CN109242016B - A kind of similitude judgment method of space curve - Google Patents

A kind of similitude judgment method of space curve Download PDF

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CN109242016B
CN109242016B CN201811002453.2A CN201811002453A CN109242016B CN 109242016 B CN109242016 B CN 109242016B CN 201811002453 A CN201811002453 A CN 201811002453A CN 109242016 B CN109242016 B CN 109242016B
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curve
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point
attribute
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CN109242016A (en
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汪日伟
程瑞
刘凤连
赵津东
温显斌
李雷辉
李文龙
张静
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Tianjin University of Technology
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Abstract

The present invention relates to a kind of similitude judgment method of space curve, the starting point of two space curves to be compared the following steps are included: step 1, moved to same position by technical characterstic；Step 2, the perspective plane for constructing two space curves respectively, and two space curves are separately converted to the gray value of projection line corresponding position to attribute values such as the distance value on perspective plane, first derivative values, second derivative values, curvature values, attribute image is defined with this；The grey level histogram of step 3, statistical attribute image, calculate the grey level histogram and normalized of curve to be compared, the similarity that attribute image is obtained based on cosine similarity calculation method counts the similarity of two space curves further according to the weight that each attribute image defines the power for portraying curve shape.The present invention do not need repeatedly to translate curve, rotates and scale transform, and the Solve problems of the NP hardly possible to model are converted to a kind of new polynomial derivation algorithm.

Description

A kind of similitude judgment method of space curve
Technical field
The invention belongs to image procossings and graph transformation technical field, are related to the similitude judgment method of space curve, especially It is a kind of similitude judgment method of space curve.
Background technique
Currently, in computer picture, pattern-recognition and protein structure prediction, robot trajectory planning, control system, three The problem analysis of geometric locus is all referred in the application neighborhood such as the threedimensional model in dimension magnetic field and flow field, brain and heart, wherein The similitude judgement of curve is a basic common problem.Due to the complexity and application of similarity of curves decision problem Popularity has all made a large amount of research work there are many scholar in each related fields.
It is directed to the judgment method of space curve similitude at this stage, method and characteristic value are mainly defined using similarity function Method.It is better than method of characteristic effect to a certain extent that similarity function defines method, but in practice, curve is by discrete Point construct, it is during differentiation that the expression of the form of curve function is highly difficult, and have for the fitting of curve Curve is finally also carried out translation and stretching by very high requirement.Similarity function defines method due to needing three-dimensional space Half interval contour is transformed into two dimensional image, and will first Align Curves starting point, and constructs the perspective plane for projecting into image, then pass through projection The feature of curve distribution is extracted, the preceding preparation step for causing it to calculate similitude slightly shows numerous.Although method of characteristic identifies Fast speed, but since the method for extracting feature is numerous, each extraction characteristics algorithm is not that effect is fine, causes identification quasi- True rate reduces.
Summary of the invention
It is an object of the invention to overcome the deficiencies of the prior art and provide a kind of designs rationally, calculating process is simple, calculates The similitude judgment method for the space curve that data volume is greatly decreased and recognition speed is fast, accuracy of identification is high.
The present invention solves its technical problem and adopts the following technical solutions to achieve:
A kind of similitude judgment method of space curve, comprising the following steps:
The starting point of two space curves to be compared is moved to same position by step 1；
Step 2, the perspective plane for constructing two space curves respectively, and hanging down each point on two space curves to perspective plane Straight distance value, first derivative values, second derivative values, curvature value are converted into the gray value of subpoint corresponding position, to construct Aforementioned four attribute image out；
Step 3, the respectively histogram of statistical distance attribute image, the histogram of first derivative attribute image, second dervative The histogram of attribute image and the histogram of curvature attributes image, and normalize respectively, then calculate respective Pasteur's correlation Coefficient obtains distance property image corresponding to two curves, first derivative attribute image, second dervative attribute image, curvature category The similarities such as property image, the weight that finally power of portrayed curve shape is defined according to each attribute image, statistical inference The similarity of two space curves out.
Moreover, the specific steps of the step 1 include:
(1) arbitrary curve equation is established:
pi(t)=Ai+Bit+Cit2+Dit3, wherein t is parameter；
(2) the starting point (x of two space curves to be comparedold(t),yold(t),zold(t)) same position is moved to, Obtain new coordinate (xnew(t),ynew(t),znew(t)):
Wherein, Tx, Ty, Tz represent the coordinate translation amount of translation matrix；x(t),y(t),z(t)Any point on curve is represented to sit Mark；
Moreover, the perspective plane of two space curves of construction of the step 2 method particularly includes: with space curve to starting point The line h that A and terminal B is constituted is apart from farthest vertical line g, and wherein the intersection point C of g and h, as normal vector and crosses line h's using vertical line g Plane definition is the projection plane α of this space curve；
Moreover, vertical range value, first derivative values, two of each point to perspective plane on two space curves of the step 2 Order derivative value, the calculating step of curvature value include:
(1) normal vector known to (A, B, C), (x0, y0, z0) are some coordinates that the plane is passed through, then thus define Plane equation are as follows:
A (x-x0)+B (y-y0)+C (z-z0)=0
(2) distance value is calculated:
Arbitrary point x on curved surface(t),y(t),z(t)The distance for having arrived plane equation Ax+By+Cz+D=0 is d, wherein D=A X0+By0+Cz0, then the calculating of d is as follows:
(3) first derivative values, second derivative values and curvature value are calculated:
For arbitrary curve equation:
pi(t)=Ai+Bit+Cit2+Dit3
Wherein, t is parameter, the calculating of first derivative are as follows:
p′i(t)=Bi+2Cit+3Dit2
Its second dervative are as follows:
p″i(t)=2Ci+6Dit
For space curve f (x (t), y (t), z (t)), the calculating of curvature K is as follows:
For curvilinear equation parameter (t) point M (a, b, c) derivative:
For three-dimensional space curve f (x (t), y (t), z (t)), curvature k can be promoted:
Moreover, four attribute images of the construction of the step 2 method particularly includes: space curve is vertically thrown on the projection surface Shadow obtains two-dimensional projection line, by space curve to subpoint distance value, first derivative values, second derivative values, curvature value, conversion For the gray value of projection line corresponding position, and then construct corresponding attribute image.
Moreover, the calculation formula of Pasteur's related coefficient of the step 3 is as follows:
Wherein p (i), p'(i) histogram data that respectively represents attribute image corresponding to two space curves, to each phase With the data dot-product extraction of square root of i, to be added the result obtained later be image similarity value ρ (p, p'), range for 0 to 1 it Between；ρ1Represent the similarity of distance property image, ρ2Represent the similarity of first derivative attribute image, ρ3Represent second dervative category The similarity of property image, ρ4Represent the similarity of curvature attributes image.
Moreover, the weight of the step 3 defined according to each attribute image to the power of portrayed curve shape, statistics It is inferred to the calculation formula of the similarity of two space curves are as follows:
Ω=(ρ1×ω1+ρ2×ω2+ρ3×ω3+ρ4×ω4)
In above formula, ω1The vertical range value for representing each point to perspective plane on two space curves, which accounts for, portrays curve shape Weight；ω2The first derivative values for representing each point on two space curves account for the weight for portraying curve shape；ω3Represent two spaces The second derivative values of each point account for the weight for portraying curve shape on curve；ω4Represent the curvature value of each point on two space curves Account for the weight for portraying curve shape.
The advantages and positive effects of the present invention are:
1, the present invention carries out projection using space curve in step 1 and step 2 and forms image, in step 3 can carve Each attribute value for drawing space curve geometry constructs corresponding attribute image as the gray value of subpoint, thus by three-dimensional figure The similarity system design of shape is converted into the comparison of two dimensional image, efficiently uses the point in the geometric properties of space curve on space curve The geometrical property not influenced to the distance in specific projection face, first derivative, second dervative and curvature etc. by coordinate system, will be to sky The similitude judgement of half interval contour is converted into the processing of image；The calculation formula of coefficient of similarity is provided in step 4, judgment curves are It is no similar, it is not necessarily to data prediction, data volume greatly reduces, and operation is facilitated to store, and reduces the complexity of three-dimensional space, letter Change problem, improved recognition speed and precision, improves man-machine mutual effect.
2, the present invention is not needed repeatedly to translate curve, be rotated and scale transform, the NP to model is difficult Solve problems are converted to a kind of new polynomial derivation algorithm, reduce data processing amount, improve recognition speed and precision.
Detailed description of the invention
Fig. 1 is process flow diagram of the invention；
Fig. 2 is the grey level histogram of the distance of space curve projected image of the invention；
Fig. 3 is the grey level histogram of the first derivative of space curve projected image of the invention；
Fig. 4 is the grey level histogram of the second dervative of space curve projected image of the invention；
Fig. 5 is the grey level histogram of the curvature of space curve projected image of the invention.
Specific embodiment
The embodiment of the present invention is described in further detail below in conjunction with attached drawing:
A kind of similitude judgment method of space curve, as shown in Figure 1, comprising the following steps:
The starting point of two space curves to be compared is moved to same position by step 1；
The specific steps of the step 1 include:
(1) arbitrary curve equation is established:
pi(t)=Ai+Bit+Cit2+Dit3, wherein t is parameter；
(2) the starting point (x of two space curves to be comparedold(t),yold(t),zold(t)) same position is moved to, Obtain new coordinate (xnew(t),ynew(t),znew(t)):
Wherein, Tx, Ty, Tz represent the coordinate translation amount of translation matrix；x(t),y(t),z(t)Any point on curve is represented to sit Mark；
Step 2, the perspective plane for constructing two space curves respectively, and hanging down each point on two space curves to perspective plane Straight distance value, first derivative values, second derivative values, curvature value are converted into the gray value of subpoint corresponding position, to construct Aforementioned four attribute image E1, E2, E3, E4 as shown in Figures 2 to 5 out；
In the present embodiment, the perspective plane of two space curves of construction of the step 2 method particularly includes: with space song The line h that line is constituted to starting point A and terminal B is apart from farthest vertical line g, the wherein intersection point C of g and h, using vertical line g as normal vector and The plane definition for crossing line h is the projection plane α of this space curve；
In the present embodiment, each point is led to the vertical range value on perspective plane, single order on two space curves of the step 2 Numerical value, second derivative values, curvature value calculating step include:
(1) normal vector known to (A, B, C), (x0, y0, z0) are some coordinates that the plane is passed through, then thus define Plane equation are as follows:
A (x-x0)+B (y-y0)+C (z-z0)=0
(2) distance value is calculated:
Arbitrary point x on curved surface(t),y(t),z(t)The distance for having arrived plane equation Ax+By+Cz+D=0 is d, wherein D=A X0+By0+Cz0, then the calculating of d is as follows:
(4) first derivative values, second derivative values and curvature are calculated:
For arbitrary curve equation:
pi(t)=Ai+Bit+Cit2+Dit3
Wherein, t is parameter, the calculating of first derivative are as follows:
p′i(t)=Bi+2Cit+3Dit2
Its second dervative are as follows:
p″i(t)=2Ci+6Dit
For space curve f (x (t), y (t), z (t)), the calculating of curvature K is as follows:
For curvilinear equation parameter (t) point M (a, b, c) derivative:
For three-dimensional space curve f (x (t), y (t), z (t)), curvature k can be promoted:
In the present embodiment, the construction of the step 2 four attribute images method particularly includes: space curve is on perspective plane Upper upright projection obtains two-dimensional projection line l, by space curve to subpoint distance value, first derivative values, second derivative values, song Rate value d1, d2, d3, d4 are converted into the gray value λ 1 of projection line corresponding position, λ 2, λ 3, λ 4, and then construct corresponding category Property image E1, E2, E3, E4.
Step 3, the respectively histogram of statistical distance attribute image, the histogram of first derivative attribute image, second dervative The histogram of attribute image and the histogram of curvature attributes image, and normalize respectively, then calculate respective Pasteur's correlation Coefficient obtains distance property image corresponding to two curves, first derivative attribute image, second dervative attribute image, curvature category The similarities such as property image, the weight that finally power of portrayed curve shape is defined according to each attribute image, statistical inference The similarity of two space curves out.
The calculation formula of Pasteur's related coefficient of the step 3 is as follows:
Wherein p (i), p'(i) histogram data that respectively represents attribute image corresponding to two space curves, to each phase With the data dot-product extraction of square root of i, to be added the result obtained later be image similarity value ρ (p, p'), range for 0 to 1 it Between；ρ1Represent the similarity of distance property image, ρ2Represent the similarity of first derivative attribute image, ρ3Represent second dervative category The similarity of property image, ρ4Represent the similarity of curvature attributes image；
The weight that the power of portrayed curve shape is defined according to each attribute image of the step 3, statistical inference The calculation formula of the similarity of two space curves out are as follows:
Ω=(ρ1×ω1+ρ2×ω2+ρ3×ω3+ρ4×ω4)
In above formula, ω1The vertical range value for representing each point to perspective plane on two space curves, which accounts for, portrays curve shape Weight；ω2The first derivative values for representing each point on two space curves account for the weight for portraying curve shape；ω3Represent two spaces The second derivative values of each point account for the weight for portraying curve shape on curve；ω4Represent the curvature value of each point on two space curves Account for the weight for portraying curve shape.
In the present embodiment, the vertical range value for defining each point to perspective plane on two space curves, which accounts for, portrays curve shape The 10% of weight；The first derivative values for defining each point on two space curves, which account for, portrays the 30% of curve shape weight；Define two The second derivative values of each point, which account for, on space curve portrays the 30% of curve shape weight；Define each point on two space curves Curvature, which accounts for, portrays the 30% of curve shape weight；
The then calculation formula of the similarity of curve are as follows:
Ω=(ρ1× 10%+ ρ2× 30%+ ρ3× 30%+ ρ4× 30%)
It is emphasized that embodiment of the present invention be it is illustrative, without being restrictive, therefore packet of the present invention Include and be not limited to embodiment described in specific embodiment, it is all by those skilled in the art according to the technique and scheme of the present invention The other embodiments obtained, also belong to the scope of protection of the invention.

Claims (7)

1. a kind of similitude judgment method of space curve, it is characterised in that: the following steps are included:
The starting point of two space curves to be compared is moved to same position by step 1；
Step 2, respectively construct two space curves perspective plane, and by each point on two space curves to perspective plane it is vertical away from From the gray value that value, first derivative values, second derivative values, curvature value are converted into subpoint corresponding position, to construct four The image of a attribute；
Step 3, the respectively histogram of statistical distance attribute image, the histogram of first derivative attribute image, second dervative attribute The histogram of image and the histogram of curvature attributes image, and normalize respectively, then calculate respective Pasteur's related coefficient, Obtain distance property image corresponding to two curves, first derivative attribute image, second dervative attribute image, curvature attributes image Similarity, the weight that finally power of portrayed curve shape is defined according to each attribute image, statistical inference go out two sky The similarity of half interval contour.
2. a kind of similitude judgment method of space curve according to claim 1, it is characterised in that: the step 1 Specific steps include:
(1) arbitrary curve equation is established:
pi(t)=Ai+Bit+Cit2+Dit3, wherein t is parameter；
(2) the starting point (x of two space curves to be comparedold(t),yold(t),zold(t)) same position is moved to, is obtained New coordinate (xnew(t),ynew(t),znew(t)):
Wherein, Tx, Ty, Tz represent the coordinate translation amount of translation matrix；X (t), y (t), z (t) represent any point coordinate on curve.
3. a kind of similitude judgment method of space curve according to claim 1, it is characterised in that: the step 2 Construct the perspective plane of two space curves method particularly includes: the line h distance constituted with space curve to starting point A and terminal B Farthest vertical line g, wherein the intersection point C of g and h, by normal vector of vertical line g and to cross the plane definition of line h be this space curve Projection plane α.
4. a kind of similitude judgment method of space curve according to claim 1, it is characterised in that: the step 2 Each point is to the vertical range value on perspective plane, first derivative values, the calculating step of second derivative values, curvature value on two space curves Include:
(1) normal vector known to (A, B, C), (x0, y0, z0) are some coordinates that the plane is passed through, the then plane thus defined Equation are as follows:
A (x-x0)+B (y-y0)+C (z-z0)=0
(2) distance value is calculated:
Arbitrary point x (t) on curved surface, y (t), the distance of z (t) to plane equation Ax+By+Cz+D=0 are d, wherein D=- (Ax0 + By0+Cz0), then the calculating of d is as follows:
(3) first derivative values, second derivative values and curvature value are calculated:
For arbitrary curve equation:
pi(t)=Ai+Bit+Cit2+Dit3
Wherein, t is parameter, the calculating of first derivative are as follows:
p′i(t)=Bi+2Cit+3Dit2
Its second dervative are as follows:
p″i(t)=2Ci+6Dit
For space curve f (x (t), y (t), z (t)), the calculating of curvature k is as follows:
For curvilinear equation parameter t point M (a, b, c) derivative:
For three-dimensional space curve f (x (t), y (t), z (t)), curvature k can be promoted:
5. a kind of similitude judgment method of space curve according to claim 1, it is characterised in that: the step 2 Construct four attribute images method particularly includes: upright projection obtains two-dimensional projection line to space curve on the projection surface, will be empty Half interval contour is converted into the ash of projection line corresponding position to subpoint distance value, first derivative values, second derivative values, curvature value Angle value, and then construct corresponding attribute image.
6. a kind of similitude judgment method of space curve according to claim 1, it is characterised in that: the step 3 The calculation formula of Pasteur's related coefficient is as follows:
Wherein p (i), p ' (i) respectively represents the histogram data of attribute image corresponding to two space curves, to each identical i Data dot-product extraction of square root to be added the result obtained later be image similarity value ρ (p, p '), range is between 0 to 1；ρ1 Represent the similarity of distance property image, ρ2Represent the similarity of first derivative attribute image, ρ3Represent second dervative attribute image Similarity, ρ4Represent the similarity of curvature attributes image.
7. a kind of similitude judgment method of space curve according to claim 6, it is characterised in that: the step 3 According to the weight that each attribute image defines the power of portrayed curve shape, statistical inference goes out the similarity of two space curves Calculation formula are as follows:
Ω=(ρ1×ω1+ρ2×ω2+ρ3×ω3+ρ4×ω4)
In above formula, ω1The vertical range value for representing each point to perspective plane on two space curves accounts for the weight for portraying curve shape； ω2The first derivative values for representing each point on two space curves account for the weight for portraying curve shape；ω3Represent two space curves The second derivative values of upper each point account for the weight for portraying curve shape；ω4The curvature value for representing each point on two space curves accounts for quarter The weight of trace shape.
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