CN111723847A - Method, system, terminal device and storage medium for calculating similarity between graphs - Google Patents
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Abstract
The application provides a method, a system, a terminal device and a storage medium for calculating similarity between graphs, wherein the method comprises the following steps: respectively calculating a parameterized vector function of each polygon in the first graph and the second graph, pairing corresponding polygons according to the parameterized vector function of each polygon in the first graph and the second graph, classifying the successfully paired polygons into a paired set, and classifying the unsuccessfully paired polygons into a non-paired set; and respectively carrying out distance calculation on all polygons in the paired set and the unpaired set to obtain a plurality of distance values, carrying out weighted calculation on the distance values to obtain a graph distance, and calculating the graph similarity according to the graph distance. By respectively calculating the design of the parameterized vector function of each polygon, the graphic information of each polygon is mapped into the parameterized vector function, so that the calculation of the distance between the graphics of different shapes is facilitated, and the accuracy of similarity calculation between the graphics is improved.
Description
Technical Field
The present application belongs to the field of graphics processing technologies, and in particular, to a method, a system, a terminal device, and a storage medium for calculating inter-graphics similarity.
Background
With the continuous decrease of Critical Dimension (CD for short), the Dimension of the pattern on the semiconductor chip layout is smaller and smaller, and the process development difficulty and production requirement are higher and higher. The similarity of the graphs on the two chip layouts is measured, the method can be applied to matching key positions in a graph database, and has an important effect on aspects of accelerating the research and development of the process, applying to defect detection in the production process and the like.
The chip layout is mainly composed of polygonal graphs with various shapes, the size change and the position distribution of the graphs on one layout are complex, the size and the shape need to be measured by considering the similarity among the graphs, and the comprehensive influence of density distribution, relative position and the like needs to be considered. A good graph similarity evaluation system needs to have sufficient sensitivity to some characteristic changes on one hand, such as the change in size is generally required to have sufficient sensitivity; on the other hand, it is also required to reduce the sensitivity to some characteristics, such as the sensitivity to pattern transformation such as a minute shift and a minute unevenness at the edge of the pattern, which are generally required.
In the existing method for calculating the similarity between the graphs, 1) an XOR calculation method is adopted and is sensitive to micro translation and edge concave-convex; 2) by adopting a tangential space-based calculation method, due to the discontinuity of the angular direction in the polar coordinate system vector function, the calculation accuracy of the similarity between some graphs is low.
Disclosure of Invention
The embodiment of the application provides a method, a system, terminal equipment and a storage medium for calculating similarity between graphs, and aims to solve the problem of low calculation accuracy of the similarity between graphs caused by an XOR method or a similarity calculation method based on a tangent space in the conventional calculation process of the similarity between graphs.
In a first aspect, an embodiment of the present application provides a method for calculating inter-graph similarity, where the method includes:
acquiring a first graph and a second graph to be calculated, and calculating a parameterized vector function of each polygon in the first graph and the second graph respectively, wherein each parameterized vector function comprises two component functions;
matching corresponding polygons according to the parameterized vector function of each polygon in the first graph and the second graph, classifying the polygons which are successfully matched into a matched set, and classifying the polygons which are not successfully matched into an unpaired set;
respectively carrying out distance calculation on all polygons in the pairing set and the unpaired set to obtain a plurality of distance values;
and carrying out weighted calculation on the distance value to obtain a graph distance between the first graph and the second graph, and calculating graph similarity according to the graph distance.
Compared with the prior art, the embodiment of the application has the advantages that: by respectively calculating the design of the parameterized vector function of each polygon in the first graph and the second graph, the graph information of each polygon is mapped into the parameterized vector function, so that the calculation of the similarity between the graphs in different shapes is facilitated, the sensitivity of the graph similarity calculation method to micro translation and micro edge concave-convex in the graphs is reduced, and the calculation of the similarity between the graphs is more accurate.
Further, said calculating a parameterized vector function for each polygon in said first graph and said second graph, respectively, comprises:
determining the origin, the coordinate axis direction, the starting point and the traversing direction of the coordinate system of each polygon according to a preset selection rule;
establishing a parameter coordinate system according to the origin of the coordinate system and the coordinate axis direction, taking the origin as a reference point, and taking the normalized margin length from the reference point to any vertex in the same polygon as the value of a parameter variable in the parameterized vector function according to the traversal direction;
and taking the coordinate value of the vertex in the parameter coordinate system as a component value of the parameter variable which is equal to the long-term component of the normalized edge distance, and drawing a function curve according to the component value of the component and the parameter variable to obtain the parameterized vector function.
Further, the obtaining the parameterized vector function by using the coordinate value of the vertex in the parametric coordinate system as the component value of the parametric variable equal to the long-term component of the normalized edge distance and drawing a function curve according to the component value of the component and the parametric variable includes:
taking the coordinate value of the vertex on the x coordinate axis in the parameter coordinate system as the component value of the first component in the parameterized vector function when the parameter variable is equal to the normalized edge distance;
performing curve connection on first component coordinate points corresponding to all the vertexes to obtain a first component function, wherein the abscissa of each first component coordinate point is the normalized edge distance length between the vertex and the reference point, and the ordinate of each first component coordinate point is a component value of the first component corresponding to the normalized edge distance length;
taking the coordinate value of the vertex on the y coordinate axis in the parameter coordinate system as the component value of the second component in the parameterized vector function when the parameter variable is equal to the normalized edge distance;
and performing curve connection on second component coordinate points corresponding to all the vertexes to obtain a second component function, wherein the abscissa of each second component coordinate point is the normalized edge distance length between the vertex and the reference point, and the ordinate of each second component coordinate point is the component value of the second component corresponding to the normalized edge distance length.
Further, the pairing of the corresponding polygons according to the parameterized vector function of each polygon in the first graph and the second graph includes:
respectively calculating the minimum spacing distance between each polygon in the first graph and the polygon in the second graph according to a first distance calculation formula;
and if the minimum spacing distance is smaller than a distance threshold value, pairing the two polygons corresponding to the minimum spacing distance into a graph pair.
Further, the distance calculation for all the polygons in the paired set and the unpaired set respectively to obtain a plurality of distance values includes:
calculating the distance between two polygons in the graph pair in the pairing set by using the first distance formula to obtain a first distance value, wherein the first distance formula is as follows:
wherein a is any polygon in the first graph, b is any polygon in the second graph,
said parameterized vector function for the polygon a,
for the parameterized vector function of polygon b, dist { a, b } is the first distance value between polygon a and polygon b;
performing distance calculation on each polygon in the unpaired set by using a second distance formula to obtain a second distance value, wherein the second distance formula is as follows:
wherein c is any polygon in the unpaired set,
for the parameterized vector function of polygon c, dist { c, null } is a second distance value for polygon c in the unpaired set.
Further, the method further comprises:
carrying out graph transformation on the first graph and the second graph, and respectively calculating the graph distance between the first graph and the second graph after each graph transformation;
and outputting the parameter value of the minimum graph distance as a detection result of the graph distance detection between the first graph and the second graph.
Further, the calculation formula for calculating the graph similarity according to the graph distance is as follows:
wherein Q is the graphic similarity, DA,BFor the graph distance between the first graph and the second graph, χ is the similarity between polygons corresponding to a pairing threshold of T, T is the distance threshold, N is the sum of the numbers of elements between the first graph and the second graph, respectively, a pairing set and a no-pairing set, and e is the base number of a natural logarithm.
In a second aspect, an embodiment of the present application provides an inter-graph similarity calculation system, including:
the vector function calculation module is used for acquiring a first graph and a second graph to be calculated, and calculating a parameterized vector function of each polygon in the first graph and the second graph respectively, wherein each parameterized vector function comprises two component functions;
a polygon pairing module, configured to pair corresponding polygons according to a parameterized vector function of each polygon in the first graph and the second graph, classify successfully paired polygons into a paired set, and classify unsuccessfully paired polygons into a non-paired set;
and the graph distance calculation module is used for respectively performing distance calculation on all polygons in the pairing set and the non-pairing set to obtain a plurality of distance values, and calculating the sum of all the distance values to obtain the graph distance between the first graph and the second graph.
And the graph similarity calculation module is used for carrying out weighted calculation on the distance value to obtain a graph distance between the first graph and the second graph and calculating the graph similarity according to the graph distance.
In a third aspect, an embodiment of the present application provides a terminal device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor executes the computer program to implement the method described above.
In a fourth aspect, the present application provides a storage medium storing a computer program, and when the computer program is executed by a processor, the computer program implements the method as described above.
In a fifth aspect, the present application provides a computer program product, which when run on a terminal device, causes the terminal device to execute the inter-graph similarity calculation method according to any one of the first aspect.
It is understood that the beneficial effects of the second aspect to the fifth aspect can be referred to the related description of the first aspect, and are not described herein again.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings used in the embodiments or the description of the prior art will be briefly described below.
Fig. 1 is a flowchart of a method for calculating inter-pattern similarity according to a first embodiment of the present application;
fig. 2 is a flowchart of a method for calculating inter-pattern similarity according to a second embodiment of the present application;
FIG. 3 is a diagram illustrating a graph D and a polygon D1 according to a second embodiment of the present application;
FIG. 4 is a parameterized vector function of the polygon d1 in FIG. 3
Medium first component function Ex(p) and a second component function Ey(p) function curve;
FIG. 5 is a schematic diagram of the graphic structures of a polygon a1 and a polygon b1 according to a second embodiment of the present application;
FIG. 6 is a first component function E corresponding to the polygon a1 and the polygon b1 in FIG. 5xFunction of (p)A number curve;
FIG. 7 is a second component function E corresponding to the polygon a1 and the polygon b1 in FIG. 5y(p) function curve;
fig. 8 is a flowchart of a method for calculating inter-pattern similarity according to a third embodiment of the present application;
fig. 9 is a schematic diagram of a graphic pattern0, a graphic pattern1, and a graphic pattern2 according to a third embodiment of the present application;
fig. 10 is a schematic structural diagram of an inter-pattern similarity calculation system according to a fourth embodiment of the present application;
fig. 11 is a schematic structural diagram of a terminal device according to a fifth embodiment of the present application.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system structures, techniques, etc. in order to provide a thorough understanding of the embodiments of the present application. It will be apparent, however, to one skilled in the art that the present application may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.
It will be understood that the terms "comprises" and/or "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It should also be understood that the term "and/or" as used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.
As used in this specification and the appended claims, the term "if" may be interpreted contextually as "when", "upon" or "in response to" determining "or" in response to detecting ". Similarly, the phrase "if it is determined" or "if a [ described condition or event ] is detected" may be interpreted contextually to mean "upon determining" or "in response to determining" or "upon detecting [ described condition or event ]" or "in response to detecting [ described condition or event ]".
Furthermore, in the description of the present application and the appended claims, the terms "first," "second," "third," and the like are used for distinguishing between descriptions and not necessarily for describing or implying relative importance.
Reference throughout this specification to "one embodiment" or "some embodiments," or the like, means that a particular feature, structure, or characteristic described in connection with the embodiment is included in one or more embodiments of the present application. Thus, appearances of the phrases "in one embodiment," "in some embodiments," "in other embodiments," or the like, in various places throughout this specification are not necessarily all referring to the same embodiment, but rather "one or more but not all embodiments" unless specifically stated otherwise. The terms "comprising," "including," "having," and variations thereof mean "including, but not limited to," unless expressly specified otherwise.
Example one
Referring to fig. 1, a flowchart of a method for calculating inter-pattern similarity according to a first embodiment of the present application is shown, which includes the steps of:
step S10, acquiring a first graph and a second graph to be calculated, and calculating a parameterized vector function of each polygon in the first graph and the second graph respectively;
wherein each graph contains a polygon group, e.g., the first graph A contains a polygon group of { a }iThe polygon set contained in the second graph B is { B }j}。
Let notation of the parameterized vector function
p is a parameter, a function
Having two component functions respectively Ex(p) and Ey(p) in which polygon groups { a } are calculated, respectivelyiAnd a set of polygons bjA parameterized vector function for each polygon within the polygon such that the graphical features of the polygon are focused on the edge information of the polygon, and the edge information of each polygon is mapped into a parameterized vector function.
Step S20, matching corresponding polygons according to the parameterized vector function of each polygon in the first graph and the second graph;
and when judging that the polygons between the first graph and the second graph have similar polygons, judging that the two polygons corresponding to the similar polygons are successfully paired.
Step S30, classifying the successfully matched polygons into a matched set, and classifying the unsuccessfully matched polygons into an unpaired set;
for example, the set of polygons { a ] is subjected to a parameterized vector functioniAnd a set of polygons { b }jPairing polygons, and classifying successfully paired polygons into a pairing set { (a)n,bm)}matchedAnd matching the successfully-matched polygons from the polygon groups { a }iAnd a set of polygons bjIs removed, and finally the polygon set { a }is removediAnd a set of polygons bjThe remaining polygons in the (b) are put into a pairless set (a)n,null),(bmnull)}unmatched。
Step S40, respectively carrying out distance calculation on all the polygons in the paired set and the unpaired set to obtain a plurality of distance values;
wherein, when the polygon group { a }iAnd a set of polygons { b }jSuccess of polygon pairing betweenDuring the process, two polygons may be classified into the paired set by using a graph pair, so that, for polygons in the paired set, a corresponding distance value may be obtained by calculating a distance between two polygons in each graph pair, and for polygons in the unpaired set, a corresponding distance value may be obtained by calculating an integral value of each polygon as a distance contribution.
Step S50, carrying out weighted calculation on the distance value to obtain the graph distance between the first graph and the second graph, and calculating the graph similarity according to the graph distance;
preferably, the setting of the weighting factors corresponding to the paired sets and the unpaired sets can adopt the following two modes or two modes in combination: 1) the area of a single pattern or the average area of a pair of patterns; 2) the reciprocal of the distance of the center of the graph from the left origin.
In this embodiment, by designing the parameterized vector function of each polygon in the first graph and the second graph, the graph information of each polygon is mapped into the parameterized vector function, which facilitates the calculation of the similarity between the two graphs in different shapes, reduces the sensitivity of the graph similarity calculation method to the tiny translation and the tiny edge concave-convex in the graphs, and makes the calculation of the similarity between the graphs more accurate.
Example two
Referring to fig. 2, a flowchart of a method for calculating inter-pattern similarity according to a second embodiment of the present application is shown, which includes the steps of:
step S11, acquiring a first graph and a second graph to be calculated, and determining the origin, the coordinate axis direction, the starting point and the traversing direction of the coordinate system of each polygon according to a preset selection rule;
the preset selection rule can be set according to the requirements of a user, and the origin, the coordinate axis direction, the starting point and the traversal direction of the coordinate system of each polygon can be set at willFor example, the first graph A contains a polygon group { a }iThe second graph B contains a polygon set { B }jThe midpoints of the first graph A are taken as a polygon group { a }iThe origin of the coordinate system of all polygons in the graph is defined by the midpoint of the second graph B as the polygon set { B }jThe origin of the coordinate system of all polygons in.
Preferably, the coordinate axis direction defined in the graphic storage file format (such as OASIS or GDSII format) may be used as the coordinate axis direction, in this embodiment, any vertex in the polygon may be set as the starting point, for example, the lower left corner vertex of each polygon may be used as the starting point.
Further, in this embodiment, a uniform traversal direction needs to be set for the polygons in the first graph and the second graph, as a direction to traverse each vertex of each polygon, for example, a counterclockwise direction may be selected as a traversal direction of vertices in all polygons.
Step S21, establishing a parameter coordinate system according to the coordinate system origin and the coordinate axis direction, and taking the starting point as a reference point, and taking the normalized margin length between the reference point and any vertex in the same polygon as the value of the parameter variable in the parameterized vector function according to the traversal direction;
specifically, referring to fig. 3, the area formed by the dotted line is the graph D, the area formed by the vertices S1 to S6 is the polygon D1 in the graph D, and for the polygon D1, the vertex S1 is the starting point, and the counterclockwise direction is the traversal direction, the normalized edge distance length l between the vertex S1 and any vertex Si is setiAs the same parameterized vector function
Value of parameter variable p, i ═ 2, 6]The point S1 itself has a p value of 0.
Preferably, the normalized margin length is defined as: from the reference vertex, along the boundary of the polygon, following the traversal direction, the side length sum of each side passed by reaching a certain vertex from the reference vertex is divided by the perimeter of the polygon, and further, the normalized side length multiplied by any factor can still be used as the normalized side length without affecting the basic function of the embodiment.
Step S31, using the coordinate value of the vertex in the parameter coordinate system as the component value of the parameter variable equal to the long-term component of the normalized margin, and drawing a function curve according to the component value of the component and the parameter variable to obtain the parameterized vector function;
specifically, in this step, the coordinate value of the vertex in the parameter coordinate system is used as a component value of the parameter variable equal to the long-term component of the normalized edge distance, and a function curve is drawn according to the component value of the component and the parameter variable to obtain a parameterized vector function, including:
step S310, using coordinate values of the vertex on an x coordinate axis in the parameter coordinate system as component values of a first component in the parameterized vector function when the parameter variable is equal to the normalized edge distance;
wherein, for the polygon d1, the coordinate value x of the vertex Si on the x coordinate axis of the graph coordinate systemiAs a
At p ═ liThe component value of the first component is such that the first component coordinate point (variable parameter-component value of the first component) corresponding to any vertex Si of the polygon d1 is (l)i,xi)。
Step S311, performing curve connection on the first component coordinate points corresponding to all the vertexes to obtain a first component function;
the abscissa of the first component coordinate point is the normalized edge distance length between the vertex and the reference point, and the ordinate is the component value of the first component corresponding to the normalized edge distance length;
specifically, in a rectangular coordinate system formed by using parameter variables and a first component function as coordinate parameters, a set of first component coordinate points corresponding to all vertexes { (l)i,xi) Get ExFunction of (p) (first component function).
Step S312, using coordinate value of said vertex on y coordinate axis in said parameter coordinate system as component value of second component in said parameterized vector function when said parameter variable is equal to said normalized edge distance;
wherein, the coordinate value y of the polygon d1 is defined by the vertex Si on the y coordinate axis of the graphic coordinate systemiAs a
At p ═ liThe second component value of time is such that the second component coordinate point corresponding to any vertex Si of the polygon d1 is (l)i,yi)。
Step S313, performing curve connection on second component coordinate points corresponding to all the vertexes to obtain a second component function;
the abscissa of the second component coordinate point is the normalized edge distance length between the vertex and the reference point, and the ordinate is the component value of the second component corresponding to the normalized edge distance length;
specifically, in a rectangular coordinate system formed by using parameter variables and a second component function as coordinate parameters, a set of second component coordinate points corresponding to all vertexes { (l)i,yi) Are connected in turn to give Ey(p) (second component function), see FIG. 4, which is a parameterized vector function of the polygon d1 in FIG. 3
Medium first component function Ex(p) and a second component function Ey(p) function curve.
Step S41, respectively calculating a minimum distance between each polygon in the first graph and the polygon in the second graph according to a first distance calculation formula;
wherein the first distance formula is:
in the above formula, a is the first graphOf the polygon a, a parameterized vector function of
b is any polygon in the second graph, and the parameterized vector function of the polygon b is
dist { a, b } is the separation distance between polygon a and polygon b.
Specifically, in this step, the polygon group { a }is selectediAny polygon a innAnd a set of polygons { bjCalculating the distance of all polygons in the polygon group to obtain a plurality of spacing distances, acquiring the minimum value of the spacing distances, and setting the minimum value as the polygon group { a }iCurrent polygon in the polygon list and polygon set { b }jMinimum separation distance between polygons in the (z) }.
Further, please refer to fig. 5, which is a schematic diagram of the graph structures of the polygon a1 (solid line) and the polygon b1 (dashed line) in the present embodiment, wherein the function curves in fig. 6 are the first component functions E corresponding to the polygon a1 and the polygon b1, respectivelyx(p) second component functions E corresponding to the polygons a1 and b1 are plotted in FIG. 7y(p), there is mainly a translational gap between the polygon a1 and the polygon b1, and the separation distance is 28.28 as calculated according to the first distance formula.
Step S51, if the minimum distance is smaller than the distance threshold, pairing the two polygons corresponding to the minimum distance into a graph pair, and moving the two polygons corresponding to the graph pair from the first graph and the second graph into the pairing set;
wherein, the distance threshold value can be set according to the requirement of the user by judging the polygon group { aiEach polygon in the set { b } with a polygon set { bjJudging whether the minimum spacing distance between the polygons in the set is smaller than a distance threshold value or not to judge the polygon set { a }iEach polygon in the group { b } and the group of polygonsjWhether or not between polygons in (c) }And matching the two polygons which are successfully matched into a graph pair and moving the graph pair into a matching set.
Specifically, in this embodiment, if the minimum spacing distance is greater than or equal to the distance threshold, the minimum spacing distance is within the polygon group { a }iAnd a set of sides bjThe corresponding two polygons in the (h) are grouped in the unpaired set.
Step S61, putting the remaining polygons in the first graph and the second graph into the unpaired set;
wherein, when the polygon group { a ] is determinediWhen the polygon is empty, the polygon is grouped into { b }jThe remaining polygons in the set are grouped into unpaired sets, preferably, a set of polygons { a }iThe remaining polygons in the polygon list and the polygon set bjThe minimum spacing distances between polygons in the set are all greater than or equal to a distance threshold, i.e., the set of polygons { a }iThe remaining polygons in the polygon list and the polygon set bjAll polygons in the } are unpaired.
Step S71, respectively carrying out distance calculation on all the polygons in the paired set and the unpaired set to obtain a plurality of distance values;
specifically, in this step, the performing distance calculation on all the polygons in the paired set and the unpaired set respectively to obtain a plurality of distance values includes:
calculating the distance between two polygons in the graph pairs in the pairing set by adopting the first distance formula to obtain a first distance value, wherein the first distance value is the minimum spacing distance between two polygons in each graph pair;
performing distance calculation on each polygon in the unpaired set by using a second distance formula to obtain a second distance value, wherein the second distance formula is as follows:
wherein c is any polygon in the unpaired set,
for the parameterized vector function of the polygon c, dist { c, null } is a second distance value of the polygon c in the unpaired set, wherein, by designing distance calculation for each polygon in the unpaired set by using a second distance formula, an integral value (null distance) of the polygon in the unpaired set is used as a distance contribution thereof to obtain a corresponding distance value.
Step S81, calculating the sum of all the distance values to obtain the graph distance between the first graph and the second graph, and calculating the graph similarity according to the graph distance;
and calculating the sum of all the first distance values and all the second distance values to obtain the graph distance between the first graph and the second graph.
Specifically, in this step, the calculation formula for calculating the graph similarity according to the graph distance is as follows:
wherein Q is the graphic similarity, DA,BFor the graph distance between the first graph and the second graph, χ is the similarity between polygons corresponding to a pairing threshold of T, T is the distance threshold, N is the sum of the numbers of elements between the first graph and the second graph, respectively, a pairing set and a no-pairing set, and e is the base number of a natural logarithm.
In the embodiment, the design of the parameterized vector function of each polygon in the first graph and the second graph is respectively calculated, so that the graph information of each polygon is mapped into the parameterized vector function, the calculation of the distance between the two graphs in different shapes is facilitated, the design of calculating the first distance value by adopting the first distance formula and calculating the second distance value by adopting the second distance formula can effectively carry out numerical calculation on the size, the position and the shape difference of the polygon between the two graphs, the sensitivity of the size change of the polygon in the graph is improved, the low sensitivity effect of graph translation and small disturbance is met, and the accuracy of the similarity calculation between the graphs of the first graph and the second graph is improved.
EXAMPLE III
Please refer to fig. 8, which is a flowchart illustrating a method for calculating inter-pattern similarity according to a third embodiment of the present application, including the steps of:
step S12, acquiring a first graph and a second graph to be calculated, and calculating a parameterized vector function of each polygon in the first graph and the second graph respectively;
wherein each of the parameterized vector functions comprises two component functions.
Step S22, matching corresponding polygons according to the parameterized vector function of each polygon in the first graph and the second graph;
step S32, classifying the successfully matched polygons into a matched set, and classifying the unsuccessfully matched polygons into an unpaired set;
step S42, respectively carrying out distance calculation on all the polygons in the paired set and the unpaired set to obtain a plurality of distance values;
step S52, calculating the sum of all the distance values to obtain the graph distance between the first graph and the second graph;
step S62, performing graph transformation on the first graph and the second graph, and calculating the graph distance between the first graph and the second graph after each graph transformation;
in order to meet the requirement of graph symmetry, the graphs need to have certain transformation invariance, and the symmetry comprises 90-degree rotation and reflection invariance along an X axis or a Y axis, so that the first graph and the second graph can be subjected to multiple different graph transformations, graph distances among the transformed graphs are respectively calculated, and multiple graph distances are obtained.
For example, the pattern transformation of the first pattern and the second pattern may be performed in 8 transformation manners, and the 8 transformations may be formed by a combination of (0, 90, 180,270) degree rotation and (X, Y) axis reflection transformation.
Step S72, outputting the parameter value of the minimum graph distance as a detection result of the graph distance detection between the first graph and the second graph;
step S82, calculating the graph similarity between the first graph and the second graph according to the graph distance and the distance threshold;
specifically, the similarity value calculated by two identical graphs is equal to 1, the greater the difference between the two graphs is, the closer the similarity value is to 0, and in practical application, a user can set the values of T and χ according to requirements.
For example, referring to fig. 9, a graph structure diagram of three graphs provided in this embodiment is shown, and calculation results obtained according to the first calculation formula, the second calculation formula, and the similarity calculation formula are: the pattern distance between the pattern0 pattern and the pattern1 pattern is 71.96, the similarity is 0.85, the pattern distance between the pattern0 pattern and the pattern2 pattern is 697.26, the similarity is 0.33, as can be seen from the pattern structure of the three patterns, the pattern0 and the pattern1 each comprise two polygons with similar shapes, and as can be seen from the overlapped graph, certain displacement positions and disturbance differences exist among the polygons; however, similar polygons are not included between the pattern2 and the pattern0, and although there are many overlapped portions of the polygons included between the figures, the similarity between the two figures is low in view of the figure characteristics, and the result of the calculation based on the figure similarity can better reflect the expectation of the judgment of the figure similarity.
In the embodiment, the design of calculating the graph similarity between the first graph and the second graph according to the graph distance and the distance threshold value to provide quantitative reference about the similarity between the two graphs can be applied to scanning and extracting the positions of similar keys from the layout, and the graph similarity between the two graphs can be effectively calculated through the graph distance between the two graphs obtained through calculation and the preset distance threshold value.
Example four
Fig. 10 is a schematic structural diagram of an inter-pattern similarity calculation system 100 according to a fourth embodiment of the present application, which corresponds to the inter-pattern similarity calculation method described in the foregoing embodiments, and only shows portions related to the embodiments of the present application for convenience of description.
Referring to fig. 10, the system includes: a vector function calculation module 10, a vector function pairing module 11, a graph distance calculation module 12 and a graph similarity calculation module 14, wherein:
the vector function calculation module 10 is configured to obtain a first graph and a second graph to be calculated, and calculate a parameterized vector function of each polygon in the first graph and the second graph, where each parameterized vector function includes two component functions.
Wherein the vector function calculation module 10 is further configured to: determining the origin, the coordinate axis direction, the starting point and the traversing direction of the coordinate system of each polygon according to a preset selection rule;
establishing a parameter coordinate system according to the origin of the coordinate system and the coordinate axis direction, taking the origin as a reference point, and taking the normalized margin length from the reference point to any vertex in the same polygon as the value of a parameter variable in the parameterized vector function according to the traversal direction;
and taking the coordinate value of the vertex in the parameter coordinate system as a component value of the parameter variable which is equal to the long-term component of the normalized edge distance, and drawing a function curve according to the component value of the component and the parameter variable to obtain the parameterized vector function.
Preferably, the vector function calculation module 10 is further configured to: taking the coordinate value of the vertex on the x coordinate axis in the parameter coordinate system as the component value of the first component in the parameterized vector function when the parameter variable is equal to the normalized edge distance;
performing curve connection on first component coordinate points corresponding to all the vertexes to obtain a first component function, wherein the abscissa of each first component coordinate point is the normalized edge distance length between the vertex and the reference point, and the ordinate of each first component coordinate point is a component value of the first component corresponding to the normalized edge distance length;
taking the coordinate value of the vertex on the y coordinate axis in the parameter coordinate system as the component value of the second component in the parameterized vector function when the parameter variable is equal to the normalized edge distance;
and performing curve connection on second component coordinate points corresponding to all the vertexes to obtain a second component function, wherein the abscissa of each second component coordinate point is the normalized edge distance length between the vertex and the reference point, and the ordinate of each second component coordinate point is the component value of the second component corresponding to the normalized edge distance length.
A polygon pairing module 11, configured to pair corresponding polygons according to a parameterized vector function of each polygon in the first graph and the second graph, classify the successfully paired polygons into a paired set, and classify the unsuccessfully paired polygons into a non-paired set.
Wherein the polygon pairing module 11 is further configured to: respectively calculating the minimum spacing distance between each polygon in the first graph and the polygon in the second graph according to a first distance calculation formula;
and if the minimum spacing distance is smaller than a distance threshold value, pairing the two polygons corresponding to the minimum spacing distance into a graph pair.
And the graph distance calculation module 12 is configured to perform distance calculation on all the polygons in the paired set and the unpaired set respectively to obtain a plurality of distance values.
Wherein the graph distance calculation module 12 is further configured to: calculating the distance between two polygons in the graph pair in the pairing set by using the first distance formula to obtain a first distance value, wherein the first distance formula is as follows:
wherein a is any more than one of the first graphsA polygon, b being any polygon of the second pattern,
said parameterized vector function for the polygon a,
for the parameterized vector function of polygon b, dist { a, b } is the first distance value between polygon a and polygon b;
performing distance calculation on each polygon in the unpaired set by using a second distance formula to obtain a second distance value, wherein the second distance formula is as follows:
wherein c is any polygon in the unpaired set,
for the parameterized vector function of polygon c, dist { c, null } is a second distance value for polygon c in the unpaired set.
In addition, in this embodiment, the inter-pattern similarity calculation system 100 further includes:
a graph transformation module 13, configured to perform graph transformation on the first graph and the second graph, and respectively calculate the graph distance between the first graph and the second graph after each graph transformation;
and outputting the parameter value of the minimum graph distance as a detection result of the graph distance detection between the first graph and the second graph.
And the graph similarity calculation module 14 is configured to perform weighted calculation on the distance value to obtain a graph distance between the first graph and the second graph, and calculate a graph similarity according to the graph distance.
Wherein, the calculation formula adopted for calculating the graph similarity according to the graph distance is as follows:
wherein Q is the graphic similarity, DA,BFor the graph distance between the first graph and the second graph, χ is the similarity between polygons corresponding to a pairing threshold of T, T is the distance threshold, N is the sum of the numbers of elements between the first graph and the second graph, respectively, a pairing set and a no-pairing set, and e is the base number of a natural logarithm.
In the embodiment, by respectively calculating the design of the parameterized vector function of each polygon in the first graph and the second graph, the graph characteristics of the first graph and the second graph are focused in the edge information of the polygons contained in the first graph and the second graph, and the edge information of each polygon is mapped into the parameterized vector function, so that the calculation of the distance between the graphs in different shapes is facilitated, the size, the position and the shape difference of the polygon between the two graphs can be effectively calculated by adopting the design of calculating the first distance value by adopting the first distance formula and calculating the second distance value by adopting the second distance formula, the sensitivity of the polygon size change in the graphs is improved, the effect of low sensitivity of graph translation and micro-disturbance is satisfied, and the accuracy of the calculation of the similarity between the graphs of the first graph and the second graph is improved, the design of calculating the graph similarity between the first graph and the second graph according to the graph distance and the distance threshold value to give quantitative reference about the similarity between the two graphs can be applied to scanning and extracting similar key positions from a layout, and the graph similarity between the two graphs can be effectively calculated through the graph distance between the two graphs obtained through calculation and the preset distance threshold value.
It should be noted that, for the information interaction, execution process, and other contents between the above-mentioned devices/modules, the specific functions and technical effects thereof are based on the same concept as those of the embodiment of the method of the present application, and reference may be made to the part of the embodiment of the method specifically, and details are not described here.
Fig. 11 is a schematic structural diagram of a terminal device 2 according to a fifth embodiment of the present application. As shown in fig. 11, the terminal device 2 of this embodiment includes: at least one processor 20 (only one processor is shown in fig. 11), a memory 21, and a computer program 22 stored in the memory 21 and executable on the at least one processor 20, the steps of any of the various method embodiments described above being implemented when the computer program 22 is executed by the processor 20.
The terminal device 2 may be a desktop computer, a notebook, a palm computer, a cloud server, or other computing devices. The terminal device may include, but is not limited to, a processor 20, a memory 21. Those skilled in the art will appreciate that fig. 11 is merely an example of the terminal device 2, and does not constitute a limitation of the terminal device 2, and may include more or less components than those shown, or combine some components, or different components, such as an input/output device, a network access device, and the like.
The Processor 20 may be a Central Processing Unit (CPU), and the Processor 20 may be other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic device, discrete hardware component, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory 21 may in some embodiments be an internal storage unit of the terminal device 2, such as a hard disk or a memory of the terminal device 2. The memory 21 may also be an external storage device of the terminal device 2 in other embodiments, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like, which are provided on the terminal device 2. Further, the memory 21 may also include both an internal storage unit and an external storage device of the terminal device 2. The memory 21 is used for storing an operating system, an application program, a BootLoader (BootLoader), data, and other programs, such as program codes of the computer program. The memory 21 may also be used to temporarily store data that has been output or is to be output.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-mentioned division of the functional units and modules is illustrated, and in practical applications, the above-mentioned function distribution may be performed by different functional units and modules according to needs, that is, the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-mentioned functions. Each functional unit and module in the embodiments may be integrated in one processing unit, or each unit may exist alone physically, or two or more units are integrated in one unit, and the integrated unit may be implemented in a form of hardware, or in a form of software functional unit. In addition, specific names of the functional units and modules are only for convenience of distinguishing from each other, and are not used for limiting the protection scope of the present application. The specific working processes of the units and modules in the system may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
An embodiment of the present application further provides a network device, where the network device includes: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor, the processor implementing the steps of any of the various method embodiments described above when executing the computer program.
The embodiments of the present application further provide a computer-readable storage medium, where a computer program is stored, and when the computer program is executed by a processor, the computer program implements the steps in the above-mentioned method embodiments.
Claims (10)
1. An inter-figure similarity calculation method, characterized by comprising:
acquiring a first graph and a second graph to be calculated, and calculating a parameterized vector function of each polygon in the first graph and the second graph respectively, wherein each parameterized vector function comprises two component functions;
matching corresponding polygons according to the parameterized vector function of each polygon in the first graph and the second graph, classifying the polygons which are successfully matched into a matched set, and classifying the polygons which are not successfully matched into an unpaired set;
respectively carrying out distance calculation on all polygons in the pairing set and the unpaired set to obtain a plurality of distance values;
and carrying out weighted calculation on the distance value to obtain a graph distance between the first graph and the second graph, and calculating graph similarity according to the graph distance.
2. The inter-figure similarity calculation method according to claim 1, wherein the calculating the parameterized vector function for each polygon in the first figure and the second figure, respectively, comprises:
determining the origin, the coordinate axis direction, the starting point and the traversing direction of the coordinate system of each polygon according to a preset selection rule;
establishing a parameter coordinate system according to the origin of the coordinate system and the coordinate axis direction, taking the origin as a reference point, and taking the normalized margin length from the reference point to any vertex in the same polygon as the value of a parameter variable in the parameterized vector function according to the traversal direction;
and taking the coordinate value of the vertex in the parameter coordinate system as a component value of the parameter variable which is equal to the long-term component of the normalized edge distance, and drawing a function curve according to the component value of the component and the parameter variable to obtain the parameterized vector function.
3. The method for calculating similarity between graphics according to claim 2, wherein said obtaining said parameterized vector function by using coordinate values of said vertices in said parametric coordinate system as component values of said parametric variable equal to said normalized margin long-term component and plotting a function curve based on the component values of said component and said parametric variable comprises:
taking the coordinate value of the vertex on the x coordinate axis in the parameter coordinate system as the component value of the first component in the parameterized vector function when the parameter variable is equal to the normalized edge distance;
performing curve connection on first component coordinate points corresponding to all the vertexes to obtain a first component function, wherein the abscissa of each first component coordinate point is the normalized edge distance length between the vertex and the reference point, and the ordinate of each first component coordinate point is a component value of the first component corresponding to the normalized edge distance length;
taking the coordinate value of the vertex on the y coordinate axis in the parameter coordinate system as the component value of the second component in the parameterized vector function when the parameter variable is equal to the normalized edge distance;
and performing curve connection on second component coordinate points corresponding to all the vertexes to obtain a second component function, wherein the abscissa of each second component coordinate point is the normalized edge distance length between the vertex and the reference point, and the ordinate of each second component coordinate point is the component value of the second component corresponding to the normalized edge distance length.
4. The inter-figure similarity calculation method according to claim 1, wherein the pairing of the corresponding polygons according to the parameterized vector function of each polygon in the first figure and the second figure comprises:
respectively calculating the minimum spacing distance between each polygon in the first graph and the polygon in the second graph according to a first distance calculation formula;
and if the minimum spacing distance is smaller than a distance threshold value, pairing the two polygons corresponding to the minimum spacing distance into a graph pair.
5. The inter-pattern similarity calculation method according to claim 4, wherein the distance calculation for all the polygons in the paired set and the unpaired set, respectively, to obtain a plurality of distance values comprises:
calculating the distance between two polygons in the graph pair in the pairing set by using the first distance formula to obtain a first distance value, wherein the first distance formula is as follows:
wherein a is any polygon in the first graph, b is any polygon in the second graph,
said parameterized vector function for the polygon a,
for the parameterized vector function of polygon b, dist { a, b } is the first distance value between polygon a and polygon b;
performing distance calculation on each polygon in the unpaired set by using a second distance formula to obtain a second distance value, wherein the second distance formula is as follows:
wherein c is any polygon in the unpaired set,
for the parameterized vector function of polygon c, dist { c, null } is a second distance value for polygon c in the unpaired set.
6. The inter-figure similarity calculation method according to claim 1, further comprising:
carrying out graph transformation on the first graph and the second graph, and respectively calculating the graph distance between the first graph and the second graph after each graph transformation;
and outputting the parameter value of the minimum graph distance as a detection result of the graph distance detection between the first graph and the second graph.
7. The inter-figure similarity calculation method according to claim 4, wherein the calculation formula for calculating the figure similarity based on the figure distance is:
wherein Q is the graphic similarity, DA,BFor the graph distance between the first graph and the second graph, χ is the similarity between polygons corresponding to a pairing threshold of T, T is the distance threshold, N is the sum of the numbers of elements between the first graph and the second graph, respectively, a pairing set and a no-pairing set, and e is the base number of a natural logarithm.
8. An inter-figure similarity calculation system, comprising:
the vector function calculation module is used for acquiring a first graph and a second graph to be calculated, and calculating a parameterized vector function of each polygon in the first graph and the second graph respectively, wherein each parameterized vector function comprises two component functions;
a polygon pairing module, configured to pair corresponding polygons according to a parameterized vector function of each polygon in the first graph and the second graph, classify successfully paired polygons into a paired set, and classify unsuccessfully paired polygons into a non-paired set;
the figure distance calculation module is used for respectively calculating the distances of all the polygons in the pairing set and the unpaired set to obtain a plurality of distance values;
and the graph similarity calculation module is used for carrying out weighted calculation on the distance value to obtain a graph distance between the first graph and the second graph and calculating the graph similarity according to the graph distance.
9. A terminal device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the method according to any of claims 1 to 7 when executing the computer program.
10. A storage medium storing a computer program, characterized in that the computer program, when executed by a processor, implements the method according to any one of claims 1 to 7.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113361226A (en) * | 2021-06-25 | 2021-09-07 | 青岛信芯微电子科技股份有限公司 | Method for reducing size of layout file and electronic equipment |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101071272A (en) * | 2006-05-10 | 2007-11-14 | 中芯国际集成电路制造(上海)有限公司 | Method for seeking target area for integrated circuit layout design |
| CN101533422A (en) * | 2008-12-12 | 2009-09-16 | 昆山锐芯微电子有限公司 | Method for inspecting layout |
| US8490030B1 (en) * | 2012-06-01 | 2013-07-16 | Synopsys, Inc. | Distance metric for accurate lithographic hotspot classification using radial and angular functions |
| US20140372958A1 (en) * | 2013-06-14 | 2014-12-18 | Taiwan Semiconductor Manufacturing Co., Ltd. | Triple-pattern lithography layout decomposition |
| US20160306914A1 (en) * | 2015-04-14 | 2016-10-20 | Dae-Kwon Kang | Layout design system, system and method for fabricating mask pattern using the same |
| US20190012571A1 (en) * | 2017-07-07 | 2019-01-10 | Mapbox, Inc. | Identifying a visual center of a polygon |
| US20190051013A1 (en) * | 2017-08-10 | 2019-02-14 | Here Global B.V. | Method, apparatus, and system for an asymmetric evaluation of polygon similarity |
| US20190066328A1 (en) * | 2017-08-22 | 2019-02-28 | Here Global B.V. | Method, apparatus, and system for a vertex-based evaluation of polygon similarity |
-
2020
- 2020-05-21 CN CN202010437909.9A patent/CN111723847A/en active Pending
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101071272A (en) * | 2006-05-10 | 2007-11-14 | 中芯国际集成电路制造(上海)有限公司 | Method for seeking target area for integrated circuit layout design |
| CN101533422A (en) * | 2008-12-12 | 2009-09-16 | 昆山锐芯微电子有限公司 | Method for inspecting layout |
| US8490030B1 (en) * | 2012-06-01 | 2013-07-16 | Synopsys, Inc. | Distance metric for accurate lithographic hotspot classification using radial and angular functions |
| US20140372958A1 (en) * | 2013-06-14 | 2014-12-18 | Taiwan Semiconductor Manufacturing Co., Ltd. | Triple-pattern lithography layout decomposition |
| US20160306914A1 (en) * | 2015-04-14 | 2016-10-20 | Dae-Kwon Kang | Layout design system, system and method for fabricating mask pattern using the same |
| US20190012571A1 (en) * | 2017-07-07 | 2019-01-10 | Mapbox, Inc. | Identifying a visual center of a polygon |
| US20190051013A1 (en) * | 2017-08-10 | 2019-02-14 | Here Global B.V. | Method, apparatus, and system for an asymmetric evaluation of polygon similarity |
| US20190066328A1 (en) * | 2017-08-22 | 2019-02-28 | Here Global B.V. | Method, apparatus, and system for a vertex-based evaluation of polygon similarity |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113361226A (en) * | 2021-06-25 | 2021-09-07 | 青岛信芯微电子科技股份有限公司 | Method for reducing size of layout file and electronic equipment |
| CN113361226B (en) * | 2021-06-25 | 2022-11-11 | 青岛信芯微电子科技股份有限公司 | Method for reducing size of layout file and electronic equipment |
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