CN115375891A

CN115375891A - Cultural relic fragment similarity identification and transformation matching method based on machine learning

Info

Publication number: CN115375891A
Application number: CN202210966747.7A
Authority: CN
Inventors: 赵书良; 穆翔宇; 孙婧涵; 杨依涵; 丁雪怡
Original assignee: Hebei Normal University
Current assignee: Hebei Normal University
Priority date: 2022-08-12
Filing date: 2022-08-12
Publication date: 2022-11-22

Abstract

The invention discloses a cultural relic fragment similarity identification and transformation matching method based on machine learning, which comprises the steps of image preprocessing, contour line extraction, feature point clustering, similar contour line pair extraction, judgment of similarity of two contour lines, calculation of a rotation angle and a movement distance between the two similar contour line segments to form a rigid transformation matrix, and circular splicing of cultural relic fragments from bottom to top. According to the invention, the image binarization and machine learning are combined by a maximum between-class variance method, so that the problems of more interference contour lines when the ceramic cultural relic fragments are subjected to contour line extraction and difficulty in selecting feature points when the contour lines are matched are solved, ceramic fragment samples can be spliced into a complete image, and the robustness is better.

Description

Cultural relic fragment similarity identification and transformation matching method based on machine learning

Technical Field

The invention relates to a cultural relic fragment similarity recognition and transformation matching method, in particular to a cultural relic fragment similarity recognition and transformation matching method based on machine learning, and belongs to the technical field of computer vision.

Background

In the archaeological field, a large amount of ceramic fragments are excavated, and if similarity identification and matching are carried out only by the pure manual work of experts, the efficiency is very low. With the development of the technical field of computer vision, a computer can be used for intelligently identifying similar ceramic fragments and carrying out correct rotation transformation on the similar ceramic fragments so as to prepare for splicing work. At present, chinese and foreign scholars make more researches on splicing work of fragments, and Jizhou dynasty proposes a two-dimensional fragment contour matching algorithm for representing contours by using the position relationship between each point and six adjacent points in a novel contour matching method of two-dimensional fragments. The method is very simple in calculation processing, and can efficiently improve the matching speed of the outline of the fragment, but the algorithm cannot process the situation when the fragment rotates. Dujiali et al propose to use B-spline curve in "matching of object contour curve based on B-spline representation" to approximate the contour curve of two-dimensional debris and extract data points based on the contour curve, and match and splice by using the curvature of the data points and the flexibility of the data points as the feature set of the contour line. Leitao, A Multi-scale method for the reconstruction of two dimensional fragmented objects, proposes a method of multi-scale based fragment stitching in which the contours of the fragments are represented by using the curvature of each discrete point. However, in this method, the selection of discrete points of the contour line is only simple by adopting different sampling scales, and the inherent shape characteristic information of the contour line is not well utilized. Most existing defragmentation synthesis algorithms in splicing work will use some greedy strategy, such as best first, spanning tree growth or variants thereof, such as the method used by k.zhang and x.li in a graph-based optimization for fragmented image reconstruction, but if a similar contour line pair is encountered with an incorrect judgment and has a high matching score, the contour line pair will be easily selected for global splicing and will occupy the positions of other correct contour line pairs, eventually leading to global splicing work failure due to such local minimum.

Disclosure of Invention

The invention aims to provide a cultural relic fragment similarity identification and transformation matching method based on machine learning.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a cultural relic fragment similarity identification and transformation matching method based on machine learning comprises the following steps:

step 1: image preprocessing: performing two-dimensional sampling on the archaeological ceramic fragments to obtain m & n pixel cultural relic fragment images, and converting the cultural relic fragment images into binary cultural relic fragment images;

and 2, step: contour line extraction: extracting contour lines, extracting contour lines in the binary cultural relic fragment image one by one through a contour tracing algorithm, and constructing a contour line set CL = { CL = ₁ ,cl ₂ ,...,cl _cj ,...,cl _lks Lks is the number of extracted contour lines;

and step 3: characteristic point clustering: the characteristic point clustering extracts the characteristic points of each contour line one by one through a K-means clustering method, and a characteristic point set K of each contour line is constructed _i ＝{k _i,1 ,k _i,2 ...k _i,j ...k _i,km }; i represents a contour line to which the current feature point set belongs, and the value range of i is more than or equal to 1 and is not more than lks; the feature points in the feature point set of each contour line have the same number, namely km;

and 4, step 4: extracting similar contour line pairs one by one, comprising the following specific steps:

step 4-1: the curvature of the characteristic points of each contour line is calculated one by one to construct each contour lineFeature point curvature set Q of contour line _i ＝{q _i，1 ,q _i,2 ,...,q _i,j ,...,q _i,qmi I represents a contour line to which the current feature point set belongs, wherein the value range of i is more than or equal to 1 and is not more than lks; dividing each 3 continuous characteristic points on the contour line into a section of characteristic segment; qmi represents the number of feature segments of the ith contour,

the curvature of the jth characteristic segment of the ith contour line is calculated by the following method:

m (j) is the abscissa of three characteristic points of the j-th characteristic segment of the i-th contour line

A first parameter equation is fitted, n (j) is the ordinate of three characteristic points of the j characteristic segment of the i contour line

Fitted second parametric equation, a ₁ ,a ₂ ,a ₃ First to third coefficients of the abscissa equation, b ₁ ,b ₂ ,b ₃ First to third coefficients for an ordinate equation, m '(j), m "(j) being the first and second derivatives of the parametric equation m (j), n' (j), n" (j) being the first and second derivatives of the parametric equation n (j);

step 4-2: sequentially calculating the Euclidean distance of the curvature of the corresponding characteristic segment of each two contour lines, and constructing the Euclidean distance sets of the two contour lines, namely the Euclidean distance sets of the ith 1 contour line and the ith 2 contour line

Euclidean distance of the ith feature segment

The calculation method comprises the following steps:

step 4-3: judging two contour lines cl one by one _i1 ,cl _i2 Whether the characteristic segments of (a) are similar: if the Euclidean distance of the feature segments of the two contour lines

If the number of the similar characteristic segments is less than a preset first threshold value, judging the similar characteristic segments, and adding 1 to the number of the similar characteristic segments of the ith 1 contour line and the ith 2 contour line;

step 4-4: calculate two contour lines cl one by one _i1 ,cl _i2 Is given a similarity score of FS _i1,i2 ：

XST in the formula _i1,i2 The number of similar characteristic segments of the ith 1 contour line and the ith 2 contour line is set;

and 4-5: determine two contour lines cl _i1 ,cl _i2 Whether or not they are similar: if two contour lines cl _i1 ,cl _i2 Is given a similarity score of FS _i1,i2 Greater than a second predetermined threshold, two contour lines cl _i1 ,cl _i2 Similar contour lines;

and 5: calculating two similar contour line segments cl one by one _i1 ,cl _i2 The rotation angle delta and the moving distance between the two rigid body transformation matrixes form a rigid body transformation matrix;

horizontal direction movement distance:

vertical direction movement distance:

rigid body transformation matrix GT _i1,i2 ：

Wherein (x) _g ,y _g ),(x _h ,y _h ) For two similar contours cl _i1 ,cl _i2 Coordinates of the selected feature points; delta is contour line cl _i1 ,cl _i2 Fitting the included angle of two crossed straight lines through linear regression;

step 6: splicing cultural relic fragments circularly from bottom to top, which comprises the following specific steps:

step 6-1: build an induced cycle set L ₀ ＝{l ₀ ,l ₁ ,...,l _lp ,l _lQ ,...l _ln H, ln is equal to or greater than 1 and less than lks: each contour line is a node, edges are established between similar contour lines, and connected subgraphs form a connected subgraph set W = { W = ₁ ,...,w _wj ,...,w _zt And zt is the number of connected subgraphs, whether the product of rigid body transformation matrixes of similar contour lines corresponding to edges in each connected subgraph is a unit matrix or not is judged one by one, and if yes, the connected subgraphs are used as induction cycles l _lj Adding an induction cycle set;

step 6-2: merging induction circulation: in the induction cycle set L ₀ In (1), searching one by one whether there is a combinable induction cycle L _lp And L _lQ Delete L _lp And L _lQ Common edge in between, will L _lp And L _lQ Are combined into an induced cycle set L ₁ The process is executed iteratively to obtain an induced loop set L ₂ ，L ₃ ，..，L _ln Induction cycle set L _ln There are no induction cycles that can be combined;

combinable induction cycles L _lQ And L _lQ Simultaneously, the following conditions are met:

condition 1: induction cycle L _lp And L _lQ Having common edges, the rigid transformation moments of the common edgesArray GT _lp,lq In the induction cycle L _lp And L _lQ Medium and equal;

condition 2: after the induction cycles are combined, the rigid body transformation matrixes of all edges in the newly generated induction cycle are multiplied to be an identity matrix.

Further, the step 1 comprises the following specific steps:

step 1-1: converting the cultural relic fragment image into a gray map, and calculating the average gray value mu of the cultural relic fragment image:

wherein n (i) is the number of pixels having a pixel value of i; y is the number of pixel values; step 1-2: image division: setting i as foreground and background segmentation threshold t one by one _x And calculating the inter-class variance:

G＝W ₁ ·(μ ₁ -μ) ² +W ₂ ·(μ ₂ -μ) ²

wherein, W ₂ The proportion of background pixels in the image is taken; mu.s ₁ Is the average gray level, μ, of the foreground pixels ₂ Average gray level of background pixels and average gray level of foreground pixels ₁ Average gray level mu with background pixel ₂ The calculation method is the same, and the average gray level mu of the foreground pixel ₁ The calculating method comprises the following steps:

wherein, W ₁ In order to record the proportion of foreground pixels in the image, the calculation method comprises the following steps:

wherein, y ₁ Is the pixel value is greater than t _x The statistical number of the pixels;

step 1-3: and converting the gray-scale image of the cultural relic fragment image into a binary cultural relic fragment image according to the foreground-background segmentation threshold value when the inter-class variance is maximum.

Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:

1. the invention determines the binarization threshold value by a maximum between-class variance method so as to carry out binarization processing on the ceramic fragment image and extract the fragment image contour line, thereby effectively reducing noise caused by shooting problems.

2. The contour line feature point extraction based on clustering is a method with accurate and convenient calculation, accurately extracts the feature points of the contour line, and then performs preliminary matching on ceramic fragments by using a method of taking Euclidean distance based on feature segments as a matching contour line, thereby effectively reducing the time required by contour line matching.

3. The invention provides a novel method for calculating rigid body transformation of similar contour lines, which obtains a fitting straight line of the similar contour lines through linear regression analysis, and obtains a rigid body transformation matrix of image fragments through rotation and translation for splicing. The method effectively improves the efficiency of rigid body transformation calculation between similar contour lines and has higher accuracy.

4. The method carries out global splicing on the ceramic fragment images based on the circular splicing method, strengthens closed-loop constraint in the global splicing work, cuts out the fragment pairs with wrong similar identification but high similarity score, and has higher robustness.

Drawings

FIG. 1 is a block diagram of a model of the present invention.

Fig. 2 is an example of an induction cycle.

Fig. 3 merges examples of loops.

Fig. 4 is an original fragmentation diagram of this patent.

Fig. 5 is an effect diagram after splicing.

Detailed Description

The following examples serve to illustrate the invention.

Example 1

A cultural relic fragment similarity identification and transformation matching method based on machine learning comprises the following steps:

the step 1 comprises the following specific steps:

wherein n (i) is the number of pixels having a pixel value of i; y is the number of pixel values;

step 1-2: image division: setting i as foreground and background segmentation threshold t one by one _x And calculating the inter-class variance:

G＝W ₁ ·(μ ₁ -μ) ² +W ₂ ·(μ ₂ -μ) ²

wherein, W ₂ The proportion of background pixels in the image is taken; mu.s ₁ Is the average gray level, μ, of the foreground pixels ₂ Is the average gray level of the background pixels and the average gray level mu of the foreground pixels ₁ Average gray level mu with background pixel ₂ The calculation method is the same, and the average gray level mu of the foreground pixel ₁ The calculation method comprises the following steps:

and converting the gray-scale image of the cultural relic fragment image into a binary cultural relic fragment image according to the foreground-background segmentation threshold value when the inter-class variance is maximum.

Step 2: contour lines in the binary cultural relic fragment image are extracted one by one through a contour tracing algorithm, and a contour line set CL = { CL ] is constructed ₁ ,cl ₂ ,...,cl _cj ,...,cl _lks Lks is the number of extracted contour lines;

and 3, step 3: extracting the characteristic points of each contour line one by one through a k-means clustering method, and constructing a characteristic point set Ki = { k } of each contour line _i,1 ,k _i,2 ...k _i,j ...k _i,km }; i represents the contour line to which the current characteristic point set belongs, and the value range of i is more than or equal to 1 and is not more than lks; the feature point number of each contour line is the same, and is km, and the specific operation steps are as follows:

step 3-1: all coordinate points on the contour line are taken as a data set of the k-means clustering, k samples are randomly selected from the data set as cluster centers, and 15 cluster centers are selected in the embodiment: CZ = { CZ ₁ ,cz ₂ ,...,cz _cj ,...,cz ₁₅ And calculating Euclidean distances between all data in the data set and the K cluster centers, dividing each data into clusters where the cluster center closest to the data set is located, updating new cluster centers of all clusters through an averaging method for new clusters formed after training, and repeating the training process until no new cluster center is generated or the number of training rounds is reached, wherein in the embodiment, each K-means clustering is performed, the upper limit of the number of training rounds is 15 rounds, and the cluster center in the final result is the feature point set K of the current contour line _i ＝{k _i,1 ,k _i,2 ...k _i,j ...k _i,km }；

step 4-1: the curvature of the characteristic point of each contour line is obtained one by one, and a curvature set Q of the characteristic point of each contour line is constructed _i ＝{q _i，1 ,q _i,2 ,...,q _i,j ,...,q _i,qmi I represents a contour line to which the current feature point set belongs, wherein the value range of i is more than or equal to 1 and is not more than lks;dividing each 3 continuous characteristic points on the contour line into a section of characteristic segment; qmi represents the number of feature segments of the ith contour,

in this embodiment, 3 continuous feature points constitute a segment of feature segment, each contour line segment can be divided into 5 feature segments, and the feature point curvature set of each contour line is Q _i ＝{q _i，1 ,q _i，2 ......q _i，5 }。

The coordinates of three feature points in the feature segment are:

and

the method for calculating the curvature of the jth characteristic segment of the ith contour line of the abscissa and the ordinate of the jth characteristic point which is currently the ith contour line segment comprises the following steps:

A first parameter equation is fitted, n (j) is the ordinate of three characteristic points of a j characteristic segment of a characteristic segment of an i contour line

Fitting of the firstTwo parameter equation a ₁ ,a ₂ ,a ₃ First to third coefficients of the abscissa equation, b ₁ ,b ₂ ,b ₃ First to third coefficients for an ordinate equation, m '(j), m "(j) being the first and second derivatives of the parametric equation m (j), n' (j), n" (j) being the first and second derivatives of the parametric equation n (j);

Euclidean distance of the ith feature segment

The calculation method comprises the following steps:

step 4-3: judge one by one two contour lines cl _i1 ,cl _i2 Whether the characteristic segments of (a) are similar: if the Euclidean distance of the feature segments of the two contour lines

If the number of the similar characteristic segments is less than a preset first threshold value, judging the similar characteristic segments, and adding 1 to the number of the similar characteristic segments of the ith 1 contour line and the ith 2 contour line; the first threshold value in this embodiment is 0.001;

step 4-4: calculate two contour lines cl one by one _i1 ,cl _i2 (ii) a similarity score FS _i1,i2 ：

and 4-5: determine two contour lines cl _i1 ,cl _i2 Whether or not they are similar: if two contour lines cl _i1 ,cl _i2 Is given a similarity score of FS _i1,i2 Greater than a second predetermined threshold, two contour lines cl _i1 ,cl _i2 Similar contour lines; in this embodiment, the second threshold is 0.6, that is, there are more than 3 feature segments that are similar, and the contour segments are considered to be similar.

And 5: two contour lines cl _i1 ,cl _i2 Inputting the characteristic points into a linear regression analysis model, and calculating two similar contour lines cl one by one through two straight lines fitted by the linear regression analysis model _i1 ,cl _i2 The rotation angle delta and the moving distance between the two rigid body transformation matrixes form a rigid body transformation matrix:

horizontal direction movement distance:

vertical direction movement distance:

rigid body transformation matrix GT _i1,i2 ：

In the formula (x) _g ,y _g ),(x _h ,y _h ) In the present embodiment two similar contours cl _i1 ,cl _i2 Coordinates of the median of (a); δ is the contour line cl _i1 ,cl _i2 Fitting an included angle of two crossed straight lines through linear regression;

in the embodiment, a feature point set K of two similar contour line segments i, j is used _i ＝{k _i，1 ,k _i，2 ......k _i，30 }、K _j ＝{k _j，1 ,k _j，2 ......k _j，30 Are respectively input into a linear regression analysis model to fit two straight lines l ₁ ，l ₂ Calculating the intersection point of the two straight lines as lambda (x) _λ ,y _λ ) Randomly on two straight lines l ₁ ，l ₂ Selecting each point alpha (x) _α ,y _α )，β(x _β ,y _β ) Calculating the rotation angle delta of two straight lines through three points of alpha, lambda and beta, and selecting the median M (x) of the two contour lines _m ,y _m ),N(x _n ,y _n ) As a reference point for calculating the contour line movement distance, the horizontal direction movement distance and the vertical direction movement distance are calculated. And forming a 3x3 rigid body transformation matrix GT by the calculated rotation angle, the horizontal moving distance and the vertical moving distance.

And 6: the method for splicing cultural relic fragments circularly from bottom to top comprises the following specific steps:

condition 1: induction cycle L _lp And L _lQ Rigid transformation matrix GT with common edges _lp,lq In the induction cycle L _lp And L _lQ Medium and equal;

condition 2: after the induction cycles are combined, the rigid body transformation moments of all sides in the newly generated induction cycleThe matrix multiplication is an identity matrix. In the embodiment, the archaeological ceramic fragments are photographed and subjected to two-dimensional sampling to obtain fragment images, the fragments are spliced as much as possible by a circular splicing method according to the similarity between the fragments calculated in the step 3 and the rigid body transformation matrix between the similar fragments calculated in the step 4, and the algorithm undergoes a bottom-up merging stage and then a top-down merging stage. Two nouns are defined in a specific step, an induction cycle and a combination cycle; in the induction loop, the fragments are compared with nodes in the loop, if two nodes have connected edges, the fragments represented by the two nodes are considered to be similar in pairs and can be spliced, and each edge is associated with a rigid transformation matrix GT _i,j ，GT _i,j Indicating that the patches i, j are similar and that patch j passes through the rigid body transformation matrix GT _i,j And the position spliced with the fragment i can be transformed, if the rigid body transformation matrixes of 3 and 4 fragments which are similar pairwise are multiplied into an identity matrix, the fragment set can form an induction cycle, and the induction cycle is shown in figure 3.

In step 4-1, the similar fragments are firstly formed into a plurality of small induction cycles, the induction cycles are merged and spliced with other induction cycles through the common edges to form a merged cycle, see fig. 4, the common edges in the merged cycle are deleted to form a larger induction cycle, and the process is continuously cycled in a bottom-up and top-down mode to finally generate a complete image.

The bottom-up merge begins with a small induction cycle of approximately 3, 4 in length generated in step 5-1. The set of induction cycles found in this step is denoted L ₀ ＝{l ₀ ，l ₁ ......l _n }. We are at L ₀ The internal trial searches for induction cycles that can be combined with the following conditions:

condition 1: two combinable induced loops have a common edge and the rigid transformation matrix GT associated with the common edge _i,j Equal in both inductive loops.

Condition 2: after the two induction loops are merged and a new induction loop is generated, the rigid transformation matrix GT associated with each edge in the loop satisfies the formula (17).

When both combinable cycles satisfy condition 1 and condition 2, we can splice them into one larger induction cycle. This will generate an effective composite picture. If any of the two loops that can be spliced violates any of the conditions, the loop after splicing is discarded, effectively pruning the pairs of fragments whose similarity identification is wrong but whose similarity score is high.

We merge data from L ₀ And adding the newly combined induction cycle to the new set L ₁ In (1). Then, we iteratively repeat the process to obtain L ₂ ，L ₃ ，..，L _n Until no more cycles can be combined. With the increase of compatible cycles, set L in the last cycle _n In (1), we select a cycle containing the most fragments and denote it as L ^* 。L ^* Is the image of the largest reassembled fragment that we have obtained so far through the bottom-up merging process.

If all fragments are combined into one large cycle, L ^* Giving the final stitched image, but L ^* Not all fragments may be contained, i.e. the induction cycle. Some tiles that are stitched correctly, such as induced loops, that may not be detected and similarly stitched because of their relatively poor compatibility, may need to be stitched to the main tile composite map by individual edge connections. Therefore, we further perform a top-down merge to stitch these remaining fragments, i.e., the loop.

Merge from L from top to bottom ^* Initially, first check L ^n-1 Each cycle of steps. If a cycle is found with L ^* Compatible, and newly discovered induction cycles are different from L ^* Node(s) in (c), then we merge the newly discovered induction cycle into L ^* . We proceed by iteratively matching L ^* And from L ^n-1 Are combined to increase L ^* The contained fragment, then L ^n-2 And finally L ⁰ 。

The method combines the otus algorithm and machine learning, and solves the problems of more interference contour lines when the ceramic cultural relic fragments are subjected to contour line extraction and difficult feature point selection when the contour lines are matched. The otus algorithm automatically computes a threshold value in the bimodal image according to the histogram of the bimodal image to binarize the image. And the clustering randomly divides the contour feature points into K clusters, and takes the mean value of the data values in each cluster as the center of the cluster. Linear regression analysis fits the discrete points to a straight line and minimizes the loss function. A rigid body transformation matrix between similar contour lines can be calculated through linear regression analysis, closed loop constraint in global Splicing work is strengthened and contour line pairs which are incorrect but have high scores are pruned through a Layered Circular Splicing (LCS) method, and compared with a greedy strategy, layered Circular Splicing has higher robustness. The ceramic fragment sample can be spliced into a complete image by the method.

The invention combines image binaryzation and machine learning by a maximum between-class variance method, and solves the problems of more interference contour lines when the ceramic cultural relic fragments are subjected to contour line extraction and difficult feature point selection when the contour lines are matched. The image binarization is carried out by a maximum inter-class variance method, wherein a certain threshold value is used, a gray level image is divided into a foreground part and a background part according to the size of gray level, and when the inter-class variance of the two types is maximum, the obtained threshold value is the optimal binarization threshold value. The clustering randomly divides the contour feature points into K clusters, and takes the mean value of the data values in each cluster as the center of the cluster. Linear regression analysis fits the discrete points to a straight line and minimizes the loss function. A rigid body transformation matrix between similar contour lines can be calculated through linear regression analysis, closed loop constraint in global splicing work is strengthened and contour line pairs which are incorrect but have high similarity scores are pruned through a circular splicing method, and circular splicing has higher robustness compared with a greedy strategy. The ceramic fragment sample can be spliced into a complete image by the method.

Need to explain: at present, the method of the invention has developed application investigation in a small scale range, and the investigation result shows that the user satisfaction is higher, which lays a foundation for wide application, and meanwhile, the applicant also performs intellectual property risk early warning investigation.

Claims

1. A cultural relic fragment similarity identification and transformation matching method based on machine learning is characterized by comprising the following steps:

step 2: contour line extraction: contour lines in the binary cultural relic fragment image are extracted one by one through a contour tracing algorithm, and a contour line set CL = { CL ] is constructed ₁ ,cl ₂ ,...,cl _cj ,...,cl _lks Lks is the number of extracted contour lines;

and step 3: characteristic point clustering: extracting the characteristic points of each contour line one by one through a k-means clustering method, and constructing a characteristic point set Ki = { k ] of each contour line _i,1 ,k _i,2 ...k _i,j ...k _i,km }; i represents a contour line to which the current feature point set belongs, and the value range of i is more than or equal to 1 and is not more than lks; the feature points in the feature point set of each contour line have the same number, namely km;

step 4-1: the curvature of the characteristic point of each contour line is obtained one by one, and a curvature set Q of the characteristic point of each contour line is constructed _i ＝{q _i，1 ,q _i,2 ,...,q _i,j ,...,q _i,qmi I represents a contour line to which the current feature point set belongs, wherein the value range of i is more than or equal to 1 and is not more than lks; dividing every 3 continuous feature points on the contour line into a segment of feature segment; qmi represents the number of feature segments of the ith contour,

Fitted second parametric equation, a ₁ ,a ₂ ,a ₃ First to third coefficients of the abscissa equation, b ₁ ,b ₂ ,b ₃ First to third coefficients for ordinate equations, m '(j), m "(j) being the first and second derivatives of the parametric equation m (j), n' (j), n" (j) being the first and second derivatives of the parametric equation n (j);

Euclidean distance of the ith feature segment

The calculation method comprises the following steps:

step 4-3: judging two contour lines cl one by one _i1 ,cl _i2 Whether the characteristic segments of (a) are similar: if the Europe of the feature segments of the two contour linesDistance between two adjacent points

and 4-5: determine two contour lines cl _i1 ,cl _i2 Whether it is similar: if two contour lines cl _i1 ,cl _i2 (ii) a similarity score FS _i1,i2 Greater than a second predetermined threshold, two contour lines cl _i1 ,cl _i2 Similar contour lines;

and 5: calculating two similar contour line segments cl one by one _i1 ,cl _i2 The rotation angle delta and the moving distance between the two parts form a rigid body transformation matrix;

horizontal direction movement distance:

vertical direction movement distance:

rigid body transformation matrix GT _i1,i2 ：

In the formula (x) _g ,y _g ),(x _h ,y _h ) For two similar contours cl _i1 ,cl _i2 Coordinates of the selected feature points; delta is the contour linecl _i1 ,cl _i2 Fitting the included angle of two crossed straight lines through linear regression;

step 6: the method for splicing cultural relic fragments circularly from bottom to top comprises the following specific steps:

step 6-1: build an induced cycle set L ₀ ＝{l ₀ ,l ₁ ,...,l _lp ,l _lQ ,...l _ln And ln is more than or equal to 1 and less than lks: each contour line is a node, edges are established between similar contour lines, and connected subgraphs form a connected subgraph set W = { W = ₁ ,...,w _wj ,...,w _zt And (5) judging whether the product of rigid body transformation matrixes of similar contour lines corresponding to edges in each connected subgraph is a unit matrix one by one, if so, connecting the subgraphs as an induction cycle l _lj Adding an induction cycle set;

2. The method for identifying and transforming matching of cultural relic fragment similarity based on machine learning of claim 1, wherein:

the step 1 comprises the following specific steps:

G＝W ₁ ·(μ ₁ -μ) ² +W ₂ ·(μ ₂ -μ) ²

wherein, W ₂ The proportion of background pixels in the image is taken; mu.s ₁ Is the average gray level, mu, of the foreground pixels ₂ Is the average gray level of the background pixels and the average gray level mu of the foreground pixels ₁ Average gray level mu with background pixel ₂ The calculation method is the same, and the average gray level mu of the foreground pixels ₁ The calculation method comprises the following steps:

wherein, y ₁ Is the pixel value is greater than t _x The statistical number of pixels of (2);