JP3521049B2 - Curve generating device and curve generating method - Google Patents

Description

Detailed Description of the Invention

[0001]

[Table of Contents] The present invention will be described in the following order. TECHNICAL FIELD OF THE INVENTION Conventional Technology Means for Solving Problems to be Solved by the Invention Embodiments of the Invention (1) Overall Configuration (FIG. 1) (2) Configuration of Curve Generation Unit (FIG. 2) (2) -1) Configuration of Input Coordinate Division Unit (FIGS. 3 and 4) (2-1-1) Configuration of Curvature Calculation Circuit (FIGS. 5 to 7) (2-1-2) Curvature Discrimination Circuit and Division Point Detection Circuit (FIGS. 8 and 9) (2-2) Configuration of connection condition calculation unit (FIGS. 10 and 11) (2-3) Configuration of curve approximation unit (FIG. 12) (2-4) Operation of embodiment And Effects (FIGS. 13 and 14) (3) Other Embodiments (FIGS. 15 to 19)

[0002]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a curve generation device and a curve generation method, for example, as continuous data from shape data composed of a plurality of coordinate data discretely acquired as an outline of an object existing in an image. It is suitable for application when generating a curve.

[0003]

2. Description of the Related Art Conventionally, a technique for converting shape data composed of a plurality of discrete coordinate data (hereinafter referred to as a coordinate list) into a curve as continuous data is a data analysis as an interpolation method or an approximation method. It is used in various fields such as. Here, the coordinate list represents data in which a plurality of coordinate data is stored in order, and the storage format does not matter, such as a simple array, a list structure, and a line graphic binary image. A curve refers to a shape represented by one or more mathematical expressions, and can be described by a method of storing the coefficient value of the next term, for example. The storage format of the curve does not matter.

There are various interpolating methods or approximation methods as described in "Numerical calculation handbook" (Yutaka Ono, Kazuo Isoda, Ohmsha, 1990), and they are classified from the background of the principle. , Polynomial interpolation method, piecewise polynomial interpolation method and polynomial approximation method by least square method.

In addition, "Shape processing engineering by computer display [I] [II]" (Fujio Yamaguchi, Nikkan Kogyo Shimbun, 1982) and "Computer Graphics Principles and P"
practice "(Foly, VanDam, Feiner, and Hughes, Addi
According to Son Wesley, 1990), curve representations using piecewise polynomials are computer graphics and CAD (Comput).
er Aided Design), there are several known methods for approximating a piecewise polynomial from a given coordinate list. Such a piecewise polynomial expression can have properties different from those of the interpolation method and the approximation method. Here, the most typical curve approximation method using a B-spline polynomial will be described.

In the polynomial interpolation method, when a coordinate list consisting of n coordinates is given, one polynomial that passes through all coordinate lists is calculated. A generally known polynomial interpolation method is to obtain an n-th degree polynomial that passes through n + 1 coordinates. This method is effective when it is always desired to pass through the coordinate list, but there is a problem that the degree of the polynomial increases as the number of coordinates increases and the curve easily vibrates. A typical polynomial interpolation method is Lagrange interpolation.

In the piecewise polynomial interpolation method, when a coordinate consisting of n pieces of coordinates is given, a separate polynomial is applied to each small section of the whole coordinate list to generate a curve in which the sections are smoothly connected. is there. For example, when the number of coordinate data in a certain small section is k, the piecewise polynomial in this small section is k
It can be expressed by a polynomial of degree −1. Therefore, in each small section, the shape of the curve is the k-1 order. This piecewise polynomial interpolation method also always passes through the coordinate list, and the degree of each polynomial is smaller than that of the polynomial approximation using one polynomial, so that there is an advantage that there is no extra vibration. Natural spline is a typical piecewise polynomial interpolation method.
There is.

The curve approximation method using the B-spline polynomial can generate a curve that smoothly passes through a given coordinate list without passing through it, using a piecewise polynomial. A typical example is the B-spline approximation method. For example, when the number of coordinate data of a certain small section is k, the piecewise polynomial in this small section can be expressed by a polynomial of degree k−1, and a curve in which each small section is smoothly connected is generated. Therefore, in each small section, the shape of the curve is the k-1 order.

This B-spline is an effective method for obtaining a curve obtained by smoothing a given coordinate list. Also, B-splines have the property of local uniqueness. Here, the local uniqueness is a property that even if any one of the coordinate list is changed, only a local curve change is required. This property is a property that is effective when connecting two curves, and is a property that is not present in Lagrangian curves or natural spline curves.

The approximation method by the least squares method assumes an error between a given coordinate list and the shape formed by the coordinate list,
This is a method of obtaining a curve that minimizes the sum of squared errors. In the usual least squares method, the form of the function of the curve is arbitrary, but the least squares approximation method using a polynomial is widely used because of its simple calculation. In this method, since the shape of the curve equation to be approximated is set in advance, the order of the curve is determined in advance and does not depend on the number of coordinate data.

[0011]

By the way, the shape of a given coordinate list is high-order and unknown, and the number of data of the given coordinate list and the degree of the shape are irrelevant. When the curve approximation is performed using the conventional interpolation method or approximation method as described above under the four conditions that noise is included and the curve approximation is performed as efficiently as possible, the following problems occur. It was

That is, in the method of expressing a curve by one polynomial such as Lagrangian interpolation, the degree of the polynomial is determined by the number of coordinate data in the coordinate list, so that the degree of the shape originally desired and the degree of the curve do not match. However, there is a problem that the curve approximation cannot be performed efficiently. In addition, the polynomial interpolation method generates a curve that passes through all coordinate lists, but since the target coordinate list contains noise, passing through the entire coordinate list reverses the accuracy of curve approximation. Will be lowered. That is, there is a problem that unnecessary bending is likely to occur.

An interpolation method using a piecewise polynomial such as a natural spline can form a curve with a relatively low-order polynomial, but since it passes through the entire coordinate list, it is included in the coordinate list as in the Lagrangian interpolation. It is unavoidable that unnecessary vibration is caused by noise. Further, since the degree of the piecewise polynomial is determined by the number of coordinate data of the small section, the degree of the curve does not match the degree of the shape to be obtained, and there is a problem that the curve cannot be approximated efficiently.

In the B-spline, since the obtained curve has a shape obtained by smoothing the coordinate list, noise included in the coordinate data can be reduced, but local coordinates that determine individual piecewise polynomials are used. Since the number of and the degree of the desired shape do not match, there is a problem that the curve approximation cannot be performed efficiently as in the case of the piecewise polynomial interpolation like the natural spline.

The curve approximation by the method of least squares is a method suitable in principle for curve approximation of a coordinate list including noise. Further, the curve approximation by the least squares method can determine the order of the shape to be approximated regardless of the number of data in the coordinate list, and thus has an advantage that efficient approximation can be performed depending on the determined order. However, since it is necessary to check in advance what order the shape of the coordinate list is to be approximated, there is a problem that the curve approximation work becomes complicated.

The present invention has been made in consideration of the above points, and an object thereof is to propose a curve generation device and a curve generation method capable of improving the efficiency of curve approximation.

[0017]

In order to solve such a problem, in the present invention, a plurality of discrete coordinate data
In a curve generation device that generates an approximate curve of the shape indicated by the coordinate data, a division point calculation unit that calculates a division point that divides the shape into a plurality of segments, and a connection point that connects adjacent segments for each division point Considering at least each consolidation condition, and the consolidation condition calculation means for calculating the consolidation condition,
Curve division means for curve-approximating each segment so as to satisfy the connection condition at each division point, and the division point calculation means has a length of a predetermined line segment obtained based on coordinate data of three points sampled from the coordinate data. Then, it is determined whether or not the division point is calculated based on the length of the line segment.

According to the present invention, when the division points for dividing the shape into a plurality of segments are calculated, it is determined whether or not the division is performed based on the length of a predetermined line segment obtained based on the coordinate data of the three points. By performing the curve approximation of each segment so as to satisfy the connection condition at each division point of the determination result, it is possible to efficiently perform the curvature approximation with a predetermined approximation accuracy when connecting each segment.

[0019]

BEST MODE FOR CARRYING OUT THE INVENTION An embodiment of the present invention will be described in detail below with reference to the drawings.

(1) Overall Structure In FIG. 1, reference numeral 1 denotes a key signal generating apparatus to which the present invention is applied as a whole, and generates a soft key of an object existing in a plurality of continuous images. The key signal generator 1 is
It is composed of a contour extraction unit 2 and a key calculation unit 3,
Based on the contour curve of the object calculated by the contour extraction unit 2 and the gradient vector of the contour of the object, the key calculation unit 3 generates a soft key of the object.

The key signal generating device 1 uses the mouse 4 as an input means to input the line information indicating the rough shape of the contour, the broken line information, the curve information, or the traced information with a thick brush, which is input by the operator. Mask image information S1
Is received by the estimated contour calculation unit 5 of the contour extraction unit 2. The estimated contour calculation unit 5 obtains the estimated contour information S2 corresponding to the estimated shape of the contour of the object (hereinafter referred to as the estimated contour) based on the line segment information, polygonal line information, curve information or mask image information S1. , And sends the estimated contour information S2 to the contour candidate area determination unit 6.

The contour candidate area determining section 6 estimates the estimated contour information S.
Based on 2, the area in which a contour is considered to exist (hereinafter, referred to as a contour candidate area) is calculated, the edge position and the edge direction are calculated, and the contour candidate area information S3 corresponding to the contour candidate area is calculated. Then, the edge position e as the edge position information and the edge direction d as the edge direction information are sent to the gradient vector calculation unit 7.

The gradient vector calculation unit 7 generates the gradient gradient vector information I _i by calculating the gradient intensity value in the contour candidate region based on the contour candidate region information S3, and the gradient vector information I _i. The contour path search unit 8 and the key calculation unit 3
Send to.

The contour path search unit 8 generates a list P of pixels passing through the center of the contour (hereinafter, referred to as a coordinate list P) based on the gradient vector information I _i, and sets the coordinate list P. It is sent to the curve generator 9. The curve generation unit 9 generates a curve group C based on the coordinate list P, and obtains the contour curve information C corresponding to the curve group from the key calculation unit 3
Send to. Here, the coordinate list is a two-dimensional coordinate (x,
y), the curve generation unit 9 outputs data representing a curve on two-dimensional coordinates.

Here, in the key signal generating apparatus 1, apart from the method of obtaining the estimated contour information S2 from the line segment information, the broken line information, the curve information or the mask image information S1, the image i- which is the previous frame. By using the contour curve information C of No. 1 and estimating where the contour curve of the image i-1 has moved in the current image i by the motion vector estimation process, the estimated contour information S2 in the current image i can be obtained. It is made possible.

That is, the motion vector estimation unit 10 is obtained for the previous image i-1 via the contour candidate region determination unit 6, the gradient vector calculation unit 7, the contour route search unit 8, and the curve generation unit 9. The contour curve information C is used to estimate where the contour curve corresponding to the contour curve information C has moved in the current image i, and the result is estimated contour information S
2 is sent to the contour candidate area determination unit 6. in this case,
The processing from the contour candidate area determination unit 6 to the curve generation unit 9 is
The method is similar to that described above. Therefore, the estimated contour information S2
When the motion vector estimation unit 10 is selected as a method for obtaining the following, the curve generation unit 9 outputs the contour curve information C to the delay circuit 11
The motion vector estimating unit 10 is fed back via the.

The key calculator 3 receives the gradient vector information I _i and the contour curve information C at the two-end curve calculator 12. The both-end curve calculation unit 12 calculates the width between two curves (hereinafter, referred to as both-end curves) representing both ends of the contour based on the gradient vector information I _i and the contour curve information C, and the both ends. Both-end curve information S according to the width between curves
4 is sent to the soft key generation unit 13. The softkey generation unit 13 generates a curved surface whose height smoothly changes from “0” to “1” between the two curved edges based on the curved edge information S4, and the height of this curved surface is softkeyed. The soft key is calculated and output by performing a process of writing the value as a value in the image.

Thus, the key signal generating device 1 can generate the soft key of the object existing in the image.

(2) Structure of Curve Generating Unit FIG. 2 shows the structure of the curve generating unit 9 according to the embodiment of the present invention. As shown in FIG. 2, the curve generation unit 9 inputs the coordinate list P supplied from the contour route search unit 8 as shape data composed of a plurality of discrete coordinate data into the input coordinate division unit 21,
The connection condition calculation unit 22 and the curve approximation unit 23 receive it.

The input coordinate dividing unit 21 generates a list of coordinates of dividing points (hereinafter referred to as a dividing point coordinate list) E which divides the shape represented by the coordinate list P, as dividing point calculating means. Then, this is sent to the connection condition calculation unit 22 and the curve approximation unit 23. Here, the coordinate data of the division points (hereinafter, simply referred to as coordinates) represent the end points when the shape represented by the coordinate list P is divided into a plurality of segments, and accordingly the division point coordinate list E is It is a subset of the coordinate list P. Further, the input coordinate dividing unit 21 divides the coordinate list P 1 so that each segment can be efficiently approximated by a curve, as will be described later.

The linking condition calculating unit 22 as linking condition calculating means calculates linking conditions at each dividing point e _i , that is, linking conditions satisfying G1 continuity, based on the coordinate list P and the dividing point coordinate list E, The connection condition list RV is sent to the curve approximation unit 23. That connection condition calculating unit 22, as will be described later, of the coordinate r _i connecting position for matching the coupling position of each division point e _i, a velocity vector v _i for matching the velocity direction in the connecting position The pair is calculated as the connection condition list RV. In this case, the coordinate r _{i of the} connection position and the coordinate e _{i of the} division point do not necessarily match.

The curve approximating unit 23, as a curve approximating means,
Based on the coordinate list P, the division point coordinate list E, and the connection condition list RV, the segment of the shape indicated by the coordinate list P divided by the division point e _i and the division point e _{i + 1} is set to the division point e.
By performing curve approximation so as to satisfy the connection condition between _i and the division point e _{i + 1} , the division point e _i and the division point e _{i + 1}
An approximated curve c _i (that is, an approximated curve in the i-th segment) is calculated, and the approximated curve group C is sent to the both-ends curve calculation unit 12 as contour curve information C. Hereinafter, specific configurations of the input coordinate division unit 21, the connection condition calculation unit 22, and the curve approximation unit 23 will be described in order.

(2-1) Configuration of Input Coordinate Division Unit The configuration of the input coordinate division unit 21 is shown in FIG. 3, and the division processing of the coordinate list P in the input coordinate division unit 21 will be described using the flow chart shown in FIG. To do. The input coordinate division unit 21 starts the division processing of the coordinate list P 1 at step SP1, and the curvature calculation circuit 31 receives the coordinate list P 1 at step SP2. Next, the input coordinate dividing unit 21
At step SP3, each coordinate p _i (i = 0 to n−
The curvature ρ _i (i = 0 to n−1) in 1) is calculated, the curvature list Ρ formed by these curvatures ρ is generated in the curvature calculation circuit 31, and is sent to the curvature determination circuit 32.

Here, regarding the curvature calculation method from such a sequence of discrete points, "On the calculation of the curvature of the curve represented by the discrete points" (Naoki Ono, Ryuzo Takiyama, IEICE Technical Report, IE93-74)
, Pp.7-14, 1993), three methods are described.
According to this document, the coordinates at a point in the sequence of discrete points are
It is described that it can be calculated if the points sampled equidistantly in the front and rear of the vicinity are known. Therefore, in the curvature calculation circuit 31, for each coordinate p _i of the given coordinate list P 1, the front and rear coordinates are sampled at equal intervals, and the curvature calculation method of the discrete point sequence is used to calculate each coordinate p _i.
The curvature ρ _{i of} is calculated.

Then, the input coordinate dividing section 21 determines the step S.
In P4, based on the coordinate list P and the curvature list Ρ, the determination result τ _i (i = _i) of the curvature ρ _i at each coordinate p _i
0 to n-1) are calculated in the curvature determination circuit 32, and the determination result list T including these determination results τ _i is sent to the division point detection circuit 33. Here, the discrimination result list Τ
Is a discrete value indicating the result of classification according to the discrimination algorithm described later.

Next, the input coordinate dividing section 21 determines the step S
In P5, based on the coordinate list P 1, the curvature list Ρ, and the discrimination result list Τ, the division point detection circuit 33 divides the shape represented by the coordinate list P 1 into division point coordinates e.
₀ , e ₁ , ..., E _m-1 are extracted from the coordinate list P to generate a division point coordinate list E, and step SP6
At, the division point coordinate list E is sent to the connection condition calculation unit 22, and the division processing of the coordinate list P is ended at step SP7.

(2-1-1) Constitution of Curvature Calculation Circuit The calculation method of the curvature is not limited to the method described in the above-mentioned document "Calculation of the curvature of the curve represented by discrete points". Absent. Here, a method capable of obtaining an approximation accuracy similar to that described in this document is shown in FIG.
6 and FIG. 6, the curvature calculation process in the curvature calculation circuit 31 when the method is used will be described.

FIG. 5A shows the definition of curvature in continuous curve data, and FIG. 5B shows the definition of curvature in a sequence of discrete points. In FIG. 5A, if the change in the tangential direction between points s + ds separated by a distance ds from the point s on the curve is dθ, the curvature κ (s) at the point s is d
The limit of θ, that is,

[Equation 1] Is defined by Here, lim [s → 0] means the limit where s is brought close to “0”.

On the other hand, in FIG. 5B, the point p on the point sequence is
and _i, p _ij and the point in terms of before and after the point p _i p _{i + j} is equal intervals d
When obtained in s, it can be considered a line segment connecting the point p _ij and the point p _i and the tangent at the midpoint between the point p _ij and the point p _i. Similarly, the tangent line between the points p _i and p _{i + j} is the point p
It is given by the line segment connecting _i and the point p _{i + j} . The change in the tangential direction is dθ. Since the limit cannot be taken with a sequence of discrete points,
If dθ of the minimum ds obtained is substituted for the limit value,
The curvature of a sequence of discrete points is defined by

[Equation 2] Given in. Therefore, in the discrete point sequence, the curvature can be calculated by obtaining the minimum distance ds and the angle change dθ.

A method for obtaining dθ by approximation calculation without using a trigonometric function will be described with reference to FIGS. 6 (A) and 6 (B). FIG. 6A shows a method of calculating curvature, and when a point p _i , a point p _ij, and a point p _{i + j} that give the minimum distance ds obtained and θ at that time are given, a point p _ij And point p
The length φ of the perpendicular line drawn from the point p _{i with} respect to the line segment connecting _{i + j} is obtained. FIG. 6B is a graph showing the relationship between the perpendicular length φ and θ, and the change in θ from 0 to π / 2 is almost 2
It can be seen that φ can be approximated. For example, the approximation error at θ = π / 2 is about 10%.

Now, the curvature calculation processing in the curvature calculation circuit 31 will be described using the flow chart shown in FIG. The curvature calculation circuit 31, as a curvature calculation means, starts the curvature calculation process from step SP1 and receives the coordinate list P from the contour route search unit 8 at step SP2.
Subsequently, the curvature calculation circuit 31 determines in step SP3 that
In each coordinate p _i, samples the coordinates p _ij and p _{i + j} before and after the coordinate p _i at intervals j set in advance, the coordinates p _i,
Based on the coordinates p _ij and the coordinates p _{i + j} , the sample coordinate interval ds (in this case, the interval j) is calculated.

Thereafter, the curvature calculating circuit 31 determines the coordinates p _i ,
Based on the coordinates p _ij and coordinates p _{i + j,} and calculates the length φ of a perpendicular line drawn from the coordinate p _i with respect to a line segment connecting the coordinates p _ij and the coordinates p _{i + j,} the length of the perpendicular line After doubling the length φ, 2φ / ds is calculated to obtain the curvature ρ _i at the coordinate p _i to generate the curvature list Ρ. In step SP4, the curvature list Ρ is calculated.
And the curvature calculation process is ended in step SP5.

In the case of a noisy sequence of discrete points, the sample interval j when the minimum reliable interval ds is given is not necessarily "1". Also, the coordinate list P defines the sample intervals as j, assuming that the data are given at almost equal intervals, but in order to improve the calculation accuracy, a rule is set to make the sample intervals j equal to each other as much as possible. The sample interval j may be variably determined.

(2-1-2) Constitution of Curvature Discrimination Circuit and Division Point Detection Circuit The processing in the curvature discrimination circuit 32 and division point detection circuit 33 will be described using the flow chart shown in FIG.
The input coordinate dividing unit 21 starts the division processing of the coordinate list P using the curvature from step SP1 in the curvature discriminating circuit 32 and the division point detecting circuit 33, and in step SP2, the curvature list Ρ supplied from the curvature calculating circuit 31. Is received by the curvature determination circuit 32.

Subsequently, in step SP3, the input coordinate dividing section 21 causes the curvature discriminating circuit 32 as the curvature discriminating means.
, The absolute value of the curvature ρ _i at each coordinate p _i (| ρ
_i )), a binarized value obtained by performing threshold processing using a preset threshold T is calculated as the discrimination result τ _i , and the discrimination result list Τ
To generate. Next, at step SP4, the input coordinate dividing section 21 detects a point where the value of the discrimination result τ changes as a division point on the basis of the discrimination result list T in the division point detecting circuit 33 as the division point detecting means. A division point coordinate list E including the coordinates of the division points is generated. As a result, the shape represented by the coordinate list P can be divided into almost straight lines and curved lines.

That is, the input coordinate division unit 21 generates a division point coordinate list E representing the end points of the segment obtained by dividing the shape represented by the coordinate list P at the division points in the division point detection circuit 33. To do. Next, the input coordinate division unit 21 sends the division point coordinate list E to the connection condition calculation unit 22 in step SP5, and ends the process in step SP6.

In the case of this embodiment, the absolute value (| ρ _i |) of the curvature ρ _i and the threshold value equal to or smaller than a predetermined value are set to “0”.
The discriminant result τ _i is calculated using a threshold value T 1 which is close to.
A method of dividing the coordinate list P using the absolute value (| ρ _i |) of the curvature ρ _{i and} the threshold value T close to “0” will be described with reference to FIG.

The curve of FIG. 9A shows the shape represented by the coordinate list P. Since this shape is bent at two points, it can be relatively well approximated by a cubic curve. However, since the linear portion is long, it is possible to improve the approximation accuracy of each by linearly approximating the linear portion, that is, by approximating the curved portion by the cubic curve.

Here, when dividing at the position X as shown in FIG. 9 (B), a linear portion still remains in the divided right-hand curved portion. Therefore, considering the approximation accuracy, FIG. 9 (C)
Further division is required at the position X1 as shown in. However, as shown in FIG. 9C, position X and position X
If it is divided by 1, the linear portion that should be approximated by one straight line will be divided by two portions, so the approximation efficiency is not good. Therefore, in the case of this embodiment, the curvature list Ρ
On the basis of the above, the region where the shape is bent and the region where the shape is not bent are discriminated, and the shape represented by the coordinate list P is divided at these boundaries. Accordingly, as shown in FIG. 9D, the line can be divided into a straight line and a curved line, and the approximation efficiency can be improved.

Thus, the input coordinate division unit 21 calculates the curvature ρ at each coordinate p, thresholds the curvature ρ, and uses the magnitude of the curvature ρ as a reference to form the shape represented by the coordinate list P. By detecting the split points that split
The shape represented by the coordinate list P can be efficiently divided without depending on the number of coordinate data, and the shape represented by the coordinate list P can be divided into shapes that can be represented by a small order. Has been done.

(2-2) Structure of the connection condition calculation unit The structure of the connection condition calculation unit 22 is shown in FIG. 10, and the connection condition calculation processing in the connection condition calculation unit 22 will be described using the flow chart shown in FIG. Connection condition calculation unit 2
2 starts the connection condition calculation processing from step SP1,
In step SP2 and step SP3 respectively,
The division point curve approximation circuit 41 receives the coordinate list P and the division point coordinate list E.

[0052] In the following step SP4, coupling condition calculating unit 22, the division point curve approximation circuit 41 as a dividing point curve approximation means, at each division point e _i based on the division point coordinate list E, the division point e _i The j coordinates before and after are sampled from the coordinate list P, and these j sample coordinates are used to approximate the shape of the region in the vicinity of the division point e _i among the shapes represented by the coordinate list P. Curve c
e _i is calculated, and the curve list Ce including each curve ce _i is sent to the tangent line calculation circuit 42. Since this approximation processing is for estimating a local shape, the degree of the curve to be approximated may be set to an appropriately low value. The curve ce _i is represented by a parameter t (0 <= t <= 1), for example, t
= 0.5, it is required to pass near the division point e _i .

As for the concrete method of curve approximation, the above-mentioned "numerical calculation handbook", "shape processing engineering by computer display [I] [II]" and "Computer" are used.
Graphics Principles and Practice ". If the coordinate list P contains noise, the least squares method can be used for curve approximation to obtain a curve ce _i that is not affected by noise, and the spline approximation can be used for curve approximation. Since the calculation of can be simplified, it can be used properly according to the situation.

Next, at step SP5, the connection condition calculation unit 22 causes the tangent line calculation circuit 42 as a tangent line calculation means.
In the basis of the curve list Ce for each curve ce _i, to calculate the position passing through the vicinity of the division point e _i in curves ce _i as the connecting position r _i, the connecting position r _i
The velocity vector (tangential direction vector) v _i is calculated, and in step SP6, the pair of the coupling position r _i and velocity vector v _i calculated for each curve ce _i is sent to the curve approximation unit 23 as the coupling condition list RV. And step SP
In 7, the linking condition calculation process ends. Since here sought curve ce _i as described above in the parameter t, the curve ce _i (t = 0.5) connecting position r _i and the velocity vector v of
_Just calculate _i .

[0055] Thus connected condition calculating circuit 22, the position r _i and the tangential direction vector v _i of the curve ce _i at the division point e _i vicinity of dividing a shape expressed Te coordinate list P Niyotsu
By calculating and by local curve approximation, G
It is possible to calculate connection conditions that satisfy one continuity, and
By performing the local curve approximation using the least-squares method, the connection condition can be surely calculated even when the coordinate list P contains noise.

(2-3) Constitution of curve approximation unit The curve approximation unit 23 has a coordinate list P and a division point coordinate list E.
And a curve that approximates the respective division points is generated based on the connection condition list RV. In this embodiment, assuming that the coordinate list P contains noise, an approximation method using the least square method will be described. The approximate curve equation is
The case of using a cubic Bezier curve considering the connection condition will be described.

In general, the cubic Bezier curve is

[Equation 3] Can be represented by Where f, q0, q1, q
2 and q3 are vectors on a two-dimensional plane (x, y), and a ** b represents a to the power b.

When the connecting positions q0 and q3 and the tangential direction vectors u0 and u3 are given by the connecting condition of the dividing points of the curve, the equation (3) is given by

[Equation 4] Can be expressed as Here, h and k are scalars. A curve equation can be created by giving coordinate data f (t) and obtaining the scalars h and k by the least square method. That is, according to the method of least squares,

[Equation 5] Can be converted into a problem to solve the simultaneous equations of.

Here, A and F are values determined by the coordinate data f (t) and t, and B, C, D, E, G, H,
I and J are values determined by the inner product value of q0, q3, u0, u3. Therefore, when h0 and u3 are orthogonal, the scalars h and k are

[Equation 6] Can be obtained by

[Equation 7] Can be obtained by In this case, the curve f∧ (t) is simplified by the quadratic and linear approximations.

Here, the curve approximation processing in the curve approximation unit 23 will be described with reference to the flow chart shown in FIG. The curve approximating unit 23 starts the curve approximating process from step SP1 and receives the coordinate list P, the end point coordinate list E and the connection condition list RV at steps SP2, SP3 and SP4, respectively.

Subsequently, the curve approximating section 23 determines the step SP5.
In, the Bezier curve approximation by the above-mentioned least square method is performed on the coordinate list P 1 divided at each division point.
That is, the curve approximating unit 23 first samples, as the data f (t), a segment delimited by the division points e _i and e _{i + 1} in the shape represented by the coordinate list P ₁ . At this time, t is f (0) = e _i , f (1) = e _{i + 1}
Determine appropriately so that

Thereafter, the curve approximating unit 23 determines q0, q3, u0 and u3 based on the linking condition list RV, and then uses q0, q3, u0 and u3 in accordance with the method of least squares calculation. , The above A, B, C, D, E, F,
Calculate G, H, I and J. Next, the curve approximation unit 23
Is a scalar k and h from the calculated A, B, C, D, E, F, G, H, I and J using the equation (6) or the equation (7).
To calculate.

Next, the curve approximating unit 23 receives the scalars k and h.
And the curve f∧ (t) is calculated from the equation (4), and the calculation result is i
The approximate curve c _i in the th segment and step S
The process in P5 ends. In step SP6, the curve approximating unit 23 outputs the approximate curve group C composed of the approximate curves c _i calculated in step SP5 as the contour curve information C, and ends the curve approximating process in step SP7.

(2-4) Operations and Effects of the Embodiment With the above configuration, the curve generation unit 9 starts the curve generation processing from step SP1 shown in FIG.
2, the coordinate list P 2 composed of discrete data as shown in FIG. 14A is received from the contour route search unit 8. 14 (A) to 14 (C), the dotted line represents the shape indicated by the coordinate list P to be obtained. Here, since the coordinate list P contains noise, the point of each coordinate p given in the coordinate list P does not necessarily match the shape to be obtained indicated by the dotted line. Further, the number of coordinates does not match the order of the shape to be obtained indicated by the dotted line.

Next, the curve generator 9 creates a division point coordinate list E based on the coordinate list P in step SP3. That is, the curve generation unit 9 locally estimates the order of the shape to be obtained from the discrete arrangement of the coordinate list P 1. In this case, as shown in FIG. 14B, the coordinate list P is divided so that the degree of the shape of each divided segment does not increase. That is, since the order of the curve is determined based on the magnitude of the calculated curvature, the order in each segment is determined without depending on the number of coordinate data. Therefore, it is possible to prevent the order in each segment from increasing.

Subsequently, the curve generator 9 calculates the connection conditions r _i and v _i at each division point e _i in step SP4. That is, the curve generation unit 9 determines, as shown in FIG. 14C, each division point e _i calculated in step SP3.
Calculate an approximate curve ce _i that approximates the shape in the neighborhood,
Tangent r at division point e _i vicinity of the approximate curve ce _i
i , v _i are calculated, and these tangents are used as connection conditions for curve approximation of each segment. In this case, since the connection condition is calculated using the least squares method, the connection condition can be reliably obtained even when there is noise near the division point coordinates.

Then, in step SP5, the curve generator 9 approximates the segments delimited by the adjacent division points e _i and e _{i + 1} using the least squares method so as to satisfy the connection condition at both end points. Approximate curve c _i
Is calculated, the approximate curve group C formed of the approximate curves c _i is output as the contour curve information C in step SP6, and the curve generation processing is ended in step SP7 (FIG. 14).
(D)).

In this case, each approximated curve c is used as a connection condition at adjacent division points (that is, both end points of the segment).
calculating a tangent r _i, v _i at the division point e _i vicinity of e _i, because curve approximation is performed so as to maintain the coupling condition can be smoothly connected to each segment, Yotsute thereto The shape of each curve can be entirely matched.

Since the curve approximation is performed by using the least squares method, even if the coordinate list P contains noise, the desired order can be obtained from the coordinate list P containing noise without depending on the number of coordinate data. The curve of can be obtained. In addition, since it is possible to avoid vibrations caused by noise, it is possible to avoid a decrease in the accuracy of curve approximation and it is not necessary to check in advance what order the coordinate list should be approximated by. , It is possible to simplify the work of curve approximation.

Thus, the curve generation unit 9 has a high-order unknown shape of the coordinate list P, the number of data of the coordinate list P is irrelevant, and the coordinate list P contains noise. Even if there is, the curve can be approximated efficiently.

With the above arrangement, the shape represented by the coordinate list P is divided on the basis of the magnitude of curvature to determine the order of each segment, and the division points e _i in each approximate curve ce _i are divided. Calculate the tangent line in the neighborhood as the connection condition,
By approximating each curve ce _i so as to satisfy the connection condition, the shape represented by the coordinate list P is unknown in a high order, and the number of coordinate data in the coordinate list P and the order of the shape are irrelevant. Even if there is and the coordinate list P contains noise, curve approximation can be performed efficiently. Thus, the curve generation unit 9 capable of improving the efficiency of curve approximation
And a curve generation method can be realized.

(3) Other Embodiments In the above embodiment, the absolute value of the curvature ρ _i | ρ _i
For the magnitude of |, a value obtained by thresholding using a threshold value T 1 close to “0” which is equal to or smaller than a predetermined value is calculated as the discrimination result τ _i , and the discrimination result τ _i is calculated. it has dealt with the case of calculating the subdividing points for subdividing a shape expressed Te coordinate list P Niyotsu based, the present invention is not limited to this, as shown in step SP3 in FIG. 8, the calculated curvature [rho _i of with respect to the size, value was calculated as the determination result tau _i a value obtained by thresholding using a threshold value T of "0", the coordinate list P on the basis of the determination result tau _i You may make it calculate the division | segmentation point which divides the shape represented by this.

[0073] That is for making seamless connection between each approximated curve ce _i, it is better to divide the shape coupling conditions are represented Te coordinate list P Niyotsu at the position is stable to be used.
Therefore, the position where the curvature ρ _i is “0” is the most stable in the tangential direction, and therefore the point where the curvature ρ _i is “0” in the shape represented by the coordinate list P, that is, the coordinate list P is By calculating the bending points in the shape shown as the division points, the approximate curves ce _i can be connected more smoothly.

Further, as shown in step SP3 of FIG.
A value obtained by thresholding the absolute value of the curvature ρ _i | ρ _i | using a threshold value T equal to or greater than a predetermined value is calculated as a discrimination result τ _i , and the discrimination is performed. It is also possible to calculate division points for dividing the shape represented by the coordinate list P based on the result τ _i . in this case,
In the shape represented by the coordinate list P 1, a point where the curvature ρ _i has a peak is calculated as a division point.

Here, like the input coordinate dividing unit 50 shown in FIG. 15 in which parts corresponding to those in FIG. 3 are assigned the same reference numerals, threshold setting means 34 is provided to specify the range to be thresholded in the shape data. At the same time, the value of the threshold T may be set according to the specified range. That is, by setting the threshold value T 1 as a function of the coordinate data (x, y), the value of the threshold value T 2 and the range to be thresholded can be set freely, which allows the shape data to be set. Thresholding can be performed according to the position of the shape represented by In this case, the threshold function T (x,
y) may be a discrete function called the function T (P) of the coordinate list P 1.

A curvature smoothing unit 61 is provided between the curvature calculating unit 31 and the curvature discriminating unit 32 as in the input coordinate dividing unit 60 shown in FIG. 16 in which the portions corresponding to those in FIG. , Small variations in the curvature ρ _i due to noise may be avoided. Here, the division processing of the coordinate list P 1 in the input coordinate division unit 60 will be described using the flow chart shown in FIG.

The input coordinate division unit 60 starts the division process of the coordinate list P at step SP1 and receives the curvature list Ρ generated by the curvature calculation unit 31 at step SP2 at the curvature smoothing unit 61. Then in step SP3,
The input coordinate division unit 60 performs smoothing processing on the curvature list Ρ in the curvature smoothing unit 61 as the curvature smoothing means, and sends it to the curvature determination unit 32 as the curvature list Ρs. In this case, the smoothing is performed using a linear smoothing filter given by the sum of products calculation or a non-linear filter such as a median filter. This gives the curvature ρ
Even if a slight change in _i occurs due to noise, the effect of noise can be removed, and the precision of the division points can be further improved.

Next, at step SP4, the input coordinate dividing section 60 specifies the value of the threshold value T so that the curvature discriminating section 32 has a hysteresis characteristic such that the curvature increasing direction and the curvature decreasing direction have different hysteresis characteristics. Means 34
Then, threshold value processing is performed using the threshold value T 1 for the curvature list Ρs that has been set and smoothed to generate the determination result list Τ. As a result, step SP4
Since the input / output has a hysteresis as shown in (3), it is possible to avoid minute fluctuations in the vicinity of the threshold value and further improve the accuracy of the division points.

Subsequently, in step SP5, the input coordinate division section 60 generates the division point coordinate list E based on the discrimination result list T in the division point detection section 33, and outputs the division point coordinate list E in step SP6. Then, in step SP7, the division processing of the input coordinate list P 1 is completed.

Here, in the input coordinate dividing unit 60, each curvature ρ is smoothed, and the smoothed curvature ρ is subjected to thresholding processing using a threshold value T having a hysteresis characteristic. However, the present invention is not limited to this, and each curvature ρ is smoothed, or a threshold value T having a hysteresis characteristic is used for each curvature ρ. By performing either one of the threshold processing, it is possible to avoid the minute fluctuation of the curvature due to noise.

In the above embodiment, the case where the connection condition calculation unit 22 as shown in FIG. 10 is used as the connection condition calculation means has been described, but the present invention is not limited to this.
A connection condition calculating unit 70 as shown in FIG. 18 in which the same parts as those in FIG. 10 are denoted by the same reference numerals may be used as the connection condition calculating means.

The connection condition calculation processing in the connection condition calculation unit 70 will be described using the flow chart shown in FIG. The connection condition calculation unit 70 starts the connection condition calculation processing from step SP1, and in step SP2 and step SP3, the coordinate list P and the division point coordinate list E are divided by the division point curvature calculation circuit 71 and the division point curve approximation circuit 41, respectively. receive. Then, in step SP4, the connection condition calculation unit 70 calculates the curvature ρ _i at each division point e _i in the division point curvature calculation circuit 71 as the division point curvature calculation means. Here, the division point curvature calculation circuit 71 calculates the curvature ρ _i at each division point e _{i by} the same method as the curvature calculation method in the curvature calculation unit 31 described above, and sends it to the sample range calculation circuit 72.

Then, in step SP5, the linking condition calculating unit 70 uses the function shown in step SP5 of FIG. 19 in the sample range calculating circuit 72 as the coordinate data extraction range calculating means, based on the curvature ρ. , An extraction range (sample range) j for extracting coordinate data in the vicinity of each division point e _i from the coordinate list P 1, and sends the sample range j to the division point curve approximation circuit 41. By calculating the sample range j like this function,
Where the curvature ρ is large, the sample range can be made small so that the curve can be approximated by a curve of a low order.

That is, in the case of quadratic or higher approximation in the curve approximation, the calculation becomes complicated because the least squares method and the spline approximation require matrix calculation. Therefore, the linear approximation can simplify the calculation. . When approximating a tangent line by linear approximation, the coordinate list P
The accuracy of curve approximation can be maintained by controlling the sample range so that the bent portion in the shape represented by the above does not fall within the sample range.

Subsequently, in step SP6, the connection condition calculating unit 70 extracts the coordinate data in the vicinity of each dividing point e ₁ in the dividing point curve approximating circuit 41 by using the sample range j _i and uses the extracted coordinate data. And approximates the curve to generate an approximated curve ce _i . Here, even with a simple method such as approximation with a line segment connecting both ends of the sampled coordinates, the sampling range j
_i has been determined.

Next, in step SP7, the connection condition calculating section 70 calculates the tangent lines r _i , v _i in the vicinity of each dividing point e _i in each approximate curve ce _i in the tangent line calculating circuit 42, and in step SP8 the relevant tangent lines r _i , v _i are calculated. Tangent list R
V is output, and the connection condition calculation process is ended in step SP9.

Therefore, since the connection condition calculating unit 70 controls the sample range so that the bent portion in the shape represented by the coordinate list P is not included in the sample range, even in a simple curve approximation calculation. It is possible to calculate a connection condition with a small error.

Further, in the above-mentioned embodiment, the curvature ρ in each coordinate data is calculated, and the division points for dividing the shape represented by the coordinate list P are calculated based on the calculated curvature ρ. However, the present invention is not limited to this, and the division point for dividing the shape represented by the coordinate list P is set to the number of coordinate data based on the shape represented by the coordinate list P. The shape may be specified visually by the operator without depending on it. The point is to divide the shape represented by the coordinate list P so that it does not depend on the number of coordinate data and the order of each segment does not increase. If possible, the shape represented by the coordinate list P may be divided by various other methods.

Further, in the above-mentioned embodiment, the case where the present invention is applied to the key signal generating device has been described, but the present invention is not limited to this, and the essential points such as an object recognizing device, an object tracking device, an image synthesizing device, The present invention can be applied to various other items as long as it is necessary to generate a curve from shape data composed of a plurality of discrete coordinate data. In particular, in the image processing as in the embodiment, it is necessary to convert the 8-neighbor line figure represented by the image into a curve, and such a line figure is particularly effective because it includes a quantization error due to a pixel grid. .

[0090]

As described above, according to the present invention, when a division point for dividing a shape into a plurality of segments is calculated, division is performed based on the length of a predetermined line segment obtained based on coordinate data of three points. It is determined whether or not it is, and the curve approximation is performed for each segment so that the connection condition at each division point of the determination result is satisfied. Therefore, when connecting each segment, the curvature approximation with a predetermined approximation accuracy can be efficiently performed. It can be carried out.

[Brief description of drawings]

FIG. 1 is a block diagram showing an overall configuration of a key signal generation device to which the present invention is applied.

FIG. 2 is a block diagram showing a configuration of a curve generation unit according to an embodiment.

FIG. 3 is a block diagram showing a configuration of an input coordinate division unit.

FIG. 4 is a flowchart for explaining a processing procedure of coordinate list division processing.

FIG. 5 is a schematic diagram for explaining a curvature calculation in a continuous curve and a sequence of discrete points.

6A and 6B are schematic diagrams (A) and graphs (B) for explaining calculation of approximate curvature in a sequence of discrete points.

FIG. 7 is a flowchart for explaining a processing procedure of curvature calculation processing.

FIG. 8 is a flow chart for explaining a processing procedure in a discrimination circuit and a division point detection circuit.

FIG. 9 is a flowchart for explaining a method of dividing a coordinate list.

FIG. 10 is a block diagram showing the configuration of a connection condition calculation unit.

FIG. 11 is a flowchart for explaining the processing procedure of the connection condition calculation processing.

FIG. 12 is a flowchart for explaining a processing procedure of curve approximation processing.

FIG. 13 is a flowchart for explaining a processing procedure of curve generation processing.

FIG. 14 is a schematic diagram showing a state of a curve generation process.

FIG. 15 is a block diagram showing a configuration of an input coordinate dividing unit according to another embodiment.

FIG. 16 is a block diagram showing a configuration of an input coordinate division unit according to another embodiment.

FIG. 17 is a flow chart showing a processing procedure of coordinate list division processing according to another embodiment.

FIG. 18 is a block diagram showing a configuration of a connection condition calculation unit according to another embodiment.

FIG. 19 is a flowchart for explaining the processing procedure of the connection condition calculation processing according to another embodiment.

[Explanation of symbols]

1 ... Key signal generation device, 2 ... Contour extraction unit, 3 ... Key calculation unit, 4 ... Input means, 5 ... Estimated contour calculation unit, 6
...... Contour candidate region determination unit, 7 …… Gradient vector calculation unit, 8 …… Contour route search unit, 9 …… Curve generation unit,
10 ... Motion vector estimation unit, 11 ... Delay circuit, 12
...... End curve calculation part, 13 ...... soft key generation part, 2
1, 50, 60 ... Input coordinate division unit, 22, 70 ... Connection condition calculation unit, 23 ... Curve approximation unit, 31 ... Curvature calculation circuit, 32 ... Curvature discrimination circuit, 33 ... Division point detection circuit , 34 ... Threshold setting means, 41 ... Dividing point curve approximation circuit, 42 ... Tangent calculating circuit, 61 ... Curvature smoothing section, 71 ... Dividing point curvature calculating circuit, 72 ... Sample range calculating circuit .

Continuation of front page (56) Reference JP-A-5-290159 (JP, A) (58) Fields investigated (Int.Cl. ⁷ , DB name) G06T 11/00-11/20 G06T 7 / 00,7 / 60

Claims (12)

(57) [Claims] 1. A curve generation device for generating an approximate curve of a shape indicated by the coordinate data from a plurality of discrete coordinate data, and dividing point calculation means for calculating a dividing point for dividing the shape into a plurality of segments. A connection condition calculating means for calculating a connection condition for connecting the adjacent segments for each of the division points, and at least the connection conditions are taken into consideration so that the connection condition at each of the division points is satisfied. Curve dividing means for curve approximating each of the segments, and the dividing point calculating means for sampling from the coordinate data.
A curve generation device, characterized in that a length of a predetermined line segment obtained based on coordinated data of three drawn points is obtained, and whether or not a division point is calculated is determined based on the length of the line segment. 2. A curve generation device for generating an approximate curve of a shape indicated by the coordinate data from a plurality of discrete coordinate data, and dividing point calculation means for calculating a dividing point for dividing the shape into a plurality of segments. A connection condition calculating means for calculating a connection condition for connecting the adjacent segments for each of the division points, and at least the connection conditions are taken into consideration so that the connection condition at each of the division points is satisfied. A curve approximating means for approximating each segment by a curve, and the connection condition calculating means extracts coordinate data in the vicinity of each division point from the shape data, and uses the extracted coordinate data to convert the shape data according to the shape data. Dividing point curve approximation means for generating an approximation curve approximate to the shape in the vicinity of each dividing point among the shapes shown, and the dividing point curve approximation Curve generation apparatus characterized by comprising a tangent in the vicinity of the division point in each of the approximation curve generated by stage and tangent calculating means for calculating as a coupling condition in the above division point. 3. The division point calculating means calculates a curvature in each coordinate data based on the shape data, and a curvature calculating means for each curvature in each coordinate data calculated by the curvature calculating means. 3. A curvature discriminating means for threshold value processing, and a division point detecting means for detecting the division point from the shape data based on the discrimination result of the curvature discriminating means. The described curve generator. 4. The threshold value is at least one of a threshold value below a predetermined value, a threshold value of “0”, a threshold value above a predetermined value, or a threshold value having a hysteresis characteristic. The curve generation device according to claim 3, wherein: 5. The division point calculation means specifies the range to be thresholded in the shape data, and sets the threshold value according to the range to be thresholded in the shape data. 5. The curve generation device according to claim 4, further comprising a threshold value setting means for performing the setting. 6. The dividing point calculating means includes a curvature smoothing means for smoothing each curvature in the coordinate data calculated by the curvature calculating means, and the curvature discriminating means is the curvature smoothing means. The curve generation device according to claim 3, wherein the threshold processing is performed on each of the curvatures smoothed by. 7. The connection condition calculating means extracts coordinate data near each of the division points from the shape data, and uses the extracted coordinate data to extract each of the shapes represented by the shape data. A dividing point curve approximating means for generating an approximate curve approximate to a shape near the dividing point, and a tangent line in the vicinity of the dividing point in each of the approximate curves generated by the dividing point curve approximating means is a connecting condition at each of the dividing points. The curve generation device according to claim 1, further comprising: a tangent calculation unit that calculates 8. The curve generation device according to claim 2, wherein the dividing point curve approximating means generates the approximation curve by using a least square method or a spline approximation method. 9. The coordinate data extraction range calculation means for calculating the extraction range for extracting the coordinate data in the vicinity of each of the division points from the shape data based on the calculation result of the division point curvature calculation means. The dividing point curve approximating means is represented by the shape data using the coordinate data existing in each of the extraction ranges calculated for each of the dividing points by the coordinate data extraction range calculating means. The curve generation device according to claim 7, wherein an approximate curve that approximates the shape near each of the division points of the shape is generated. 10. The curve generating device according to claim 1, wherein the curve approximating means approximates the respective curves by a least square method. 11. A curve generation method for causing an information processing apparatus to generate an approximate curve of a shape indicated by the coordinate data from a plurality of discrete coordinate data, wherein the information processing apparatus divides the shape into a plurality of segments. A division point calculation step of calculating a division point, and causing an information processing apparatus to execute a connection condition calculation step of calculating a connection condition for connecting adjacent segments for each of the division points. The apparatus is caused to execute a curve approximation step of curve-approximation of each segment so as to satisfy the connection condition at each division point in consideration of at least each connection condition, and in the division point calculation step, the coordinate data is obtained. From Sun
A method for generating a curve, characterized in that a length of a predetermined line segment obtained based on coordinated data of three pulled points is determined, and whether or not to calculate a division point is determined based on the length of the line segment. 12. A curve generation method for causing an information processing device to generate an approximate curve of a shape indicated by the coordinate data from a plurality of discrete coordinate data, wherein the information processing device divides the shape into a plurality of segments. A division point calculation step of calculating a division point, and causing an information processing apparatus to execute a connection condition calculation step of calculating a connection condition for connecting adjacent segments for each of the division points. In the apparatus, at least the connection conditions are considered, and a curve approximation step of curve-applying the segments is performed so as to satisfy the connection conditions at the division points, and further, in the connection condition calculation step, Coordinate data in the vicinity of each division point is extracted from the shape data, and is represented by the shape data using the extracted coordinate data. A division point curve approximation step that generates an approximation curve that approximates the shape near each of the division points of the shape is executed, and a tangent line near the division point in each of the approximation curves generated by the division point curve approximation step The method for generating a curve is characterized in that a tangent line calculation step for calculating as a connection condition at each of the division points is executed.