CN111382794B - Curve similarity calculation method - Google Patents
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Abstract
The invention discloses a curve similarity calculation method. The existing two-dimensional curve similarity calculation method is not stable enough under the transformation of curve scaling, resampling and the like. The invention firstly calculates the distance adjacency matrix and the angle adjacency matrix of the two curves respectively, then calculates the characteristic value sequence of the two curves, and calculates the weighted distance between the two curves based on the characteristic value sequence, wherein the smaller the distance is, the more similar the two curves are. The invention relates to a two-dimensional curve similarity calculation method without calibration, which is free from global scaling and rotation translation transformation.
Description
Technical Field
The invention belongs to the fields of image graph retrieval and machine vision, and provides a similarity calculation method for calculating two curves, which can be used for retrieving two-dimensional contours or curves.
Background
The curve similarity calculation refers to calculating the similarity degree or distance between two curves through a certain measurement criterion, wherein the curves can be unsealed or sealed. It is a fundamental problem for computer vision and pattern recognition, and is also a fundamental problem in many scientific fields.
Disclosure of Invention
The invention aims to provide a method for calculating the similarity between two curves, and the process of the method does not need to establish a point-to-point corresponding relation between the two curves.
The invention adopts a distance adjacency matrix and an angle adjacency matrix which are unchanged by rotation scaling transformation as characteristics, compares the similarity of two curves, and specifically comprises the following steps:
input: the two-dimensional curves are respectively A and B, and are uniformly discretized and represented by corresponding point sequences: a= (a) 1 ,a 2 ,a 3 ,…,a n ),B＝(b 1 ,b 2 ,…,b m )。
And (3) outputting: the distance ρ (a, B) between the two curves. The smaller the distance, the more similar the two curves are.
The method comprises the following specific steps:
step (1) calculating a distance adjacency matrix of the curve A and the curve B, and performing normalization processing to obtain D A 、D B 。
Step (2) calculating an angle adjacency matrix omega of the curve A and the curve B A 、Ω B 。
Step (3) calculating matrix D A 、D B 、Ω A And omega B And normalized.
And (4) calculating the distance between the two curves.
Further, the ith row and jth column elements in the distance adjacency matrix in step (1)
The calculation is as follows:
d ij ＝‖k i -k j ‖ 2
where k.epsilon.A or B.
The normalization in step (1) refers to dividing all elements in the distance adjacency matrix by the median of the matrix.
Further, the ith row and jth column elements in the angle adjacency matrix are points k i And point k j The included angle between the connecting line and the X axis of the coordinate axis is in the range of [0, pi/2 ]]。
Further, the characteristic values in the characteristic value sequence are arranged in a descending order.
Further, the normalization of the characteristic value sequence is to perform a difference operation on each item in the characteristic value sequence and the first item.
Further, the distance between the two curves is calculated as follows:
wherein w is λ And w ξ For the weighting coefficients, k=min (n, m), n is the number of eigenvalues of the distance adjacency matrix, m is the number of eigenvalues of the angle adjacency matrix,
for D A I-th eigenvalue in the eigenvalue sequence of (a) and +.>
For D B I-th eigenvalue in the eigenvalue sequence of (a) and +.>
Is omega A I-th eigenvalue in the eigenvalue sequence of (a) and +.>
Is omega B I-th eigenvalue in the eigenvalue sequence of (a).
The invention has the beneficial effects that: the invention relates to a two-dimensional curve similarity calculation method without calibration, which is free from global scaling and rotation translation transformation.
Detailed Description
The input and output of the method of the invention are:
input: the two-dimensional curves are respectively A and B, and are uniformly discretized and represented by corresponding point sequences: a= (a) 1 ,a 2 ,a 3 ,…,a n ),B＝(b 1 ,b 2 ,…,b m )。
And (3) outputting: the distance ρ (a, B) between the two curves. The smaller the distance, the more similar the two curves are.
The method comprises the following specific steps:
step (1) calculating a distance adjacency matrix of the curve:
taking curve A as an example, calculate its distance adjacency matrix D A Its ith row and jth column element
Identical squareThe method also calculates a distance adjacency matrix D of curve B B 。
Step (2) calculating a normalized distance matrix:
D A ＝D A /median(D A )；D B ＝D B /median(D B )
where media represents a median taking operation. The normalized result is still recorded as D A And D B 。
Step (3) calculating an angle adjacency matrix:
taking curve A as an example, its angular adjacency matrix Ω is calculated A Its ith row and jth column element
For point a i And point a j The included angle between the connecting line and the X axis of the coordinate axis is in the range of [0, pi/2 ]]. The same method also calculates the angular adjacency matrix Ω of curve B B 。
Calculating the eigenvalue sequence of each adjacent matrix and normalizing the eigenvalue sequence:
calculation D A Is marked as the characteristic value sequence from small to large
And performs the following normalization operation, the calculation result is still recorded as lambda A ：
Calculation of D by the same method B 、Ω A And omega B Normalized eigenvalue sequences of (a), respectively denoted as lambda B 、ξ A And xi B 。
Step (5) calculating the distance between the two curves: taking k=min (n, m), the distance between the calculation curves a and B is calculated:
wherein w is λ And w ξ Is the weighting coefficient that needs to be set.
Claims (4)
1. A method for retrieving curves in images is characterized in that: the similarity of two curves in the image is compared by adopting a distance adjacency matrix and an angle adjacency matrix which are unchanged by rotation scaling transformation as characteristics, and the method specifically comprises the following steps:
input: two-dimensional curves in the two images are respectively A and B, and the two curves are uniformly discretized and expressed by corresponding point sequences: a= (a) 1 ,a 2 ,a 3 ,…,a n ),B＝(b 1 ,b 2 ,…,b m )；
And (3) outputting: the distance ρ (a, B) between the curves in the two images; the smaller the distance, the more similar the two curves are;
the method comprises the following specific steps:
step (1) calculating a distance adjacency matrix of the curve A and the curve B, and performing normalization processing to obtain D A 、D B ；
Step (2) calculating an angle adjacency matrix omega of the curve A and the curve B A 、Ω B ；
Step (3) calculating matrix D A 、D B 、Ω A And omega B Is normalized;
step (4) calculating the distance between the two curves:
wherein w is λ And w x As the weighting coefficient, k=min (n, m), n is the number of eigenvalues of the distance adjacency matrix, m is the number of eigenvalues of the angle adjacency matrix, λ i A For D A The ith eigenvalue, lambda, in the eigenvalue sequence of (a) i B For D B I-th eigenvalue, ζ in the eigenvalue sequence of (a) i A Is omega A I-th eigenvalue, ζ in the eigenvalue sequence of (a) i B Is omega B Characteristic value sequence of (2)The i-th eigenvalue of (a);
the j-th column element d of the i-th row in the distance adjacent matrix ij The calculation is as follows:
d ij ＝‖k i -k j ‖ 2
the j-th column element of the i-th row in the angle adjacent matrix is a point k i And point k j The included angle between the connecting line and the X axis of the coordinate axis is in the range of [0, pi/2 ]]The method comprises the steps of carrying out a first treatment on the surface of the Where k.epsilon.a or b.
2. The method for retrieving curves in an image according to claim 1, wherein: the normalization in step (1) refers to dividing all elements in the distance adjacency matrix by the median of the matrix.
3. The method for retrieving curves in an image according to claim 1, wherein: the characteristic values in the characteristic value sequence are arranged in a descending order.
4. A method of retrieving curves in an image according to claim 3, wherein: the normalization processing of the characteristic value sequence is to perform a difference operation on each item in the characteristic value sequence and the first item.
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| WO2017185963A1 (en) * | 2016-04-26 | 2017-11-02 | 深圳前海云汉金融科技有限公司 | Big data-based method and terminal for matching trend curve local characteristics |
| CN107392945A (en) * | 2017-06-11 | 2017-11-24 | 杭州巨实科技有限公司 | A kind of two-dimensional silhouette matching process |
| CN107657266A (en) * | 2017-08-03 | 2018-02-02 | 华北电力大学（保定） | A kind of load curve clustering method based on improvement spectrum multiple manifold cluster |
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