Method for evaluating uniformity of distribution of position points in space

Abstract

The application provides a method for evaluating the uniformity of the distribution of position points in space, which is used for evaluating the uniformity of the distribution of feature points in an image. Here, "space" refers to a mathematical description of the analysis object, for example, we can consider a picture as a two-dimensional rectangular space, and the feature points extracted from the image are the position points in this space. This method is suitable for evaluating the uniformity of point distribution in the fields of image processing and geographic information analysis. This method uses the space occupied by the points to calculate the distribution of the points, and then compares it with the ideal state of point distribution to evaluate the uniformity of the point distribution. The "ideal state of point distribution" refers to the situation that if the points are uniformly distributed in the space, each point should occupy the same size of space. Compared with the traditional method, the method of the application has a wider range of application, can evaluate the uniformity of point distribution in any dimension, does not need to define parameters in advance, is not limited by the number of points, and can compare the uniformity of point distribution in different spaces with a large difference in the number of points. In addition, the method is simple to calculate, has a small amount of calculation, and is fast in calculation. In practical applications, the method can be applied to the fields of image processing and geographic information analysis, and provides an efficient and accurate analysis tool for related industries.

Description

TECHNICAL FIELD

[0001] The present application relates to the fields of image processing, geographic information analysis, etc., and in particular to the technical field of evaluating the uniformity of the distribution of location points in space. BACKGROUND

[0002] In the fields of image processing, geographic information analysis, etc., it is necessary to evaluate the uniformity of the distribution of location points in space. Currently, commonly used methods for evaluating the uniformity of point distribution include distance-based methods, grid-based methods, and density-based methods, etc.

[0003] These methods can provide certain reference in some cases, but they also have some limitations. For example, the distance-based method requires a distance threshold to be specified in advance, and this threshold may have different effects for different data sets and application scenarios. The grid-based method usually needs to define the grid size in advance according to the characteristics of the data set, which may result in insufficient capture of local details of point distribution. The density-based method is usually sensitive to noise data and is easily affected by abnormal points.

[0004] Compared with traditional methods, the method of the present application has higher precision and wider applicability, and can more accurately evaluate the uniformity of point distribution without the need to define parameters in advance, and is suitable for estimating the uniformity of point distribution in any-dimensional space. Therefore, the method of the present application can be widely applied in the fields of image processing, geographic information analysis, etc. SUMMARY

[0005] In view of the above shortcomings of traditional methods for evaluating the uniformity of the distribution of location points in space, the present application proposes a new method for evaluating the uniformity of the distribution of location points in space, which has higher precision and wider applicability than traditional methods for evaluating the uniformity of points, and can more accurately evaluate the uniformity of point distribution.

[0006] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0007] The present application provides a method for evaluating the uniformity of the distribution of location points in space, and the theoretical calculation process of uniformity is as follows:

[0008] In an N-dimensional space, the shape of the space is arbitrary, and the size of the space is V, in which M points are distributed, and the uniformity of the distribution of these points in the space needs to be calculated:

[0009] S1, calculate the space size V that each point should occupy in the space if it is uniformly distributed p :

[0010] V p = V / M

[0011] S2. Construct a space with the same shape and size V, centered on each point. p The subspace of the created subspace is determined, and its relationship with the boundary of the larger space is also judged. Only the portion of the created subspace that is located within the larger space is retained as the subspace V of that point. p _ idea :

[0012] V p_idea =V p ∩V

[0013] S3. Summing the subspaces of the M points yields the ideal space V of these points in that space. idea :

[0014]

[0015] S4, for every two points in the subspace V p_idea_i and V p_idea_j Summing the sizes of the overlapping spaces between them, we get V. overlap :

[0016]

[0017] S5. Obtain the actual space V occupied by the subspace of M points. actually :

[0018] V actually =V idea -V overlap

[0019] S6. Obtain the uniformity U of the distribution of M points in this space:

[0020] U = V actually / V

[0021] The closer this value is to 1, the better the uniformity of the distribution of points in the space. Detailed Implementation

[0022] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0023] Example

[0024] The application provides a method for evaluating the uniformity of position point distribution in space. The method can be applied to the calculation of the uniformity of position point distribution in space of any dimension. In the case of one dimension, the uniformity of point distribution can be directly solved according to a theoretical formula, but for the calculation of the uniformity of point distribution in space of two or more dimensions, an approximate treatment is needed. This is because in the case of two or more dimensions, different space intersections in a unit space can occur, which is a complex and time-consuming process, and in actual application, some approximate treatment is needed to solve the problem. The specific approximate uniformity calculation process is as follows:

[0025] In an N (N>2) dimensional space, the space shape is arbitrary, the space size is V, and M points are distributed in the space. The uniformity of the distribution of the points in the space is calculated:

[0026] S1, the original unit space is divided into K unit spaces (K is defined according to the required accuracy of application, and the greater K is, the closer the approximate uniformity result is to the theoretical uniformity result), and the size V of the current space K is:

[0027] V K = K x V

[0028] S2, the coordinates of each point in the space are scaled

[0029]

[0030] S3, the space size that each point should occupy in the space under the condition of uniform distribution is calculated:

[0031] V p = V K / M

[0032] S4, a subspace with the same shape as the space and the size V p is constructed with the coordinates of each scaled point as the center, and the relationship between the subspace and the boundary of the large space is judged, only the part of the created subspace located in the large space is reserved as the subspace of the point, and all the unit spaces in the large space are marked as 0;

[0033] S5, the unit spaces located in the subspace of the point are marked as 1 by traversing the subspace of each point;

[0034] Wherein, the specific steps for judging whether the unit space is located in the subspace of a point are as follows:

[0035] S501, the Euclidean distance dk of the coordinates of the unit space to the coordinates of the point is calculated:

[0036]

[0037] S502, get the distance d of the point from the boundary of the subspace in the direction of the unit space coordinate;

[0038] S503, when d k ≤d, then determine that the unit space is in the subspace of the point;

[0039] Of course, the above steps are a judgment process that is generally applicable to spaces of various shapes. For more common spaces of specific shapes, such as rectangular spaces in two dimensions and cubic spaces in three dimensions, the relationship between the coordinate difference of the unit space and the length of each dimension of the subspace can be directly compared to directly determine.

[0040] S6, count the number N1 of the unit spaces marked as 1 in V K points, and obtain the approximate uniformity U of the distribution of M points in the space s :

[0041] U s =N1 / V K

[0042] The accuracy of the approximate uniformity depends on K. In actual tests, when V is large, the value of K can be small, and when V is small, the value of K needs to be large to ensure sufficient accuracy.

[0043] Through such an approximation process, the calculation process can be greatly accelerated under the premise of meeting the accuracy of uniformity calculation, which is more conducive to the practical application of the algorithm.

[0044] In order to verify the performance of the evaluation method of the distribution uniformity of the position points in the space proposed by the application, we selected ten pictures in the public data set for testing. On each picture, three different feature point distributions were obtained through different feature point extraction and processing methods, and then the sorting of the uniformity of the three feature point distributions in each picture was determined through artificial labeling.

[0045] The uniformity of the distribution of the points in the space is tested by various methods, including variance-based, entropy-based, grid-based, Ripley's K function, and the method proposed in the present application. The variance-based method uses normalized coordinates to calculate the variance of the x and y coordinates, and the average of the two variances is taken as the uniformity result. The larger the result, the more uniform the point distribution. In the entropy-based method, the space is divided into 16 intervals, and the distribution of points in each interval is calculated to obtain the entropy value as the evaluation result. The larger the result, the more uniform the point distribution. The grid-based method also divides the space into 16 grids, counts the number of points in each grid, and calculates the average distance of the points in each grid. The standard deviation of these distances is taken as the uniformity result. The larger the result, the more uniform the point distribution. In the Ripley's K function method, a fixed distance h of 30 is set, and the number of other points within h distance from each point is calculated to obtain the Ripley's K function value. The closer the result to the set distance h, the more uniform the point distribution. In the method proposed in the present application, an approximate algorithm for two-dimensional space is used, where K is set to 10. The closer the result to 1, the more uniform the point distribution.

[0046] To verify the universality of the above methods, the same parameters as above are used in 10 groups of experiments for methods that require pre-setting of related parameters. In each group of experiments, the uniformity results of the three types of point distribution are calculated using the five methods, and the results are sorted respectively. If the sorting result of the method is consistent with the artificial marking sorting result, it is considered that the method is effective in determining the uniformity of the point distribution in this group of experiments.

[0047] The experimental results are shown in the following table:

[0048] Table 1 Experimental results

[0049]

[0050]

[0051] The evaluation accuracy of the grid-based point distribution uniformity evaluation method and the Ripley's K function method in spatial statistics in 10 groups of tests is 0 / 10, and only in partial local comparison of some groups of tests, the two methods can have a certain effect, which shows that the two methods cannot complete the evaluation of the uniformity of the point distribution in the data set. This is because both methods are directly related to the number of points, and the pre-set parameters must be additionally adjusted according to the characteristics of the data set. In the 10 groups of experiments, the picture sizes are different, and the number of characteristic points in each group of experiments is also different. Therefore, the grid-based point distribution uniformity evaluation method and the Ripley's K function method in spatial statistics are difficult to effectively evaluate the point distribution in such cases.

[0052] The evaluation accuracy of the point distribution uniformity evaluation method based on variance and entropy is 6 / 10, which shows that the two methods have a certain effect on the evaluation of the uniformity of the point distribution, and the application range is wider than that of the previous two methods. However, when some special distributions occur, such as block aggregation, the uniformity result calculated by the method based on variance may be greater than that calculated in the uniform distribution.

[0053] The evaluation accuracy of the point distribution uniformity evaluation method proposed in the application is 10 / 10, which fully shows that the method proposed in the application can better reflect the judgment of people on the uniformity of the point distribution in space and is more consistent with the actual situation. At the same time, it also shows that the method proposed in the application can evaluate the uniformity of the point distribution in space under various complex conditions, and is not affected by the difference in the number of points. The uniformity of the point distribution of different numbers of points can also be compared.

[0054] The method proposed in the application has higher precision and wider applicability compared with other existing methods for evaluating the uniformity of the point distribution, can more accurately evaluate the uniformity of the point distribution in space, and does not need to define parameters in advance. At the same time, it is suitable for judging the uniformity of the point distribution in any dimensional space. Therefore, the method proposed in the application can be more widely applied in the fields of image processing, geographic information analysis and the like.

Claims

1. A method for evaluating the uniformity of the distribution of position points in a space, for evaluating the uniformity of the distribution of feature points in an image, the theoretical algorithmic process of the method being as follows: In an N-dimensional space, the shape of the space being arbitrary, the size of the space being V, M points are distributed in the space, and the uniformity of the distribution of the points in the space is to be calculated: S1, calculate the space size V each point in the space should occupy if it is uniformly distributed p : V p = V / M S2, build a sub-space with the space shape as the center of each point, and the size of the sub-space is V p , and determine the relationship between the sub-space and the boundary of the large space, and only keep the part of the created sub-space located in the large space as the sub-space V p_idea of the point V p_idea =V p ∩V S3, summing the subspaces of the M points to obtain the ideal space V of these points in this space idea : S4, summing the size of the overlap space between the subspace V p_idea_i and V p_idea_j for each pair of points. overlap : S5, obtaining the actual space V occupied by the subspace of M points actually : V actually =V idea -V overlap S6, obtaining the uniformity U of the distribution of the M points in the space: U = V actually / V The closer the value is to 1, the better the uniformity of the distribution of the position points in the space.

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