focusing on one edge pixel and moving the focused edge pixel one after another has been repeated. As a result, there is a problem that a long processing time is required.

(Object of the Invention) It is an object of the present invention to provide a method for accurately measuring an edge feature from a density pattern of pixels near an edge in a digital image.

(Means for Solving the Problems) In order to solve the above problems and achieve the object, the present invention provides an edge feature measuring method for measuring an edge position and a direction using the density of pixels near an edge in a digital image. And a first step of obtaining a mapping of a pixel near an edge onto a density pattern in consideration of a point spread function at the time of inputting a digital image with respect to a combination of a plurality of edge directions, and a plurality of steps calculated in the first step. A second step of determining a reverse mapping from the density pattern of the pixel near the edge to the edge position and the edge direction using an error back-propagation type neural network having the density as an input and the edge position and the edge direction as an output; Using the inverse mapping determined in the process, the edge position is determined from the density pattern of the pixels near the edge in the actually input arbitrary image. And a third step of calculating the position and the edge direction.

(Operation) In the present invention, not only the edge position and the edge direction which have been conventionally used as parameters as the edge feature, but also the point spread in the scanning line direction and the direction orthogonal to the scanning line direction as a function representing the image deterioration at the time of image input. Step edges are modeled taking into account the function. As a result, as shown by the solid line in FIG. 2, it is possible to use a more practical edge model in which an ideal step edge is blurred. In the following, this edge model is referred to as a real edge model e
Call it m '. The broken line in FIG. 2 is a conventional step edge model em. Using this edge model, an edge feature is obtained as follows.

Now, let the edge position and the edge direction be a two-dimensional vector q, and let the density of a plurality of pixels near the edge be g (x, y).
The mapping to (x, y) is A ', and the inverse mapping of A', that is, g
(X, y), the mapping from the q, q, g (x, y), the relationship of A, q = A (g (x 1, y 1), g (x 2, y 2), .., G (x _i , y _i ),...), (X _i , y _i ) ∈D (10) Therefore, the mapping A can be determined by obtaining the relationship between q and g (x, y).

In general, the problem of finding a mapping from q to g (x, y) is called a problem with good properties, but the inverse problem belongs to a problem with poor properties as in this case. It is difficult. As described above, the ideal step edge was approximately solved by Hueckel using an orthonormal function, but the density pattern of a plurality of pixels near the edge was compared to the actual input image to which various degradations such as blurring were added. It is difficult to analytically obtain a mapping A that obtains the edge position and the edge direction from the image.

Therefore, in the present invention, the mapping A is obtained as follows.
In determining the mapping A, the density g of the directly input image
Instead of handling (x, y), the density m (x, y, σ _x , σ _y ,
Use q). Here, σ _x and σ _y are the spreads of the point spread functions in the horizontal and vertical directions, respectively.

Now, the t-th edge feature is represented by a subscript t, and the evaluation function e _t
Let e _t = {q _t −A (m (x, y, σ _x , σ _y , q _t ))} ² (11) the evaluation function E of the sum of e _t for all of the elements of q, Is determined to minimize. Here, noting that the least mean square error method can be applied to the evaluation functions of Expressions (11) and (12), the mapping A for obtaining the edge feature from the density pattern of the pixel near the edge shown in Expression (10) is expressed as , Using a back propagation type neural network. Using the mapping A determined in this way, g (x, y), that is, the mapping of the density pattern of the pixels near the edge is obtained for the actual input image, thereby measuring the edge feature.

As described above, the present invention considers a point spread function at the time of image input, considers an actual edge model that matches the edge density pattern of the actual input image, and further converts the density pattern of pixels near the edge to the edge feature. The mapping is obtained using a neural network. This allows
In general, real edge models that cannot be solved analytically
This mapping A can be obtained using em '.

(Embodiment) Hereinafter, an embodiment of the present invention will be described with reference to FIGS. 5 to 13 and each of the drawings in the order of the principle of measuring edge features and a measurement example based on this principle.

(A) Principle of Edge Feature Measurement Regarding the principle of edge feature measurement, a method of modeling an edge and a method of obtaining a mapping (A ′) from an edge feature to a density pattern of a pixel near an edge, and its inverse mapping, that is, a density pattern of a pixel near an edge Will be described in the order of how to obtain the mapping A from to the edge feature.

(A) Method of Modeling Edge and Method of Determining Mapping A 'to Density Pattern of Pixels Near Edge from Edge Features The above-described FIG. 1 is used as a model of a step edge. However, a sign is given to the edge position ρ such that the direction from the lower density to the higher density is the same as the direction from the origin O to the point P, and conversely, the opposite is negative. On the other hand, the edge direction θ takes a positive angle counterclockwise from the positive direction of the x-axis and ranges from 0 ° to 360 °.

Here, a pixel whose edge always crosses one of the x-axis and the y-axis is defined as an edge pixel as an image to be a reference for calculation. That is, if the edge passing through the pixel satisfies the condition of -1 / 2x <1/2 at y = 0, or -1 / 2y <1/2 at x = 0, the pixel becomes It is an edge pixel. Therefore, from equation (1) and inequality (13), in order to be an edge pixel, the edge position ρ and the edge direction θ must be min ｛−1/2 | cosθ |, −1/2 | sinθ |｝ ρ <max ｛1/2 | cosθ |, 1 / 2sinθ |｝, 0 ゜ θ <360 ゜ (14) The range of ρ and θ is shown as a region by hatching in FIG.

The density g (x _s , y _s ) of the pixel near the edge in the case of such a step edge is Can be calculated by Here, the subscript s indicates the center coordinates of the sampled pixel, and the step edge density function f (x, y) is It is represented by

Now, when the lens blur and afterimages point spread function at the time of image input, including such as the h (x, y), the concentration g (x _s, y _s) of pixels near an edge in the input image, Equation (16 ) And the step edge density function f (x, y) and the following equation (1
The density g (x _s , y _s ) of the real edge model is obtained as convolution calculation with the point spread function h (x, y) in 8). Can be obtained by However, the integration of α and β is performed in a range where the point spread function h (x, y) has an influence. The spread function differs depending on the image input system used. However, in general, the point spread function h (x, y) is used in the present invention because the point spread function of the lens blur can be approximated to a normal distribution, and the photoelectric conversion is independent in the horizontal and vertical directions and does not affect each other. approximated by ^{- {- 1/2 · (x 2} / σ x 2 + y 2 / σ y 2)} ...... (18) the h (x, y) = 1 / (2πσ x σ y) · exp. In Expression (18), σ _x and σ _y are the standard deviations of the horizontal and vertical spreads, respectively. Equation (16), which is the step edge density function f (x, y), and equation (18), which indicates the point spread function h (x, y), are converted into the density g (x _s , y _s of the real edge model of equation (17). substituted in), horizontal, for vertical each direction to determine the density of each pixel of the actual edge model by integrating the range from x-3 [sigma] _x to x + 3 [sigma] _x, or from y-3 [sigma] _y to y + 3 [sigma] _y.

The σ _x and σ _y are measured by focusing on the following relationship. There is a relationship that the line spreading function of the line light source is equal to the first derivative of the image of the step edge parallel to the line (translated by Shin Nagao: "Digital Image Processing", pp. 212-216, Modern Science Co., Ltd.). Therefore, the step edges in the vertical direction, ie, θ = 0 ° and in the horizontal direction, ie, θ = 90 °, are imaged and input to the computer. Then, the first derivative is calculated in the direction orthogonal to the edge, and the coordinates of the pixel and the first derivative there are regressed to a normal distribution, thereby obtaining σ _x , σ _y as the standard deviation of this distribution.

(B) How to Determine Mapping A from Density Pattern of Pixels Near Edge to Edge Feature A method of obtaining mapping A from density pattern of pixels near edge to edge feature is shown in FIG. As mentioned earlier, the expression (1
Noting that the least mean square error method can be applied to the evaluation functions 1) and (12), the mapping A for obtaining the edge feature from the density pattern of the real edge model shown in Expression (11) is expressed as 3
It is determined using an error back propagation type neural network composed of layers.

As shown in FIG. 6, the input layer of this neural network
The IN concentration m of a plurality of pixels near an edge, which is calculated from the actual edge model _{(x s, y s, σ} x, σ y, q) is input. Incidentally, in addition to the edge position and the edge direction, there is also information on the edge contrast, that is, the density of the edge as the edge feature. However, if modeling is performed including this density information, the number of density patterns to be learned is enormous. Therefore, in order to cope with a change in edge contrast, a normalized density normalized so that the minimum density is 0 and the maximum density is 1 in each density pattern is used, and eight pixels around the edge pixel, that is, The normalized density of 9 pixels of 3 × 3 is input to the input layer IN. Note that the number of input pixels is not limited to nine, and the input layer units may be prepared by the number of input pixels. In the neural network used this time, the number of units in the middle layer H is the input layer
As many as the number of IN units, each input layer unit is connected to all intermediate layer units. The output from the output layer OUT is an edge position ρ and an edge direction θ.

Now, the input layer IN, the intermediate layer H, and the output layer OUT are denoted by subscripts I, H,
O, the output from the i-th unit in the input layer is v _i ^I , the input to the j-th unit in the hidden layer is u _j ^H , the weight of the connection between both units w _ij ^IH , Assuming that the offset value in the j-th unit is r _j ^H , these relationships can be expressed as follows.

v _j ^I = s (u _j ^H ) (20) s (u _j ^H ) = 1 / ｛1 + exp (−2 u _j ^H / c) (21) where c is a constant. Similarly, the relationship between the output layer and Here, r _k ^o can be expressed as an offset value v _k ^o = s (u _k ^o ) in the K-th unit of the output layer (23). The weights and offset values of such a neural network are modified as follows.

w _jk ^HO → w _jk ^HO + ε _w δ _k ^o v _j ^H …… (24) w _ij ^IH → W _ij ^IH + ε _w δ _j ^H v _i ^I …… (25) r _k ^o → r _k ^o + ε _r δ _k ^o (26) r _j ^H → r _j ^H + ε _r δ _j ^H (27) where ε _w and ε _r are constants for determining the learning speed. When t _k is a teacher signal, the correction amounts δ _k ^o , δ
_j ^H is δ _k ^o = (t _k −v _k ^o ) ∂s (u _k ^o ) / ∂u _k ^o (28) Is calculated.

Since the value range of equation (21) is from 0 to 1, the edge position ρ
Uses a value obtained by linearly converting -0.5 to 0.5 from 0 to 1 and an edge direction θ from 0 to 360 from 0 to 1. For learning of the neural network, a density pattern calculated using Δρ pixels as the increment of the edge position ρ and Δθ ゜ as the increment of the edge direction θ is used. In this case, since the number of divisions of the edge feature input to the neural network differs between the edge position ρ and the edge direction θ, efficient correction cannot be simultaneously performed on the edge position ρ and the edge direction θ by the correction using the equation (29). . Therefore, in order to increase the learning speed, learning is performed by weighting the correction amount of the edge position ρ and the edge direction θ in proportion to the number of divisions as the correction amount.
That is, instead of equation (29) Is used. However, if k = 0 and 1 correspond to the edge position ρ and the edge direction θ, respectively, α ₀ = (1 / Δρ) / (360 / Δθ + 1 / Δρ) α ₁ = 1−α ₀ .

(A) Specific Example A specific edge feature measuring method will be described based on the principle of edge feature measurement described in (A) above.

(A) Apparatus FIG. 7 shows an outline of an apparatus for carrying out the present edge feature measuring method. An analog video signal output from the camera 1 composed of a CCD fixed image pickup device is converted into an A / D converter (not shown) by 256
256 and 2 in the horizontal and vertical directions
The data is sampled into 40 pixels and input to a computer memory (not shown). In the experimental apparatus used this time, the image sensor and the pixel of the memory correspond one to one.

An object 2 whose brightness changes stepwise was created by attaching papers having different reflectances on a flat plate, and an image of the object 2 was taken and an edge image was input. The object 2 is mounted on a moving stage 3 and fixed to a base 4, and moves in a horizontal direction while being orthogonal to the optical axis of the camera 1. Thus, the edge position ρ in the image shown in FIG. 1 can be changed. Next, in the image, 2 pixels separated by about 20 pixels
Measure the edge position at a location with an accuracy of 0.1 pixel (Japanese Patent Application No. Sho 6
No. 3-196007, Nomura et al .: "Measurement method of edge position"), the distance between two edge positions ρ in real space was actually measured with a micrometer 5 with an accuracy of 0.001 mm.

As a result, the ratio between the real space size and the pixel size is horizontal,
It was found that both directions were 1.062 mm / pixel. On the other hand, the camera 1 is mounted on a base via a rotary stage 6, and can rotate around the optical axis with an accuracy of 0.1 °. Thereby, the edge direction θ shown in FIG. 1 can be changed. By these movement and rotation mechanisms, any edge feature can be obtained. Note that all measurements were performed near the center of an image with small image distortion.

(B) Measurement Example A specific example of edge feature measurement will be described. Measurement is the first
It consists of three steps from a step to a third step.

First Step In the first step, for a combination of a plurality of edge positions ρ and a plurality of edge directions θ, a mapping A ′ of a pixel near an edge onto a density pattern is considered in consideration of a point spread function when a digital image is input. This is the step of obtaining. Therefore, first, the spread of the point spread function h (x, y) shown in Expression (18) is obtained. The result of imaging the step edge in the vertical direction, that is, θ = 0 °, and measuring the change in density in the horizontal direction near the edge is indicated by a black circle in FIG. Also, the result of measuring the density change in the density direction in the vertical direction using the step edge of the horizontal direction, that is, θ = 90 °, is shown in FIG.
Indicated by Here, the horizontal axis in FIG. 8 is the coordinate of the pixel in the horizontal or vertical direction, and is indicated by a relative value. In order to obtain the standard deviations σ _x and σ _y of the point spread function of the equation (18), FIG. 8 shows the result of calculating the first derivative and regressing it to a normal distribution. Here, horizontal, vertical first derivative of _{dg (x s + 0.5, y} s) / dx = g (x s + 1, y s) -g (x s, y s) ...... (31) dg _{(x s, y s +0.5)} / dy = g (x s, y s +1) -g (x s, y s) was calculated from the ... (32). The black circles and white circles in FIG. 9 are the values of the first derivative calculated for the vertical and horizontal edges, respectively. In the convolution calculation of equation (17),
Since a larger weight is applied to the vicinity of the center than the peripheral portion of the distribution and the influence of the point spread function appears greatly, regression calculation was performed for one pixel before and after the center of the pixel at which the first derivative is maximum, that is, three pixels.

The solid and broken lines shown in FIG. 9 are the normal distribution curves applied to the black circles and the white circles, respectively. σ _x , σ _y
Is about 5% centered on the average value depending on the edge position ρ in the edge pixel, so that σ _x and σ _y are measured by changing the edge position ρ by one pixel in each of the horizontal and vertical directions by 0.1 pixel. Then, the average values of 1.03 pixels and 0.77 pixels were used.

From the point spread function and the edge feature obtained in this way, the density pattern of the corresponding pixel near the edge can be calculated. The density pattern is obtained while changing the edge position ρ by 0.1 pixel and the edge direction θ by 1 °.
However, the integral calculation of equation (17) was performed here by dividing one pixel into 11 parts in each of the horizontal and vertical directions, that is, dividing one pixel into 121 partial areas. Since a normalized value is used as the concentration, any number of f ₁ and f _{2 in} FIG. 1 may be used, and the calculation is performed with f ₁ being 0 and f ₂ being 1. As an example of the calculation result of the density pattern of the pixel near the edge, FIG. 10 shows a case where θ = 0 when ρ = 0 and θ = 30 ° when ρ = 0.2. In FIG. 10, the central pixel is an edge pixel, and the numerical value written in the pixel is the normalized density.

Second Step The second step is a reverse mapping of the mapping A 'calculated in the first step, that is, a mapping A in the edge position and the edge direction from the density pattern of the plurality of pixels near the edge is input to the density and This is a step of determining using an error back propagation type neural network that outputs ρ and the edge direction θ.
The edge position ρ is from −0.5 to 0.4 pixels, and the edge direction θ is from 0 to 90 °.
Were learned 50,000 times by inputting 900 kinds of normalized density patterns, with 0.1 as a pixel and a step Δθ in the edge direction θ of 1 °.

In order to speed up the learning, the edge direction θ is set every 5 ° for the first 20,000 times, and only the density pattern of 0 °, 5 °, 10 °,..., 90 ° is used. The edge direction θ is shifted by 1 ° so as to make one round in five times, that is, 0 °, 5 °, 10 °, ..., 1 °, 6 °, 11 °,
…, 2 ゜, 7 ゜, 12 ゜,…, 3 ゜, 7 ゜, 13 ゜,…, 4 ゜, 9 ゜, 14
Learning was performed in 1 ゜ increments by repeatedly using the density patterns of ゜,. The initial values of the weights and the offset values in Equations (19) and (22) are given by generating random numbers between 0 and 1.

In addition, c, ε _w , ε _r in Expression (21) and Expressions (24) to (27)
Are 1.2, 0.6, 0.6, respectively. FIG. 11 (a) shows the result of calculating the sum of squares of the output difference between the teacher signal and the neural network, that is, the square error, by such learning. FIG. 11B shows the absolute value of the maximum edge feature measurement error in all the patterns at each learning count. The horizontal axis in FIG. 11 indicates the number of times of learning, and the vertical axis in FIG. 11 (a) indicates the square error normalized by the result calculated for the first time. 11 (a) and 11 (b), the dashed line shows the result of the edge position ρ, and the solid line shows the result of the edge direction θ, and data sampled every 20 times is shown in the figure. From Fig. 11, the neural network has converged to 5000
It can be seen that the errors in the edge position ρ and the edge direction θ after the 0-time learning are 0.027 pixels and 0.85 ° at maximum, respectively, indicating that sufficient learning has been performed. As a result, it can be seen that the mapping A to the edge feature was determined from the density pattern of the pixel near the edge.

Third step The third step uses the mapping A determined in the second step,
This is a step of calculating an edge feature from a density pattern of pixels near the edge in an actually input arbitrary image. The result of actually inputting an image and measuring the edge characteristics will be described in the order of the edge position and the edge direction.

(I) Measurement of edge position ρ θ = 0 ゜ That is, the vertical edge is set to 0 in the image in the horizontal direction.
An edge image was input while moving by 0.106 mm as a distance in a real space corresponding to one pixel, and an edge position ρ was measured. FIG. 12 (a) shows the result measured for the movement of about one pixel. The horizontal axis in FIG. 12 is the relative position within the pixel of the edge calculated from the movement amount, and the vertical axis is the input. The edge position ρ obtained by inputting the normalized density of 3 × 3 pixels of the image to the neural network after learning is shown. White circle ○
Is a measured value, and the solid line is the result of drawing a straight line with a slope of 1 by using the least squares method. The standard deviation of the variation of the measurement result is 0.043 pixel, which indicates that the edge position is measured with high accuracy. Edge direction θ = 30 °, 4
For 5 ゜ and 90 ゜, the result of moving about 10 times in 0.1 pixel increments, that is, one pixel, as in the case of the vertical edge, is the
12 (b), (c), and (d). In each of these figures, white circles ○ are measured values, and solid lines are the fitted straight lines having a slope of 1. The standard deviation of the variation of each measurement result was 0.016, 0.018, and 0.051 pixels, and it was confirmed that the edge position could be accurately measured by this method in any case.

(Ii) Measurement of Edge Direction θ An edge direction measurement experiment was performed by rotating the camera around the optical axis to change the boundary of the object, that is, the edge direction θ from 0 ° to 90 ° in steps of 1 °. The results are shown in FIG. The horizontal axis in FIG. 13 is the set edge direction, the vertical axis is the measured edge direction, and white circles ○ are the measured values. The standard deviation of the measurement results was 0.69 ゜, and the maximum was 1.82 ゜. As a result, it was confirmed that the method can measure the edge direction with high accuracy.

(Effect of the Invention) As described above, the edge feature measuring method of the present invention has been conventionally used by introducing, as parameters, a point spread function in a scanning line direction and a direction orthogonal to the edge feature in addition to the edge feature. Compared to the ideal step edge model, the fitting to the real edge model is performed in accordance with the actual input image. Using this real edge model, a mapping from the edge feature to the density pattern of the pixels near the edge is obtained, and the inverse mapping, that is, the change from the density pattern to the edge feature, is performed using an error back propagation neural network having a three-layer structure. To decide. Then, in actual measurement, a normalized density pattern of the input image is input to the obtained inverse mapping to convert it into an edge feature. Therefore, the present method has the following advantages over the conventional method.

(I) By using the backpropagation type neural network, it can be applied to a real edge model that cannot be solved analytically.

(Ii) Since it is applied to an actual edge model that matches the edge density pattern of the input image, the edge feature can be measured with high accuracy even from local information. As a result of the edge feature measurement experiment while actually changing the edge position and the edge direction, the standard deviation values of the variation of the measurement result of the edge position and the edge direction are 0.016 to 0.051 pixels and 0.69 ゜, respectively. Was measured.

(Iii) Conventionally, a long processing time was required to sequentially process each edge pixel one by one. On the other hand, the present method can apply parallel processing, which is one of the advantages of the neural network. Edge features can be measured in real time.

(Iv) Since the edge is modeled in consideration of the point spread function, the edge feature can be accurately measured by obtaining the point spread function at the time of image input to any image input device.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining an edge feature, FIG. 2 is a diagram for explaining an edge model, FIG. 3 is a diagram for explaining nine orthonormal functions used by Hueckel, and FIG. FIG. 5 is a diagram for explaining an edge feature measuring method by referring to a table of the prior art, FIG. 5 is a diagram showing conditions to be satisfied by an edge feature because the pixel is an edge pixel, and FIG. FIG. 7 is a diagram for explaining how to obtain a mapping to a feature, FIG. 7 is a diagram showing an example of an apparatus for implementing the present invention, FIG. 8 is a diagram showing a density change near an edge in an input image; FIG. 9 is a diagram for explaining the first derivative of FIG. 8 and a method for obtaining a point spread function from the result, and FIG. 10 is an example of a density pattern of a pixel near an edge calculated using a real edge model. FIG. 11 shows the density of the pixel near the edge. Shows the state of learning of the neural network to determine the mapping from the turn to edge features, Figure 12 Figure shows the measurement result of the edge position, the 13
The figure shows the measurement results in the edge direction. 1 ... camera, 2 ... object, 3 ... moving stage, 4 ...
... Base, 5 ... Micrometer, 6 ... Rotary stage.

Continuation of the front page (72) Inventor Takayuki Yamada 1-1-6 Uchisaiwaicho, Chiyoda-ku, Tokyo Nippon Telegraph and Telephone Corporation (56) References JP-A-3-251968 (JP, A) JP-A-2-45886 (JP, A) JP-A-61-52063 (JP, A) (58) Fields investigated (Int. Cl. ⁶ , DB name) G06T 1/00-9/20

Claims (1)

(57) [Claims] An edge feature measuring method for measuring an edge position and a direction using the density of a pixel near an edge in a digital image, the method comprising: inputting a digital image to a combination of a plurality of edge positions and a plurality of edge directions; A first step of obtaining a mapping of an edge neighboring pixel to a density pattern in consideration of a point spread function; and a reverse mapping in the edge position and the edge direction from the density pattern of the plurality of edge neighboring pixels calculated in the first step. A second step of determining using an error back-propagation type neural network with density as an input and an edge position and an edge direction as an output; and using the inverse mapping determined in the second step, any actually input A third step of calculating an edge position and an edge direction from a density pattern of pixels near the edge in the image. Edge feature measurement method.