JPH04167081A - Edge feature measuring method - Google Patents

Abstract

PURPOSE:To accurately measure an edge feature from the density pattern of picture elements nearby the edge in a digital image by using point spread functions in a scanning line direction and a direction orthogonal to it as parameters together with the edge feature. CONSTITUTION:For a combination of an edge position rho and an edge direction theta, the mapping of the picture elements nearby the edge into the density pattern is obtained in consideration of the point spread functions at the time of the input of the digital image. The reverse mapping from the calculated density pattern of the picture elements nearby the edge to the edge position rho and edge direction theta is determined by using an error reverse propagation type neural network which inputs density and outputs the edge position rho and edge direction theta. Then the reverse mapping is used to calculate the edge position rho and edge direction theta from the density pattern of the picture elements nearby the edge in the optional image which is actually inputted. Consequently, the edge feature is measured with high accuracy and parallel processing is applied to measure the edge feature in real time.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a method for measuring edge features in a digital image, and is used when recognizing or measuring an object using image processing.

(Prior Art) When an image is taken of a part of an object where the brightness changes or the direction of the surface changes, that is, the boundary part of the object, the density of the boundary part of the object changes stepwise in the image. In other words, changes in the properties of the object surface (reflectance and surface orientation)
Edges are areas where the density in an image changes due to Extraction of edge features is the most basic process among various types of image processing. Information regarding edge features is essential when measuring the position of an object in an image or recognizing the object.

Edges are characterized using their location 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 0, the horizontal line passing through the origin O is taken as the y-axis, and the vertical line is taken as the y-axis. A perpendicular line is drawn from the origin 0 to the edge e, and the point of intersection with this edge e is set as P. The length of this perpendicular line OP is ρ (edge position), and the direction between the perpendicular line OP and the y-axis is θ (edge direction), p=x cos θ + y sin θ (1
) represents a step edge. The density of each area divided into two by this step edge is f,
It is represented by f, and it is assumed that f,<f. Note that the portion indicated by the broken line in FIG. 1 is the pixel boundary.

To date, many algorithms have been proposed for edge feature measurement methods. Here, as conventional techniques, we will take up a model fitting type edge feature measurement method proposed by Hueckel and an edge feature measurement method using table reference.

Hueckel's method is a typical model-fit type edge feature measurement method that belongs to the same category as the present invention, and the edge feature measurement method using table reference requires a correction table to be created in advance through experiments in order to eliminate the influence of image input. The idea is to create one.

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

(Problem to be solved by the invention) When an object is imaged, the reflected light from the object is imaged by the camera lens onto a photoelectric conversion element, where horizontal scanning is repeated and a one-dimensional video signal arranged in time series is generated. is converted to Then, this video signal output from the camera is digitized, that is, sampled and quantized, by an A/D converter, and input into the memory of the computer as a two-dimensional image.

When an image is input to a computer in this manner, the image deteriorates due to various causes such as the lens system and photoelectric conversion.

The main causes of this are blurring that is added when forming an image with a lens, afterimages that occur in the horizontal scanning direction but not in the vertical scanning direction during digitization, and in addition, in solid-state image sensor cameras that are often used these days, This includes sensitivity differences depending on the direction that occur due to differences in the shape and pitch of the photoelectric conversion elements in the vertical direction and the vertical direction. For these reasons, even if the boundary portion of the object is imaged, the image input to the computer will not have an ideal step edge.

The edge model when Hueckel's idea is applied to the step edge is shown by the broken line in Figure 2 (Sataka Mori, Toshiko Itakura: ``Image Recognition Substrate (II)'', pp. 127
-134, Ohmsha, 1990). As shown in FIG. 2, the edge model used by Hueckel is an ideal step edge model em. The calculation area used to calculate edge features is D, and the density of the input image at the coordinates (x, y) when the center 0 of D is the origin is g(x
, y). Here, the concentration there is m(x, y,
Consider an edge model with ρ). However, ρ is a parameter indicating edge position, direction, and contrast, that is, an edge feature.

Here, as the difference between the two, [fo(g(x, y)-m(x, y, ρ))'dxdy
Considering (2), we can find an edge that analytically minimizes equation (2) using the nine orthonormal functions H, (1.0 to 8) shown in Figure 3. The features are being calculated, that is, the evaluation function E = (e, coso + 6.sin
θ)” + e, cosθ+e, sinθ...
... Find the edge direction θ from the condition that minimizes (3),
This result is used to determine the edge position ρ, etc. However, e+””(1/3)””al...(4)
e, = (1/3)""a, ......(5)e
,=(2/3)”a, ・・・・・・(6)e,÷2
e, e, +(a,"+a,"-(am"+a,")
)/2 ・・・・・・(7) e, -2e, e, +e,
e, +e, e, (8), aI= fD”l (x, y)g (x+ y) d
x dy , 1=0-8--(9).

However, the edge density pattern of the input image does not become an ideal step edge model em as shown by the broken line in FIG. em' is shown. As a result, the density pattern of 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),
In order to realize H1(x+y), a circular area with a diameter of about 8 to 9 pixels, that is, 50 to 60 pixels, is used as a calculation area, so it is difficult to measure local edge features.

On the other hand, as a table reference type, Japanese Patent Application No. 2-47247
No. 2 (Ide et al. 2 ``Method for measuring edge direction for digital images''). This method inputs a number of images with different edge positions and edge directions at intervals that give the desired accuracy, and then compares the edge positions and directions obtained from these images with the actual edge positions and edge directions used for input. The difference is determined in advance as a correction value. A correction table is created for determining the true edge position and edge direction from the edge position and edge direction measured in this manner.

An example of this correction table is shown in FIG.

In FIG. 4, the horizontal and vertical axes represent the measured edge position and edge direction, respectively, and the correction values are displayed as contour lines. In this method, for example, the table in the edge direction is
In order to obtain an accuracy of 360 degrees, 360 different angle measurements must be made in advance.

Further, since it is necessary to obtain correction tables for various edge positions in each edge direction, it is difficult to efficiently create a reference correction table. moreover,
All of the conventional methods use algorithms that are difficult to process in parallel, so the process of focusing on one edge pixel, finding edge features, and moving the edge pixels of interest one after another is repeated. As a result, there was a problem in that a long processing time was required.

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

(Means for Solving the Problems) In order to solve the above problems and achieve the objects, the present invention provides an edge feature measuring method for measuring edge positions and directions using the density of pixels near edges in a digital image.
A first step of obtaining a mapping of edge-nearby pixels to a density pattern by considering a point spread function when inputting a digital image for combinations of multiple edge positions and multiple edge directions; and calculating in the first step. a second step of determining an inverse mapping from the density pattern of a plurality of edge-nearby pixels to the edge position and edge direction using an error backpropagation neural network whose input is the density and whose output is the edge position and edge direction; , a third step of calculating the edge position and edge direction from the density pattern of pixels near the edge in any actually input image using the inverse mapping determined in the second step. .

(Function) In the present invention, in addition to the edge position and edge direction, which have conventionally been used as parameters as edge features, point spread in the scanning line direction and the direction perpendicular thereto is used as a function representing image deterioration during image input. Model the step edge by taking the function into account. This allows the second
As shown by the solid line in the figure, it is possible to use a more realistic edge model in which blur is added to the ideal step edge. Below, we will convert this edge model into a real edge model em
' is called. Note that the broken line in FIG. 2 is the conventional step edge model em. Using this edge model, edge features are determined as follows.

Now, let the edge position and edge direction be a two-dimensional vector q, the density of multiple pixels near the edge be g(x, y), and from q to g
Let A' be the mapping to (x y y ), and let A be the inverse mapping of A', that is, the mapping from g(xty) to q, then q+
The relationship between g(xty) and A is q”A (g (X+
s 3' + )9g (Xmy ':jm)z '''
t g (Xn ``j t)* '')y(X+tyt
)C:D...Can be expressed as song (10). Therefore, mapping A can be determined by finding the relationship between q and g(x, y).

Generally, the problem of finding a mapping from q to g(xty) is called a problem with good properties, but the inverse problem like this one belongs to problems with bad properties, and it is usually difficult to solve this problem. It is. As mentioned above, an ideal step edge was approximately solved by Hueckel using an orthonormal function, but for an actual input image with various deteriorations such as blurring, the density pattern of multiple pixels near the edge is It is difficult to analytically obtain the mapping A that obtains the edge position and edge direction from .

Therefore, in the present invention, mapping A is obtained as follows. When determining this mapping A, the density g(x
, y), the density m(x, y, σ8
．． σ9. Use q). Here, σ8. σ is the spread of the point spread function in the horizontal and vertical directions, respectively.

Now, the edge feature of is expressed by the subscript t, and the evaluation function et
As, et=(Qt A(m(xty+ σ,, σytqt
)))" ・−・−(11).The evaluation function E of the sum of et for all elements of q is E=Σe, ......The mapping A that minimizes (12) Here, equation (11) and equation (1
Noting that the least mean squared error method can be applied to the evaluation function in 2), the mapping A that calculates the edge feature from the density pattern of pixels near the edge shown in equation (lO) is calculated using an error backpropagation neural network. decide. Using the mapping A determined in this way, g(
Edge characteristics are measured by determining the mapping of density patterns (x, y), that is, density patterns of pixels near the edges.

In this way, the present invention considers the point spread function at the time of image input to create an actual edge model that matches the edge density pattern of the actual input image, and then to map the density pattern of pixels near the edge to edge features. is obtained using a neural network. This results in -
There is a real edge model in the film that cannot be solved analytically.
This mapping A can be obtained using m'.

(Example) Examples of the present invention will be described below in the order of the edge feature measurement principle and measurement examples based on this principle, using FIGS. 5 to 13 and the above-mentioned figures.

(A) Edge feature measurement principle Regarding the edge feature measurement principle, how to model edges, how to obtain the mapping (A') from edge features to the density pattern of pixels near the edge, and the inverse mapping of this, that is, the density pattern of pixels near the edge. The method of obtaining the mapping A from to edge features will be explained in order.

(a) Edge modeling method and how to obtain the mapping A' from edge features to the density pattern of pixels near the edge The above-mentioned FIG. 1 is used as a step edge model.

However, the edge position ρ is given a sign such that it is positive if the direction from the low density side to the high density side is the same as the direction from the origin O to the point P, and is negative if the direction is opposite. On the other hand, the edge direction θ takes a positive angle counterclockwise from the X-axis pressure direction,
From Oo to 360”.

Here, as an image used as a reference for calculation, a pixel whose edge always intersects the y-axis or one of the y-axes is defined as an edge pixel. In other words, the edge passing through the pixel is 11/2<:x<1/2 when y=Q, or 11/2<:y<1/2 when x=O.
- If the condition (13) is satisfied, the pixel is an edge pixel. Therefore, from equation (1) and inequality (13),
In order to be an edge pixel, the edge position ρ and edge direction θ must be 5 ain (-1/21 cos θl, -1721 sin θ
1)<ρ(wax(1/21cosθ1, 1/21si
It is necessary to satisfy the following conditions: nθ1), 0° and θ<360° (14). The range of ρ and θ is shown as a region by hatching in FIG.

In the case of such a step edge, the density g(xs, yl) of a pixel near the edge can be calculated as follows (15). However, the subscript S indicates the center coordinates of the sampled pixel, and the step edge density function f (x + y) is f,,ycosθ+xsin
It is expressed as θ−ρnO.

Now, if the point spread function when inputting an image including lens blur and afterimages is h (x * y), then the density g (Xs + ys) of pixels near the edges in the input image is:
The step edge concentration function f(X, y) of equation (16) and the point spread function h (x +
y ), the density g(Xs+ys) of the real edge model is obtained as Xf(α,β)dadβd x dy −(17
) can be found. However, it is assumed that the integration of α and β is performed over the range affected by the point spread function h (x ty ). This point spread function varies depending on the image input system used. However, in general, the point spread function of 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. Therefore, in the present invention, the point spread function h(x
, y) as h (x, y)=I/(2yr a, a,
) -exp(-172・(x″/ ax″+y″/
cr, ")) (18) In equation (18), σ8.σ is the standard deviation of the spread in the horizontal and vertical directions, respectively.

Equation (16) which is the step edge concentration function f(x,y)
and the equation (]8 showing the point spread function h (x t y )
) as the concentration g (xs+
ys), and for each horizontal and vertical direction,
The density of each pixel of the actual edge model is determined by integrating over the range from x-3σ8 to x+3σ8, or from V-3σ to y+30.

This σ8. σ is measured by paying attention to the following relationship.

The relationship holds that the line spread function of a line light source is equal to several step edge images parallel to the line (translation supervised by Makoto Nagao: “Digital Image Processing”, pp. 212)
~216, Kindai Kagakusha). Therefore, step edges in the vertical direction, ie, θ=0″ and in the horizontal direction, ie, θ=90°, are imaged and input into the computer.

Then, by calculating several planes in the direction orthogonal to this edge, and regressing the coordinates of the pixel and the values for one few planes therein to a normal distribution, the standard deviation of this distribution is set to σ8. Find σ.

(b) How to find the mapping A from the density pattern of the pixels near the edge to the edge feature FIG. 6 shows how to find the mapping A from the density pattern of the pixels near the edge to the edge feature. As mentioned above, the formula (11
) and (12), the mapping A for calculating edge features from the density pattern of the real edge model shown in equation (11) is expressed as
The determination is made using an error backpropagation neural network consisting of three layers.

As shown in Figure 6, the input layer I of this neural network
The density m (x, y, σ8.σ9.q) of a plurality of pixels near the edge calculated from the actual edge model is input to N. By the way, in addition to the edge position and the edge direction, there is also information about the edge contrast, that is, the density of the edge.

However, if modeling is performed including this density information, the number of density patterns to be learned will increase to an enormous number.

Therefore, in order to deal with changes in edge contrast, we use normalized densities that are normalized so that the minimum density is 0 and the maximum density is 1 in each density pattern. 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 9, and it is sufficient to prepare input layer units equal to the number of input pixels.In the neural network used this time, the number of units in the intermediate layer H is equal to the input layer I.
Each input layer unit is connected to all hidden layer units, with the same number of N units. The output from the output layer OUT is the edge position ρ and the edge direction θ.

Now, the input layer IN, the hidden layer H2, and the output layer OUT are represented using subscripts I, H, and O, respectively, and the output from the i-th unit of the input layer is vlK, and the input to the j-th unit of the hidden layer is uJ. When the weight of the connection between both units is W1, and the offset values in the j-th unit of the intermediate layer are r and H, these relationships can be expressed as follows.

uj′=ΣWB”V1′+rJ” ・・・・・・(
19) V s”= S (u J”)
20) s(uj”)=1/(1+exp(-2u3”/
c) ・−・−(2t) Here, C is a constant.

Similarly, the relationship with the output layer is as follows: u kO=ΣwJk”vj”+ r, 0 −・−(z
z) However, r and O are the offset values in the first unit of the output layer ■,'= s (uk') −・−(23
) can be expressed as The weights and offset values of such a neural network are modified as follows.

w, -〇-WJ♂0+ ε, δh'V ノ” ””
"(24) wl j" - 4th W" + E, δ, Hvlx
,...(25)' to '-rk'+5, δk
o ・−・−(26)rJ″−4rJ″+ε,
δ? ......(27) However, ε1. ε7
is a constant for determining the learning speed. Also, if 1k is the teacher signal, the correction amount δ,. , δI is .

to δ'=(th-vk.) a s (uk')/a
ukO・−・・−(2a) δj″=as(uj″)/
auJ"ΣWj,"δ-...(29)

Since the range of equation (21) is from 0 to 1, the edge position ρ
is -0,5 to 0.5 to O to 1, and edge direction θ
Also, a value obtained by linearly converting O to 360 to O to 1 is used. For neural network learning, the edge position ρ
A density pattern calculated by setting the increments of Δρ pixels as Δθ0 and the increments of θ in the edge direction as Δθ0 is used. In this case, the number of divisions of edge features input to the neural network differs between edge position ρ and edge direction θ, so correction using equation (29) cannot proceed with efficient learning of edge position ρ and edge direction θ at the same time. Therefore, in order to speed up the learning speed, learning is performed by applying weights proportional to the number of divisions to the correction amounts of the edge position ρ and the edge direction θ. That is, instead of equation (29), δj″−as
(ul”)/au1”・Σα, Wl@”δ,...
...(30) is used. However, if k = 0.1 corresponds to the edge position ρ and edge direction θ, respectively,
α, = (1/Δρ)/(360/Δθ+1/Δρ)α,
=1-α.

becomes.

(B) Specific Example Based on the edge feature measurement principle described above in (A), a specific edge feature measurement method will be explained.

(a) Apparatus FIG. 7 schematically shows an apparatus for carrying out the present edge feature measuring method. The analog video signal output from the camera 1, which is a fixed COD image sensor, is quantized into 256 gradations by an A/D converter (circuit) and sampled into 256.240 pixels in the horizontal and vertical directions. It is input into the computer's memory (circuit). In addition, in the experimental device used this time, the image sensor and the memory pixel correspond to each other in a ratio of 1 to 1.

Create object 2 whose brightness changes stepwise by pasting papers with different reflectances on a flat plate.
This object 2 is placed on a moving stage 3 and fixed to a base 4, and moves in the horizontal direction while remaining perpendicular to the optical axis of the camera l. Thereby, the edge position ρ in the image shown in FIG. 1 can be changed. Next, two pixels located approximately 20 pixels apart in the image.
At the same time, the edge position is measured with an accuracy of 0.1 pixel (Japanese Patent Application No. 196007, Sealing Materials and 3 others: Method for Measuring Edge Position), and the distance between two edge positions ρ in real space is measured. It was actually measured with a micrometer 5 with an accuracy of 0,001wn.

As a result, it was found that the ratio between the real space dimension and the pixel dimension was 1.062 mm/pixel in both the horizontal and vertical directions. On the other hand, the camera l is attached to the base via a rotation stage 6, and can be rotated around the optical axis with an accuracy of 0 and lo. As a result, the edge direction θ shown in FIG.
can be changed.

By using these movement and rotation mechanisms, arbitrary edge characteristics can be obtained. Note that all measurements were performed near the center of the image where image distortion is small.

(b) Measurement example A specific example of edge feature measurement will be explained. The measurement consists of three steps, from the first step to the third step.

First step The first step is to map A' to the density pattern of pixels near the edge for combinations of a plurality of edge positions ρ and a plurality of edge directions θ, taking into account the point spread function when inputting a digital image. This is the process of obtaining Therefore, first, the formula (
18) Find the spread of the point spread function h(x, y). The step edges in the vertical direction, that is, θ=O°, were imaged and the density changes in the horizontal direction near the edges were measured. The results are shown in FIG. 8 by black circles. Further, the results of measuring the density change in the vertical density direction using a step edge in the horizontal direction, that is, θ=909, are also shown in FIG. 8 by a white circle O. Here, the horizontal axis in FIG. 8 is the horizontal or vertical pixel coordinates, which are expressed in relative values. Formula (1
8) The standard deviation of the point spread function σ8. In order to find σ, FIG. 8 shows calculations for several machines, and FIG. 9 shows the results of regression to a normal distribution. Here, several planes in the horizontal and vertical directions are d g (x, +0,5yys)/dX=g (Xs
+ 1 t 31'l) g (xs+ys)
・・・・・・(3I)d g (x,,y
, +0.5)/d y=g(xstys+1)-g(x
s+ys) --- Calculated from (32). The black circles and white circles O in FIG. 9 are the values for several planes calculated for the vertical and horizontal edges, respectively. In the convolution calculation of Equation (17), a larger weight is placed near the center of the distribution than in the peripheral parts, and the influence of the point spread function appears to be large. In other words, regression calculations were performed for three pixels.

The solid line and broken line shown in FIG. 9 are normal distribution curves fitted to the black circles and white circles, respectively. σ8. σ,
The value of σ changes by about 5% around the average value depending on the edge position ρ within the edge pixel, so by changing the edge position ρ by 0.1 pixel in each horizontal and vertical direction, σ8. σ was measured, and the average values of 1.03 pixels and 0.77 pixels were used.

From the point spread function and edge feature thus obtained, the corresponding density pattern of pixels near the edge can be calculated. A density pattern is obtained while changing the edge position ρ in 0.1 pixel increments and the edge direction θ in 1° increments.

However, in the integral calculation of equation (17), one pixel is divided into 11 in each of the horizontal and vertical directions, that is, 1
The pixel was divided into 121 partial regions. Note that since normalized values are used for the concentration, f in Fig. 1.
Any number of f,<f, was calculated with O,f,as 1.

As an example of the calculation result of the density pattern of pixels near the edge, FIG. 10 shows the case where ρ=0 and θ=0, and ρ=0.2 and θ=306. In FIG. 10, the central pixel is an edge pixel, and the numerical value written within the pixel is the normalized density.

Second step The second step is an inverse mapping of the mapping A' calculated in the first step,
That is, in the step of determining the mapping A from the density pattern of a plurality of edge-nearby pixels to the edge position and edge direction using an error backpropagation neural network whose input is the density and whose outputs are the edge position ρ and the edge direction θ. be. The edge position ρ is from 10, 5 to 0.4 pixels, and the edge direction θ is from 0 to 90 degrees. 500 types of normalized density patterns as input
Learned 00 times.

To speed up learning, the edge direction θ is set every 56 times for the first 20,000 times, and is set to 0°, 5', and 10°.
.

..., using only the 90° density pattern, the next 300
00 times, the edge direction θ is shifted by 1° along with the number of learning times so that it goes around once every 5 times, that is, 0°, 5°.
, 10°, ..., l', 6°, Ifo, ....

2°, 7°, 12°,..., 3°, 7°, 13°
,...

4°, 9', 146. Learning was performed in 1° increments by repeatedly using the density patterns of... Formula (+9), (22
) were given by generating random numbers between 0 and 1.

In addition, C9ε of formula (21) and formulas (24) to (27)
W.

C7 was set to 1, 2.0.6.0.6, respectively. Through such learning, the sum of squares of the difference between the teacher signal and the output of the neural network, that is, the square error, is calculated, and the results are shown in FIG. 11(a). Furthermore, the absolute value of the maximum edge feature measurement error in all patterns for each number of learning is shown in FIG. 11(b). The horizontal axis in Figure 11 is the number of learning times, and the first
The vertical axis in FIG. 1(a) shows the squared error normalized by the first calculation result. In FIGS. 11(a) and 11(b), the broken line shows the result for the edge position ρ, and the solid line shows the result for the edge direction θ, and the data sampled every 20 times are shown in the figures. As shown in Figure 1I, the neural network has converged, and the errors in edge position ρ and edge direction θ after 50,000 learnings are each up to 0.02.
It can be seen that sufficient learning has been performed with 7 pixels and 0.85''.

As a result, it can be seen that the mapping A from the density pattern of pixels near the edge to the edge feature has been determined.

Third Step The third step is a step of calculating edge features from the density pattern of pixels near the edge in any actually input image using the mapping A determined in the second step. The result of actually inputting the image and measuring the edge features is the edge position,
The explanation will be given in order of edge direction.

(i) Measurement of edge position ρ θ=0°, that is, the vertical edge is moved horizontally to 0.0° in the image.
0, 106+n as the distance in real space corresponding to 1 pixel
Input the edge image while moving by m, and set the edge position ρ
was measured. Figure 12(a) shows the measurement results for a movement of approximately one pixel.The horizontal axis in Figure 12 is the relative position within the pixel of the edge calculated from the amount of movement, 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.

The white circle O is the measured value, and the solid line is the result of drawing a straight line with a slope of 1 from O using the least squares method. The standard deviation of the variation in the measurement results is 0.043 pixels, indicating that the edge positions are measured with high accuracy. Also, in the edge direction θ = 30'', 45'', 90a, the vertical edge was moved about 10 times in 0.1 pixel increments, that is, 1 pixel, and the measurement results are shown in FIG. 12(b).

Shown in (c) and (d). In each of these figures, the white circles O are measured values, and the solid lines are fitted straight lines with a slope of 1. The standard deviation of the dispersion of each measurement result is 0
．． 016.0, 018.0.051 pixels, and it was confirmed that the edge position could be measured with high accuracy by this method in both cases.

(ij) Measurement of edge direction θ By rotating the camera around the optical axis, we performed an edge direction measurement experiment by changing the boundary of the object, that is, the edge direction θ, from 0° to 906 in 1″ steps. It is shown in Fig. 13. In Fig. 13, the horizontal axis is the set edge direction, the vertical axis is the measured edge direction, and the white circle mark O is the measured value. #The standard deviation of the dispersion of the measurement results is 0. 6
9', and the maximum value was 1.82°. As a result, it was confirmed that the present method enables accurate measurement in the edge direction as well.

(Effects of the Invention) As explained above, the edge feature measurement method of the present invention
By introducing edge features as well as point spread functions in the scanning line direction and the direction orthogonal thereto as parameters, the real edge model can more closely match the actual input image than the ideal step edge model that has been used in the past. are being fitted to. Using this real edge model, we calculate the mapping from edge features to the density pattern of pixels near the edge, and calculate the inverse mapping, that is, the change from the density pattern to edge features, using an error backpropagation neural network with a three-layer structure. decide. In actual measurement, the normalized density pattern of the input image is input to the obtained inverse mapping to convert it into an edge feature. Therefore, this method has the following advantages over conventional methods.

(i) By using an error backpropagation neural network, it is possible to fit real edge models that cannot be solved analytically.

(b) Since it is applied to a real edge model that matches the edge density pattern of the input image, edge features can be measured with high precision even from local information.

As a result of actually conducting an edge feature measurement experiment while changing the edge position and edge direction, the standard deviation value of the dispersion of measurement results for edge position and edge direction was 0.016, respectively.
0.051 pixel and 0.696, confirming that edge features can be measured with high accuracy.

(iii) Conventionally, a long processing time was required to sequentially process each edge pixel one by one, but this method allows parallel processing, which is one of the advantages of neural networks, to be applied. Edge characteristics can be measured in real time.

(iv) Since edges are modeled taking into account the point spread function, edge features can be measured with high precision by determining the point spread function at the time of image input for any image input device.

[Brief explanation of the drawing]

Figure 1 is a diagram to explain the edge features, Figure 2 is a diagram to explain the edge model, and Figure 3 is a Hueckel diagram.
Diagram for explaining the nine orthonormal functions used by
The figure is a diagram for explaining the edge feature measurement method using table reference in the prior art, Figure 5 is a diagram showing the conditions that the edge feature must satisfy in order to be an edge pixel, and Figure 6 is the density pattern of pixels near the edge. 7 is a diagram illustrating an example of an apparatus for implementing the present invention. FIG. 8 is a diagram illustrating density changes near edges in an input image. , Fig. 9 is a diagram for explaining the method of calculating the point spread function from the results of several machines in Fig. 8, and Fig. 10 is a diagram showing one of the density patterns of pixels near the edge calculated using the real edge model. A diagram showing an example,
Figure 11 is a diagram showing how the neural network is trained to determine the mapping from the density pattern of pixels near edges to edge features, Figure 12 is a diagram showing the measurement results of edge positions, and Figure 13 is FIG. 6 is a diagram showing measurement results in the edge direction. l...camera, 2...object, 3...movement stage, 4...base, 5...micrometer, 6...rotation stage. Patent applicant Nippon Telegraph and Telephone Corporation Figure 2 Figure 3 Ho)-II H
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Claims (1)

[Claims] In an edge feature measurement method for measuring edge positions and directions using the density of pixels near edges in a digital image, when inputting a digital image for a combination of a plurality of edge positions and a plurality of edge directions, a first step of obtaining a mapping of pixels near the edge to a density pattern by considering a point spread function; and an inverse mapping from the density pattern of pixels near the edge calculated in the first step to an edge position and an edge direction. a second step in which the density is determined using an error backpropagation neural network that uses the density as input and the edge position and edge direction as output; An edge feature measuring method comprising: a third step of calculating an edge position and an edge direction from a density pattern of pixels near the edge in the image.