A Healpix-based method for homogenizing and evaluating star catalogs.

Abstract

This invention belongs to the field of industrial automation technology, and particularly relates to a method for uniform segmentation and evaluation of star catalogs based on Healpix. The method includes: S1: acquiring original star catalog data and determining the Healpix grid level parameters based on the user's desired subdivision level; S2: calculating the Healpix pixel index number of each celestial body in the original star catalog data using the Healpix algorithm, based on the celestial coordinates of each celestial body in the celestial equatorial coordinate system; S3: constructing a blank star catalog and building a uniform star catalog based on the set of celestial bodies extracted by a sampling strategy and the corresponding Healpix pixel index numbers of each celestial body contained in the set; S4: constructing a U_score evaluation model and using the U_score evaluation model to score the uniform star catalog, and evaluating the uniformity of each celestial body in the uniform star catalog based on the U_score score. This invention provides an objective and quantifiable benchmark for comparing the effects of different uniformization methods.

Description

Technical Field

[0001] This invention belongs to the field of industrial automation technology, and in particular relates to a method for uniform segmentation and evaluation of star tables based on Healpix. Background Technology

[0002] With the advancement of large-scale sky surveys (such as SDSS, Gaia, LAMOST, and CSST), the size of astronomical catalogs is growing exponentially. The distribution of these catalog data across the celestial sphere is typically extremely uneven, influenced by various factors such as observational conditions, celestial object distribution, and dust obstruction, resulting in numerous voids and dense regions. This unevenness presents significant challenges to many astronomical research methods, including large-sample statistical analysis, cosmological probes (such as gravitational lensing and BAO), and machine learning sample construction.

[0003] Traditional star catalog homogenization methods primarily rely on regular grid division on a celestial coordinate system (such as right ascension and declination) or resampling techniques based on local sky density. Common methods include:

[0004] 1) Simple grid method: The celestial sphere is divided into equally spaced rectangular grids according to right ascension (RA) and declination (Dec). This method produces an approximately square shape near the equator, but in high-latitude regions, the area of ​​the grid cells shrinks drastically, leading to huge differences in the number of samples and introducing latitude effect bias.

[0005] 2) Random sampling method: Random sampling is performed throughout the star catalog. Although this method is simple, it completely ignores the spatial structure information of the sky, which will destroy the spatial correlation between celestial bodies and cannot guarantee the spatial uniformity of the sample after sampling.

[0006] 3) Density resampling method: First, calculate the local density at the location of each celestial body, and then perform probability sampling based on the density (e.g., sampling probability is low for areas with high density). This method improves uniformity to some extent, but its results heavily depend on the selection and parameter adjustment of the density estimation algorithm (e.g., k-nearest neighbor-based or kernel density estimation), resulting in high computational complexity and making it difficult to objectively and globally quantify the uniformity of the final results.

[0007] Traditional methods suffer from problems such as unequal grid cell areas, difficulty in preserving spatial structure, low computational efficiency, and lack of unified quantitative evaluation standards. Therefore, there is an urgent need for a new method for star catalog homogenization that can ensure uniform celestial coverage, high computational efficiency, and an objective evaluation system. Summary of the Invention

[0008] In view of this, the present invention aims to provide a star catalog homogenization segmentation and evaluation method based on Healpix, in order to solve the problems of unequal grid cell areas, difficulty in maintaining spatial structure, low computational efficiency, and lack of unified quantitative evaluation standards in existing technologies. The present invention provides a star catalog homogenization segmentation and evaluation method based on Healpix, which utilizes the natural equal area characteristics of Healpix celestial sphere pixelation technology to achieve efficient and uniform segmentation of star catalogs, and innovatively proposes a homogenization evaluation index to provide an objective and quantifiable comparison benchmark for the effects of different homogenization methods.

[0009] To achieve the above objectives, the technical solution created by this invention is implemented as follows:

[0010] A method for homogenization and evaluation of star catalogs based on Healpix, specifically including the following steps:

[0011] S1: Obtain the raw star catalog data and determine the Healpix grid level parameters based on the user's desired level of detail;

[0012] S2: Based on the celestial coordinates of each celestial body in the celestial equatorial coordinate system contained in the original star catalog data, the Healpix pixel index number of each celestial body is calculated using the Healpix algorithm;

[0013] S3: Construct a blank star catalog and build a uniform star catalog based on the set of celestial bodies extracted by the sampling strategy and the Healpix pixel index number of each celestial body contained in the set of celestial bodies.

[0014] S4: Construct a U_score evaluation model, use the U_score evaluation model to score the homogenized star catalog, and evaluate the homogenization of each celestial body in the homogenized star catalog based on the U_score score.

[0015] Furthermore, in step S1, the original star catalog data includes at least the right ascension coordinates, declination coordinates, and magnitude of each celestial body.

[0016] Furthermore, in step S1, the relationship between the Healpix grid level parameters and the total number of Healpix pixels divided across the entire celestial sphere is: N_pix = 12 × Nside 2 ;

[0017] Where Nside is the Healpix grid level parameter, and N_pix is ​​the total number of pixels that the entire celestial sphere is divided into.

[0018] Furthermore, step S3 specifically includes:

[0019] S31: Construct a blank star table based on the Healpix grid level parameters determined in step S1;

[0020] S32: Extract celestial bodies to a blank star catalog based on a sampling strategy. Construct a uniform star catalog based on the set of celestial bodies retained in the blank star catalog after sampling and the Healpix pixel index number corresponding to each celestial body contained in the set of celestial bodies.

[0021] Furthermore, in step S32, the sampling strategy includes a uniform partitioning strategy and a density control strategy, wherein:

[0022] The uniform segmentation strategy is as follows: within each Healpix pixel, k celestial bodies are extracted in order of magnitude from low to high, and the extracted celestial bodies are placed into the blank star table according to their corresponding Healpix pixel index numbers. All celestial bodies in Healpix pixels with fewer than k celestial bodies are placed into the blank star table according to their corresponding Healpix pixel index numbers.

[0023] The density control strategy is as follows: Set a target density threshold D_target, calculate the density of celestial bodies contained within each Healpix pixel, and if the density N_i is greater than the product of the target density threshold D_target and the area A_pix of the Healpix pixel, then extract D_target × A_pix celestial bodies in the corresponding Healpix pixel in ascending order of magnitude, and place the extracted celestial bodies into the blank star table according to their corresponding Healpix pixel index numbers; otherwise, place all celestial bodies within the corresponding Healpix pixel into the blank star table according to their corresponding Healpix pixel index numbers.

[0024] Furthermore, step S4 specifically includes:

[0025] S41: Based on the Healpix algorithm, the uniform star catalog is mapped onto the Healpix grid with selected Healpix grid level parameters, and the number of celestial objects contained in each Healpix pixel is counted to obtain a one-dimensional distribution array N;

[0026] S42: Calculate the total number of celestial bodies N_total and the total number of Healpix pixels N_pix corresponding to the Healpix grid, and obtain the expected number of celestial bodies μ for each Healpix pixel:

[0027] μ = N_total / N_pix;

[0028] S43: Based on the calculation results of step S42, construct the U_score evaluation model:

[0029] U_score = 1 - (CV) = 1 - (σ / μ);

[0030] Where U_score is the U_score score, CV is the coefficient of variation, σ is the standard deviation of the one-dimensional distribution array N, and μ is the expected number of celestial bodies;

[0031] S44: If U_score∈(0.9,1], then the celestial body distribution uniformity is highly uniform;

[0032] If U_score∈(0.7, 0.9], then the uniformity of celestial body distribution is moderately uniform.

[0033] If U_score∈(0.5, 0.7], then the uniformity of celestial body distribution is relatively non-uniform;

[0034] If U_score∈(-∞, 0.5], then the uniformity of celestial body distribution is highly non-uniform.

[0035] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0036] (1) The Healpix-based star table uniformity segmentation and evaluation method described in this invention achieves true equal area segmentation: the Healpix grid ensures that the area of ​​each pixel is strictly equal, fundamentally eliminating the area distortion problem of the traditional RA / Dec grid at high latitudes, and providing a fair benchmark for uniformity.

[0037] (2) The Healpix-based star catalog uniform segmentation and evaluation method described in this invention has high computational performance: the conversion algorithm between Healpix pixel coordinates and indices is very efficient, with a time complexity of O(1) or O(logNside), which makes it extremely fast when processing massive star catalog data.

[0038] (3) The Healpix-based star catalog homogenization segmentation and evaluation method described in this invention can maintain the spatial structure: the sampling process is carried out independently within each pixel, which preserves the spatial distribution characteristics and correlation of celestial bodies at a small scale to the greatest extent.

[0039] (4) The Healpix-based star catalog homogenization segmentation and evaluation method described in this invention provides an objective and quantitative evaluation system: the U_score evaluation index provides a standardized and repeatable measurement tool that can scientifically and objectively compare the advantages and disadvantages of different homogenization algorithms and different parameters, ending the previous situation where one could only rely on visual inspection of the sky map or subjective judgment.

[0040] (5) The Healpix-based star catalog homogenization segmentation and evaluation method described in this invention is highly flexible: by adjusting the Healpix level Nside and the sampling strategy (fixed number or density threshold), the degree of homogenization and the density of the output star catalog can be flexibly controlled to meet the needs of different scientific objectives. Attached Figure Description

[0041] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0042] Figure 1 This is a schematic flowchart of the Healpix-based star catalog homogenization segmentation and evaluation method described in an embodiment of the present invention. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0044] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0045] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0046] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0047] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0048] like Figure 1 As shown, a method for uniform segmentation and evaluation of star catalogs based on Healpix includes the following steps: S1: Obtain the original star catalog data and determine the Healpix grid level parameters based on the user's desired subdivision level; S2: Calculate the Healpix pixel index number of each celestial body in the original star catalog data using the Healpix algorithm, based on the celestial coordinates of each celestial body in the celestial equatorial coordinate system; S3: Construct a blank star catalog and construct a uniform star catalog based on the set of celestial bodies extracted by the sampling strategy and the corresponding Healpix pixel index numbers of each celestial body contained in the set; S4: Construct a U_score evaluation model and use the U_score evaluation model to score the uniform star catalog using U_score, and evaluate the uniformity of each celestial body in the uniform star catalog based on the U_score score.

[0049] Furthermore, in step S1, the original star catalog data includes at least the right ascension coordinates (RA), declination coordinates (Dec), and magnitude of each celestial body.

[0050] It should be noted that the smaller the magnitude value, the brighter the star; the larger the magnitude value, the dimmer the star.

[0051] Furthermore, in step S1, the relationship between the Healpix grid level parameters and the total number of Healpix pixels divided across the entire celestial sphere is: N_pix = 12 × Nside 2 ;

[0052] Where Nside is the Healpix grid level parameter, and N_pix is ​​the total number of pixels that the entire celestial sphere is divided into.

[0053] It should be noted that the average number of celestial objects within each Healpix pixel is determined based on the user's desired level of detail, and an appropriate Healpix grid level parameter Nside is selected. Nside determines the total number of pixels into which the entire celestial sphere is divided: N_pix = 12 × Nside 2The higher the level, the more pixels there are, and the smaller the area of ​​each pixel.

[0054] Furthermore, in step S2, for each celestial body in the original star catalog data, the right ascension coordinates (RA) and declination coordinates (Dec) of each celestial body are input into the Healpix algorithm to obtain the unique index number (ipix) of the Healpix pixel to which each celestial body belongs. The Healpix algorithm is a spherical layered equal-area and equal-latitude pixelation algorithm. Its core is to uniformly divide the sphere into multiple pixels while taking into account both equal area and layered structure. The Healpix algorithm is described in the paper "HEALPix: A FRAMEWORK FOR HIGH-RESOLUTION DISCRETIZATION AND FASTANALYSIS OF DATA DISTRIBUTED ON THE SPHERE" published by KM Go'rski et al. in 2005.

[0055] In some embodiments, step S3 specifically includes:

[0056] S31: Construct a blank star table based on the Healpix grid level parameters determined in step S1;

[0057] S32: Extract celestial bodies to a blank star catalog based on a sampling strategy. Construct a uniform star catalog based on the set of celestial bodies retained in the blank star catalog after sampling and the Healpix pixel index number corresponding to each celestial body contained in the set of celestial bodies.

[0058] In some embodiments, in step S32, the sampling strategy includes a uniform partitioning strategy and a density control strategy, wherein:

[0059] The uniform segmentation strategy is as follows: within each Healpix pixel, k celestial bodies are extracted in order of magnitude from low to high, and the extracted celestial bodies are placed into the blank star table according to their corresponding Healpix pixel index numbers. All celestial bodies in Healpix pixels with fewer than k celestial bodies are placed into the blank star table according to their corresponding Healpix pixel index numbers.

[0060] The density control strategy is as follows: Set a target density threshold D_target, calculate the density of celestial bodies contained within each Healpix pixel, and if the density N_i is greater than the product of the target density threshold D_target and the area A_pix of the Healpix pixel, then extract D_target × A_pix celestial bodies in the corresponding Healpix pixel in ascending order of magnitude, and place the extracted celestial bodies into the blank star table according to their corresponding Healpix pixel index numbers; otherwise, place all celestial bodies within the corresponding Healpix pixel into the blank star table according to their corresponding Healpix pixel index numbers.

[0061] It should be noted that intra-pixel sampling and segmentation:

[0062] Strategy A (Uniform Segmentation Strategy): Within each Healpix pixel, a fixed number of k celestial bodies are randomly selected (k>=1). If the number of celestial bodies in a Healpix pixel is less than k, all celestial bodies in that Healpix pixel are extracted, and the number of missing celestial bodies is marked according to the corresponding Healpix pixel index number.

[0063] Strategy B (Density Control Strategy): A target density threshold D_target is pre-set. For each Healpix pixel, the number of celestial bodies N_i is calculated. Since the area of ​​each Healpix pixel is equal, the density is proportional to N_i. If N_i > D_target × A_pix (where A_pix is ​​the area of ​​a Healpix pixel), then randomly sample from that pixel up to retain D_target × A_pix celestial bodies; otherwise, all celestial bodies are retained.

[0064] The sampled set of celestial bodies is output as a homogenized star catalog.

[0065] The homogenized star catalog adds a new column of data, which records the Healpix (ipix number) of each celestial object, facilitating subsequent spatial querying and analysis.

[0066] In some embodiments, step S4 specifically includes:

[0067] S41: Based on the Healpix algorithm, the uniform star catalog is mapped onto the Healpix grid with selected Healpix grid level parameters, and the number of celestial objects contained in each Healpix pixel is counted to obtain a one-dimensional distribution array N;

[0068] S42: Calculate the total number of celestial bodies N_total and the total number of Healpix pixels N_pix corresponding to the Healpix grid, and obtain the expected number of celestial bodies μ for each Healpix pixel:

[0069] μ = N_total / N_pix;

[0070] S43: Based on the calculation results of step S42, construct the U_score evaluation model:

[0071] U_score = 1 - (CV) = 1 - (σ / μ);

[0072] Where U_score is the U_score score, CV is the coefficient of variation, σ is the standard deviation of the one-dimensional distribution array N, and μ is the expected number of celestial bodies;

[0073] CV values ​​are generally set as follows: 0-0.1 indicates high uniformity, 0.1-0.3 indicates moderate uniformity, 0.3-0.5 indicates relative non-uniformity, and values ​​greater than 0.5 indicate high non-uniformity. The specific values ​​are related to the application context of the star catalog.

[0074] S44: If U_score∈(0.9,1], then the celestial body distribution uniformity is highly uniform;

[0075] If U_score∈(0.7, 0.9], then the uniformity of celestial body distribution is moderately uniform.

[0076] If U_score∈(0.5, 0.7], then the uniformity of celestial body distribution is relatively non-uniform;

[0077] If U_score∈(-∞, 0.5], then the uniformity of celestial body distribution is highly non-uniform.

[0078] The theoretical range of U_score is from negative infinity to +1. The closer it is to 1, the better the uniformity. The specific value is related to the application background of the star catalog.

[0079] It should be noted that, in order to quantitatively evaluate the effect of the homogenization method, the calculation steps of this invention are as follows:

[0080] 1) Calculate the distribution of celestial objects per pixel: Map the homogenized star catalog back onto a Healpix grid of a selected level (which may differ from the level used for segmentation; typically a coarser level is chosen, such as Nside=16 or 32). Count the number of celestial objects contained in each Healpix pixel to obtain a one-dimensional distribution array N.

[0081] 2) Calculate the expected value of the ideal uniform distribution: Calculate the total number of celestial bodies N_total and the total number of pixels N_pix in the entire mapped star catalog, and obtain the expected number of celestial bodies μ=N_total / N_pix for each Healpix pixel under ideal conditions.

[0082] 3) Calculate the uniformity score U_score: U_score = 1 - (CV) = 1 - (σ / μ) where σ is the standard deviation of the one-dimensional distribution array N, μ is the expected number of celestial bodies, CV (Coefficient of Variation) is the coefficient of variation, and the value range of U_score is (-∞, 1).

[0083] The closer U_score is to 1, the smaller the fluctuation in the number of celestial bodies between pixels, indicating excellent uniformity.

[0084] A U_score close to 0 indicates that the uniformity is comparable to a random distribution.

[0085] A negative U_score indicates extremely poor uniformity and a highly concentrated distribution.

[0086] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0087] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A Healpix-based catalog homogenization partitioning and evaluation method, characterized in that: Specifically comprising the following steps: S1: obtaining original star catalog data, determining the Healpix grid level parameter based on the expected subdivision degree of the user; S2: based on the celestial coordinates of each celestial body contained in the original star catalog data in the equatorial coordinate system of the celestial sphere, using the Healpix algorithm to calculate the Healpix pixel index number of each celestial body; S3: constructing a blank star catalog, and constructing a uniformized star catalog based on the celestial body set extracted by the sampling strategy and the Healpix pixel index number corresponding to each celestial body contained in the celestial body set; S4: constructing a U_score evaluation model, and using the U_score evaluation model to score the uniformized star catalog, and evaluating the uniformity of each celestial body in the uniformized star catalog based on the U_score score; Step S4 specifically includes: S41: based on the Healpix algorithm, map the uniformized star catalog to the Healpix grid of the selected Healpix grid level parameter, count the number of celestial bodies contained in each Healpix pixel, and obtain a one-dimensional distribution array N; S42: calculate the total number of celestial bodies N_total corresponding to the Healpix grid and the total number of Healpix pixels N_pix, and obtain the expected number of celestial bodies μ for each Healpix pixel: μ=N_total / N_pix; S43: based on the calculation result of step S42, construct a U_score evaluation model: U_score=1-(CV)=1-(σ / μ); Wherein, U_score is the U_score score, CV is the coefficient of variation, σ is the standard deviation of the one-dimensional distribution array N, and μ is the expected number of celestial bodies; S44: if U_score∈(0.9, 1], the celestial body distribution uniformity is highly uniform; If U_score∈(0.7, 0.9], the celestial body distribution uniformity is medium uniform; If U_score∈(0.5, 0.7], the celestial body distribution uniformity is relatively uneven; If U_score∈(-∞, 0.5], the celestial body distribution uniformity is highly uneven.

2. The Healpix-based catalog uniformization partitioning and evaluation method according to claim 1, characterized in that: In step S1, the original star catalog data at least includes the right ascension coordinate, declination coordinate and star magnitude of each celestial body.

3. The Healpix-based catalog uniformization partitioning and evaluation method of claim 1, wherein: In step S1, the relationship between the Healpix grid level parameter and the total number of Healpix pixels into which the full sky is divided is: N_pix = 12 x Nside 2 ; Wherein, Nside is the Healpix grid level parameter, and N_pix is the total number of pixels divided in the whole celestial sphere.

4. The Healpix-based catalog uniformization partitioning and evaluation method of claim 1, wherein: Step S3 specifically includes: S31: constructing a blank star catalog based on the Healpix grid level parameter determined in step S1; S32: extracting celestial bodies to the blank star catalog based on the sampling strategy, and constructing a uniformized star catalog based on the celestial body set retained by the blank star catalog after sampling and the Healpix pixel index number corresponding to each celestial body contained in the celestial body set.

5. The Healpix-based catalog uniformization partitioning and evaluation method of claim 1, wherein: In step S32, the sampling strategy includes uniform segmentation strategy and density control strategy, wherein: The uniform division strategy is: in each Healpix pixel, k stars are extracted in order of magnitude from low to high, and the extracted stars are placed in the blank star catalog according to the corresponding Healpix pixel index number, and all stars in the Healpix pixel with the number less than k are placed in the blank star catalog according to the corresponding Healpix pixel index number; The density control strategy is: set a target density threshold D_target, calculate the density of the stars contained in each Healpix pixel, if the density N_i is greater than the product of the target density threshold D_target and the Healpix pixel area A_pix, then D_target×A_pix stars in the corresponding Healpix pixel are extracted in order of magnitude from low to high, and the extracted stars are placed in the blank star catalog according to the corresponding Healpix pixel index number; otherwise, all stars in the corresponding Healpix pixel are placed in the blank star catalog according to the corresponding Healpix pixel index number.

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