CN106570864B - Conic fitting method in image based on geometric error optimization - Google Patents
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Abstract
The present invention relates to a kind of conic fitting methods in image based on geometric error optimization, comprising: extracts the point m of the edge image of specific conic section M in imagei；Calculate point miTo the geometric distance d of conic section Mfa(mi,C)；To geometric distance dfa(mi, C) and linear weighted function iteration is carried out, Matrix C relevant to C is obtained with singular value decomposition method1；Using based on most short geometric distance d (mi, C) building objective function, calculating work as C=C1When small quantity Δ u when making the minimization of object functioni,ΔviAnd scale parameter λiValue, and be denoted as Δ u respectivelyi1,Δvi1And λi1；With Δ ui1,Δvi1And λi1For initial value, nonlinear optimization solution is carried out to the objective function, obtains the coefficient matrix C of conic section M2, according to coefficient matrix C2Generate the conic section M in described image after the optimization of specific conic section M2.The present invention, which realizes, combines the high efficiency of conic fitting method and high-precision ideal effect in image, and improves the precision of conic fitting in image.
Description
Technical Field
The invention belongs to the field of computer vision, and particularly relates to a quadratic curve fitting method based on geometric error optimization.
Background
In various artificial objects and natural landscapes, the quadratic curve is everywhere visible. Image quadratic curve fitting is regarded as a primary processing step for many applications and is gaining attention in the fields of computer vision, industrial measurement, computer graphics, and the like. The image quadratic curve fitting has important application value in the aspects of robot navigation, virtual reality, augmented reality and the like.
A perspective camera transforms a scene into an image by perspective projection. A particular conic in the scene is still a conic in the projected image, but the conic in the image may be a circle, ellipse, parabola or even a degenerate straight line. If we have no a priori knowledge of the scene before detecting a type of conic, it is difficult for the computer to automatically know the specific type of conic in the image. Therefore, it is necessary to study the fitting problem of the general quadratic curve (the type of quadratic curve is unknown). After the quadratic curve is fitted, the type of the quadratic curve is identified, so that automation can be realized and the method is easy. The quadratic curve fitting in the present invention refers to general quadratic curve fitting if it is not specified.
A very natural approach to the quadratic curve fitting problem is to use a linear least squares method. However, in practical tasks, the accuracy of this method is difficult to meet our requirements due to occlusion, noise, blur, and the like. Therefore, a number of different optimization algorithms have emerged to improve the accuracy of the quadratic curve fit. At present, there are three different types of optimization algorithms for improving the accuracy of quadratic curve fitting, including a statistical-based method, an algebraic distance-based method, and a geometric distance-based method. The statistical method generally assumes that the noise of the image obeys a certain distribution and is based on first-order Taylor series expansion, but because the noise distribution of the image is difficult to accurately obey the assumed distribution and the Taylor first-order series approximation fails when the noise is large, the statistical method can have a good fitting effect only when the noise is small; in the method based on the algebraic distance, the established objective function is based on algebraic distance errors, has no geometric and physical significance and can change along with geometric transformation, so that the errors can become larger after image transformation; the geometric distance-based method is an orthogonal distance method, but each image point in each iteration of the method needs to solve a 4-degree equation about an argument, so the method is extremely high in complexity and sensitive to noise. Later, the Sampson method of first order approximation appeared, but the accuracy was not high because it was only an approximate distance. In addition, there is a method based on circular transformation, in which during optimization, besides the parameters of the quadratic curve, each image point in each iteration needs to be set with another parameter, and the number of parameters to be solved is extremely large, which simplifies the solution of the 4-order equation of the orthogonal distance, but greatly increases the number of parameters to be solved, and thus the complexity is high. In summary, the conventional method for fitting a quadratic curve in an image cannot simultaneously achieve high efficiency and high precision.
The invention aims to develop a quadratic curve fitting method in a two-dimensional image, which can meet the requirements of high efficiency and high precision.
Disclosure of Invention
In order to solve the technical problem that the existing method for fitting the secondary curve in the image cannot simultaneously give consideration to high efficiency and high precision, the invention provides a method for fitting the secondary curve in the image based on geometric error optimization, which can simultaneously give consideration to the high efficiency and the high precision of the fitting of the secondary curve in the image.
The invention provides a quadratic curve fitting method in an optimized image based on geometric errors, which is characterized by comprising the following steps of:
step 1, extracting a point M of an edge image of a specific quadratic curve M in an imageiWherein m isi＝(ui vi1)T，i＝1...N；
Step 2, calculating the point miGeometric distance d to quadratic curve Mfa(miC), wherein C is a coefficient matrix of a quadratic curve M;
step (ii) of3, pair of geometric distances dfa(miC) carrying out linear weighted iteration, and obtaining a matrix C related to C by using a singular value decomposition method1；
Step 4, using the shortest geometric distance d (m)iC) constructing an objective function, and calculating when C ═ C1A minute amount Δ u when minimizing the objective functioni,ΔviAnd a scale parameter lambdaiAnd are respectively denoted as Δ ui1,Δvi1And lambdai1；
Step 5, with Δ ui1,Δvi1And lambdai1As an initial value, carrying out nonlinear optimization solution on the objective function to obtain a coefficient matrix C of a quadratic curve M2According to a coefficient matrix C2Generating an optimized conic M of a particular conic M in the image2。
Preferably, said geometric distance dfa(miAnd C) is weighted Sampson distance, and the calculation method comprises the following steps:
wherein,a. b, c, d, e, f are matrix coefficients of the quadratic curve M respectively,
preferably, the shortest geometric distance d (m)iAnd C) is as follows:
wherein, Δ ui、ΔviIn minute quantities.
The objective function is based on the shortest geometric distance d (m)iC) and a constraint function, the analytical expression formula of the objective function is as follows:
wherein,λiis a scale parameter.
The constraint function is:
in the constraint function, the function is defined as,
p+、p-is the intersection point of a straight line L 'and a quadratic curve M, L' is a passing point MiAnd with the polar line L ═ CmiA straight line in quadrature.
Preferably, for the geometric distance dfa(miAnd C) the specific method for carrying out linear weighted iteration is as follows:
step 31, calculating coefficient matrix C related to quadratic curve M(k)K represents the number of iterations;
step 32, repeating step 31 until convergence meets the condition, and recording the coefficient matrix C at the moment(k)And order C1＝C(k)。
Preferably, the coefficient matrix C related to the quadratic curve M is calculated(k)The method comprises the following steps:
when k is 0, solving the linear system by using a singular value decomposition methodN, obtaining a coefficient matrix C(0)；
When k is>At 0 hour, linear system is solved by singular value decomposition methodObtaining a coefficient matrix C related to the quadratic curve M(k)；
WhereinTo make C ═ C(k-1)And is calculated by the following formula:
preferably, the convergence condition in step 32 is:
wherein v (c) ═ (a b c d e f)TAnd epsilon is a preset threshold value.
Preferably, p in said constraint functioniThe analytic expression formula of (a) is as follows:
preferably, the coefficient matrix C is obtained in step 52Then throughTo C2Normalization, where C2||FIs represented by C2F norm of (d).
The method for fitting the quadratic curve in the image based on the geometric error optimization can be directly popularized to the fitting of the quadratic curve based on the depth image or the three-dimensional point.
The method for fitting the secondary curve in the image based on the geometric error optimization overcomes the defect that the conventional method for fitting the secondary curve in the image cannot simultaneously give consideration to high efficiency and high precision, achieves the ideal effect of simultaneously giving consideration to the high efficiency and the high precision of the method for fitting the secondary curve in the image, and improves the precision of fitting the secondary curve in the image.
Drawings
FIG. 1 is a schematic view of the polar line L of a point M with respect to a quadratic curve M;
FIG. 2 is a point miGeometric distance d (M) to quadratic curve Mi,pi) A schematic diagram;
FIG. 3 is a schematic diagram between an outer point and a quadratic curve M;
FIG. 4 is a schematic flow chart of a quadratic curve fitting method of the present invention.
Detailed Description
Preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only for explaining the technical principle of the present invention, and are not intended to limit the scope of the present invention.
In order to more clearly illustrate the technical solution of the present invention, the following describes the technical solution of the present invention in detail with reference to theoretical derivation and the specific implementation manner of the present invention.
The invention is provided aiming at the problem that the method for fitting the quadratic curve in the image in the prior art can not simultaneously consider high efficiency and high precision, and the invention provides a new method for calculating the geometric distance from the point to the quadratic curve, so that a linear weighted high-efficiency quadratic curve fitting method is designed based on the method, the shortest geometric distance is further approximated, and the method has higher precision. The method can be directly popularized to the fitting of the quadric surface based on the depth image or the three-dimensional point.
1. Derivation of the geometric distance calculation method of the invention
For the image containing the quadratic curve, extracting the edge image point M of the quadratic curve Mi＝(ui vi 1)T,i＝1...N；
The coefficient matrix C of the quadratic curve M is shown in expression (1):
in the absence of noise, one can obtain:
point miThe polar line L about the quadratic curve M is CmiWritten as Cmi＝L＝(l1,l2,l3)T. Then m isiAnd L is calculated as shown in equation (2):
where | represents the absolute value of the numerical value of the element between the two vertical lines.
Changing L to CmiSubstituting into equation (2) to point miThe distance to the epipolar line L can be updated to an expression as shown in equation (3):
wherein,the following relationship exists in G: a is2+d2≥0,(ba-d2)2≥0,det(G)＝0。
The well-known definition of the Sampson distance used to fit a quadratic curve is shown in equation (4):
substituting the derivative result into equation (4) yields equation (5):
comparing equation (3) with equation (5), it is known that the Sampson distance is point miHalf the distance to the polar line L. As shown in fig. 1(a), the distance from the point m to the epipolar line L is represented by a bold line segment, and when noise exists, the distance calculated by formula (3) is the distance from the point m to the epipolar line L is d, and d/2 is the Sampson distance; when there is no noise, M is located on the quadratic curve M, and L is a tangent at M, as shown in fig. 1(b), where both the values of equation (3) and equation (5) are 0. Since the numerator of equation (5) is usually referred to as an algebraic distance, the Sampson distance is a weighted algebraic distance.
Calculating different points m by adopting formula (3)iAnd taking the sum of squares thereof, or calculating different points m by using the formula (5)iA distance value of (a) andthe sum of their squares is taken as the cost function of fitting the quadratic curve. The two cost functions differ by a fixed scalar 4. Thus, the two cost functions are equivalent when finding the minimum C by optimization.
As shown in FIG. 2, M is a quadratic curve, MiIs a point, L ═ CmiIs the polar line. The straight line L' passes through miAnd is orthogonal to the polar line L, the intersection of the two lines being qi. Sampson distance is d (m)i,qi)/2. With point miIncrease in noise, d (m)i,qi) Becomes larger and larger, and the error of the Sampson distance becomes larger and larger. In general, the distribution of noise on images is not uniform, so for noise at points on different images, the Sampson distance should be given different weight values, but should not be a fixed 1/2.
The invention provides a new miAnd M is represented by equation (6):
d(mi,C)＝min{d(p+,mi),d(p-,mi)} (6)
order to
Then d (m)i,C)＝d(mi,pi)；
Wherein p is+、p-The two points are the intersection points of the straight line L' and the quadratic curve M.
As shown in FIG. 2, d (m)i,pi) Can be compared with d (m)i,qi) More accurate measurement of miAnd the distance between M.
To calculate d (m)iC), p needs to be calculatedi，piCan be solved by equation (7):
it is not easy to solve formula (7) directly, and the present invention provides a very concise way to obtain the explicit analytic form of formula (7), as follows:
first calculate qi。L＝CmiCan be expressed as L ═ (L)1,l2,l3)T. L' is orthogonal to L and passes through mi＝(ui vi1)T,qiIs the intersection of line L and line L'. Therefore, q can be obtainediAs shown in equation (8):
rewriting the result, qiThe calculation formula of (c) can be further transformed into formula (9).
Wherein To replace the last row of matrix C with a matrix after all 0 rows.
Due to qiOn a straight line L, thereforeCombined with L ═ CmiEquation (10) is obtained:
two solutions p+、p-And q isi、miCollinear, therefore, equation (11) can be obtained:
p±＝λ1qi+λ2mi (11)
wherein, the formula (11) is expressed by homogeneous coordinates, lambda1,λ2Are two scale parameters.
Substituting equation (11) into the first equation of equation (7) and using equation (10), equation (12) can be obtained:
in general, q isiAnd miOn both sides of the quadratic curve M. Therefore, the temperature of the molten metal is controlled,
solving equation (12) can yield equation (13):
note mi＝(ui vi 1)TIs 1, and q is in formula (9)iIs also 1, p is expressed according to formula (11)±Normalized to obtain formula (14):
then p is±Is also 1. Therefore, p±To miThe square of the distance of (a) is calculated according to the equation (15):
substituting equation (13) into equation (15) and selecting the smaller value, equation (16):
q in the formula (9)iSubstituting the expression formula (2) into the formula (16), the distance expression formula (17) can be obtained:
wherein,
and denominatorIs not 0. Compared with the formula (5), the formula (17) is a weighted Sampson distance and also a weighted algebraic distance, and has definite physical and geometric meanings.
piCan also be obtained from equation (18):
this is the solution of equation (7). And d is2(mi,pi)＝d2(miAnd C), formula (17) can be obtained.
Line of p'iIs a distance point miThe nearest point on curve M, we can get equation (19):
p'i＝pi+(Δui,Δvi,0)T (19)
wherein, Δ ui,ΔviIndicating a minute amount.
ByAndformula (20):
the expression to the left of equation (20) is denoted as CONi。
miAnd C is shown as equation (21):
if (m)i TGmi)2＜(mi TCmi)(mi TWmi) Then, m is considered to beiAre outliers and they are deleted because they are far from the quadratic curve. Fig. 3(a), 3(b), 3(c) show such points under an ellipse, a hyperbola and a parabola, respectively, and the points conforming to this case are all located in the black region.
Finally, the objective function based on the shortest geometric distance is established as shown in formula (22):
substituting the equations (20), (21) and (17) into (22) to obtain a specific objective function, as shown in equation (23):
whereinIs a scale parameter.
2. In combination with the above, the method for fitting a quadratic curve in an image based on geometric error optimization of the present invention is shown in fig. 4, and specifically includes:
step 1, extracting points M of edge images of specific quadratic curves M in imagesiWherein m isi＝(ui vi 1)TN, ═ 1.. N; and removing outer points by using a RANSAC algorithm, and fitting the points on the image into a quadratic curve M, wherein a coefficient matrix C of the quadratic curve M is shown as a formula (1).
Step 2, calculating the point miGeometric distance d to quadratic curve Mfa(mi,C)。
Said geometric distance dfa(miAnd C) is the weighted Sampson distance, which can be found by squaring equation (17).
The shortest geometric distance d (m)iC) can be obtained by squaring the equation (21).
The objective function is based on the shortest geometric distance d (m)iC) and determining a constraint function, an analytical representation of said objective functionThe formula is formula (23); the constraint function is a formula (20); constraint function of piThe analytical expression of (c) may be formula (18).
Step 3, geometric distance dfa(miC) carrying out linear weighted iteration, and obtaining a matrix C related to C by using a singular value decomposition method1；
Said pair of geometrical distances dfa(miAnd C) the specific method for carrying out linear weighted iteration is as follows:
step 31, calculating coefficient matrix C related to quadratic curve M(k)K represents the number of iterations;
step 32, repeatedly executing step 31 until the convergence condition is satisfied, and recording the coefficient matrix C at the moment(k)And order C1＝C(k)。
In this embodiment, a coefficient matrix C related to the quadratic curve M is calculated(k)The method comprises the following steps:
when k is 0, solving the linear system by using a singular value decomposition methodN, obtaining a coefficient matrix C(0)；
When k is>At 0 hour, linear system is solved by singular value decomposition methodObtaining a coefficient matrix C related to the quadratic curve M(k)；
WhereinThe calculation method comprises the following steps: let C be C(k-1)And is calculated by the formula (24):
the convergence condition described in step 32 is shown in equation (25):
wherein v (c) ═ (a b c d e f)TAnd epsilon is a preset threshold value.
Step 4, using the shortest geometric distance d (m)iC), calculating when C ═ C1A minute amount Δ u when minimizing the objective functioni,ΔviAnd a scale parameter lambdaiAnd are respectively denoted as Δ ui1,Δvi1And lambdai1；
Step 5, with Δ ui1,Δvi1And lambdai1As an initial value, the objective function is subjected to nonlinear optimization solution to obtain a coefficient matrix C2According to a coefficient matrix C2Generating an optimized conic M of a particular conic M in the image2. The coefficient matrix C is obtained in this step2Then, it is required to passTo C2Normalization, where C2||FIs represented by C2F norm of (d).
The nonlinear optimization solution of the objective function may be to optimize the formula (23) by using a nonlinear numerical optimization formula algorithm, which may be a quasi-newton method.
The method can also be directly popularized to the fitting of the quadric surface, and the specific implementation formula is consistent with the quadratic curve fitting method.
In fitting a quadric surface, constructing a quadric surface fitted objective function (26) with reference to the objective function (23):
whereinmi＝(ui vi si 1)T，
The method of the quadratic surface fitting corresponding to the formula (24) can be adjusted to the formula (27);
the method of equation (18) corresponding to the quadratic surface fitting can be adjusted to equation (28):
the method of equation (19) corresponding to the quadratic surface fitting can be adjusted to equation (29):
p'i＝pi+(Δui,Δvi,Δsi 0)T (29)
the method of fitting equation (17) to a quadric surface can be adjusted to equation (30), which is a calculation equation of the distance from a point to the quadric surface.
Those of skill in the art will appreciate that the various illustrative modules, elements, and method steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate the interchangeability of electronic hardware and software. Whether such functionality is implemented as electronic hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
So far, the technical solutions of the present invention have been described in connection with the preferred embodiments shown in the drawings, but it is easily understood by those skilled in the art that the scope of the present invention is obviously not limited to these specific embodiments. Equivalent changes or substitutions of related technical features can be made by those skilled in the art without departing from the principle of the invention, and the technical scheme after the changes or substitutions can fall into the protection scope of the invention.
Claims (9)
1. A quadratic curve fitting method in an image based on geometric error optimization is characterized by comprising the following steps:
step 1, extracting points M of edge images of specific quadratic curves M in imagesiWherein m isi＝(ui vi1)T，i＝1...N；
Step 2, calculating the point miGeometric distance d to quadratic curve Mfa(miC), where C is a coefficient matrix of a quadratic curve M;
step 3, geometric distance dfa(miC) carrying out linear weighted iteration, and obtaining a matrix C related to C by using a singular value decomposition method1；
Step 4, using the shortest geometric distance d (m)iC) constructing an objective function, and calculating when C ═ C1A minute amount Δ u when minimizing the objective functioni,ΔviAnd a scale parameter lambdaiAnd are respectively denoted as Δ ui1,Δvi1And lambdai1；
Step 5, with Δ ui1,Δvi1And lambdai1As an initial value, the objective function is subjected to nonlinear optimization solution to obtain a coefficient matrix C2According to a coefficient matrix C2Generating an optimized conic M of a particular conic M in the image2。
2. The method of claim 1, wherein the geometric distance d is a quadratic curve fit based on geometric error optimizationfa(miAnd C) is weighted Sampson distance, and the calculation method comprises the following steps:
wherein,a. b, c, d, e, f are matrix coefficients of the quadratic curve M respectively,
3. method of quadratic curve fitting in images based on geometric error optimization according to claim 2, characterized in that the shortest geometric distance d (m)iAnd C) the calculation method comprises the following steps:
wherein, Δ ui、ΔviIn minute quantities.
4. The method of claim 3, wherein the objective function is based on the shortest geometric distance d (m)iAnd C) determining a constraint function, wherein the analytical expression formula of the objective function is as follows:
wherein,λiis a scale parameter;
the constraint function is:
in the constraint function, the function is defined as,
p+、p-is the intersection point of a straight line L 'and a quadratic curve M, L' is a passing point MiAnd with the polar line L ═ CmiA straight line in quadrature.
5. According to the rightThe method of claim 3, wherein the pair of geometric distances d is a quadratic curve fit in the image based on geometric error optimizationfa(miAnd C) the specific method for carrying out linear weighted iteration is as follows:
step 31, calculating coefficient matrix C related to quadratic curve M(k)K represents the number of iterations;
step 32, repeatedly executing step 31 until the convergence condition is satisfied, and recording the coefficient matrix C at the moment(k)And order C1＝C(k)。
6. Method for quadratic curve fitting in images based on geometric error optimization according to claim 5, characterized in that the matrix of coefficients C related to the quadratic curve M is calculated(k)The method comprises the following steps:
when k is 0, solving the linear system by using a singular value decomposition methodObtaining a coefficient matrix C(0)；
When k is>At 0 hour, linear system is solved by singular value decomposition methodObtaining a coefficient matrix C related to the quadratic curve M(k)；
WhereinTo make C ═ C(k-1)And is calculated by the following formula:
7. the method of claim 6, wherein the convergence condition in step 32 is:
wherein v (c) ═ (a b c d e f)TAnd epsilon is a preset threshold value.
8. The method of claim 4, wherein p is the constraint functioniThe analytic expression formula of (a) is as follows:
9. the method of claim 8, wherein the coefficient matrix C is obtained in step 52Then throughTo C2Normalization, where C2||FIs represented by C2F norm of (d).
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102663742A (en) * | 2012-03-22 | 2012-09-12 | 浙江工业大学 | Determination method of rotary stereo visual rotation axis based on quadratic curve fitting |
| CN103258329A (en) * | 2013-05-24 | 2013-08-21 | 西安电子科技大学 | Camera calibration method based on one-dimensional feature of balls |
| CN103678788A (en) * | 2013-11-29 | 2014-03-26 | 中国科学院科技政策与管理科学研究所 | Spatial data interpolation and curved surface fitting method based on curved surface theory |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102663742A (en) * | 2012-03-22 | 2012-09-12 | 浙江工业大学 | Determination method of rotary stereo visual rotation axis based on quadratic curve fitting |
| CN103258329A (en) * | 2013-05-24 | 2013-08-21 | 西安电子科技大学 | Camera calibration method based on one-dimensional feature of balls |
| CN103678788A (en) * | 2013-11-29 | 2014-03-26 | 中国科学院科技政策与管理科学研究所 | Spatial data interpolation and curved surface fitting method based on curved surface theory |
Non-Patent Citations (1)
| Title |
|---|
| Conic Fitting Using the Geometric Distance;Peter Sturm, Pau Gargallo;《ACCV 2007, Part II, LNCS 4844》;20071231;784-795 * |
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