A reference map preparation method for image matching including angular distance information

Abstract

The application provides a reference map preparation method containing angle distance information for image matching. The method can improve the range defect of the traditional perspective gnomonic projection algorithm which cannot project the global discrete points on a sphere at equal angle distance, project the global discrete points on a sphere to obtain a reference map for image matching, and extract angle distance features for subsequent image matching from the reference map. The application firstly defines the angle distance information of the discrete points on a sphere, introduces the concept of angle distance scaling on the basis of the perspective gnomonic projection algorithm, scales the angle distance between the plane projection points at a fixed ratio, derives the calculation formula of the improved perspective gnomonic projection algorithm combined with angle distance scaling, and prepares the reference map with high-precision angle distance information. The angle distance information in the reference map is extracted by the cosine law of a spherical triangle and used as feature information for subsequent image matching.

Description

Technical Field

[0001] This invention relates to the field of reference map preparation, and in particular to a method for preparing a reference map containing angular distance information for image matching. Background Technology

[0002] With the development of technology, image matching, as a key component of computer vision, is playing an increasingly important role in the field of navigation. Projecting the actual 3D scene onto a 2D planar reference image for feature recognition is a crucial step in image matching, making the preparation of the reference image particularly important. To improve matching accuracy, a high-precision reference image is needed. Image matching technology compares the feature quantities between image feature points, with angular distance being widely used as a feature quantity in areas such as ground scene matching and star navigation. Therefore, finding a method capable of high-precision 2D representation of global 3D angular distance information is crucial. The key to this method lies in performing planar high-precision representation of the 3D angular distance information of globally discrete points on a sphere to improve the accuracy of the reference image. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention aims to solve the technical problem of providing a reference map preparation method for image matching that includes angular distance information. This method combines an improved perspective sphere center azimuth projection algorithm with angular distance scaling to obtain a high-precision image matching reference map, from which angular distance information can be extracted for image matching. By introducing a scale scaling factor based on the perspective sphere center azimuth projection algorithm, the angular distance between planar projection points is scaled at a fixed ratio. The scaling variation of the angular distance between planar projection points is compensated by redefining the two-dimensional angular distance calculation method, achieving a high-precision planar representation of the angular distance information of globally discrete points on the sphere. The angular distance difference between the angular distance information extracted from the reference map obtained in this application and the actual angular distance meets the high-precision requirement of 1 arcsecond and can achieve global correspondence.

[0004] The technical solution adopted by the present invention to solve the aforementioned technical problem is as follows:

[0005] A method for preparing a reference map containing angular distance information for image matching, characterized in that the method includes the following steps:

[0006] Establish a one-to-one mapping relationship between the three-dimensional information of any discrete point on the sphere and the three-dimensional coordinates defined by latitude and longitude, and define the angle between the center of the sphere and the line connecting two discrete points on the sphere as the three-dimensional angular distance d3 between the discrete points on the sphere.

[0007] In the calculation formula of the perspective sphere center orientation projection, a scale scaling factor k is introduced to scale the angular distance of the projected plane, establish a one-to-one correspondence between the entire sphere and the plane, and meet the requirement that all discrete points of the sphere can be projected onto the plane with high precision, so as to obtain the horizontal and vertical coordinates of the corresponding projection points, and thus obtain the reference map after the global discrete points of the sphere are projected.

[0008] After obtaining the x and y coordinates of the corresponding projection points, define a and b as two projection points on the plane, with their corresponding discrete points on the sphere being A and B, respectively. Let O be the origin of the plane, then the projection point of the origin onto the sphere is O', and P be the center of the sphere. AO’ It is the three-dimensional angular distance between discrete points A and O' on the sphere, denoted by ∠APO'; d BO’ Let ∠BPO' be the three-dimensional angular distance between discrete point B on the sphere and the spherical projection point O' of the origin of the plane; pa–pb is ∠AO'B, where pa is the spherical angle formed by discrete point A on the sphere, the spherical projection point O' of the origin of the plane, and the north pole Z, and pb is the spherical angle formed by discrete point B on the sphere, the spherical projection point O' of the origin of the plane, and the north pole Z. These spherical angles are obtained from the planar coordinates of the corresponding projection points. Then, the two-dimensional angular distance d2 between the discrete points on the sphere corresponding to two projection points a and b is calculated according to the following formula:

[0009] cos(d2)=cos(d AO' )*cos(d BO' )+sin(d AO' )*sin(d BO' )*cos(pa-pb);

[0010] The two-dimensional angular distance between any two projected points on the spherical discrete points in the reference map obtained by projection is calculated according to the above formula, and a reference map containing the two-dimensional angular distance is obtained for subsequent image matching.

[0011] The process of establishing a one-to-one mapping relationship between the three-dimensional information of any discrete point on the sphere and the three-dimensional coordinates defined by latitude and longitude is as follows: Using the center of the sphere as the origin of the three-dimensional spatial coordinate system, and the line connecting the origin with the intersection of the equator and the prime meridian (i.e., 0 longitude and 0 latitude) as the positive direction of the x-axis, a rectangular spatial coordinate system is established. Then, the latitude and longitude coordinates of the discrete point on the three-dimensional sphere... The transformation relationship between Cartesian coordinates (x, y, z) and spatial coordinates is as follows:

[0012]

[0013] Where r is the radius of the three-dimensional sphere;

[0014] The North and South Poles are uniformly represented by (0,-90) and (0,90), and 180° longitude is used instead of -180° longitude. The latitude and longitude are normalized, and a one-to-one mapping relationship is established between the three-dimensional information of any discrete point on the sphere and the three-dimensional coordinates defined by latitude and longitude.

[0015] The scaling factor k is greater than 2.

[0016] The preparation method is used in image matching for purposes such as ground scene matching and star navigation.

[0017] A camera is used to acquire a 3D image of the object, which is then used to establish spherical coordinates, determine the North Pole Z, obtain all discrete points on the sphere, and then perform planar projection.

[0018] The present invention also protects a computer-readable medium storing a computer program that causes a computer to perform processing, wherein the computer program, when run on a computer, executes the above-described method for preparing a reference map containing angular distance information for image matching.

[0019] An electronic device includes a data acquisition module, a data storage module, a display unit, and a processing unit. The processing unit executes the above-described method for preparing a reference image containing angular distance information for image matching. The acquisition module is used to acquire three-dimensional image data of an object; the data storage module is used to store relevant data; and the display unit is used to display the image matching process and related parameters.

[0020] Compared with the prior art, the beneficial effects of the present invention are:

[0021] (1) The method of this invention combines a scaling factor to project high-precision angular distance information, which improves upon the shortcomings of the original perspective sphere center orientation projection, which can only project local discrete points on the sphere. It can perform two-dimensional planar representation of global discrete points on the sphere while maintaining the angular distance information. The method for representing the angular distance information of global discrete points on the three-dimensional sphere and the two-dimensional planar points after projection is determined, ensuring the accuracy of the angular distance information before and after projection.

[0022] (2) The two-dimensional angular distance proposed in this invention can extract high-precision angular distance information of corresponding discrete points on the sphere from the planar projection points of the reference image, and extract the angular distance information contained in the reference image as the feature quantity for subsequent image matching.

[0023] (3) The method of this invention can meet the accuracy requirement of less than 1 arcsecond error between discrete points before and after projection, and can also meet the range requirement for projecting global discrete points on a sphere. It can be applied to image matching fields such as map projection, ground scene, and star navigation. In practical applications, this invention can project as much three-dimensional information as possible, make full use of three-dimensional scene information, realize the planar high-precision representation of the three-dimensional angular distance information of global discrete points on a sphere, and obtain a reference map with high-precision angular distance information, which is of great significance in image matching. Attached Figure Description

[0024] Figure 1 This is a schematic flowchart of the method for preparing a reference map containing angular distance information for image matching according to the present invention;

[0025] Figure 2 This is a schematic diagram illustrating the principle of perspective sphere center orientation projection in this invention;

[0026] Figure 3 This is a schematic diagram for calculating the perspective sphere center orientation projection and the two-dimensional angular distance between discrete points on the sphere in this invention;

[0027] Figure 4 This serves as the reference image for the high-precision planar representation of the three-dimensional angular distance information of global spherical discrete points obtained in this invention.

[0028] Figure 5 This is a mean-variance plot of the difference between the three-dimensional angular distances of discrete points on the sphere and the two-dimensional angular distances extracted from the reference map in this invention.

[0029] In the picture:

[0030] O - Origin of the plane, O' - Corresponding point of the origin of the plane on the sphere (view axis), A, B - Discrete points on the sphere, a - Projection of discrete point A on the plane, Z - North pole of the sphere, O'X - Projection of the positive horizontal axis on the plane onto the sphere, P - Center of the sphere Detailed Implementation

[0031] The technical solution of the present invention will be clearly and completely described and explained below with reference to examples and accompanying drawings, but this is not intended to limit the scope of protection of this application.

[0032] A method for preparing a reference map containing angular distance information for image matching, the steps of which are as follows: Figure 1 As shown: A camera is used to acquire a 3D image of the object, which is then used to establish spherical coordinates, determine the North Pole Z, obtain all discrete points on the sphere, and perform planar projection.

[0033] The first step is to define the three-dimensional information of discrete points on the sphere and quantify the projection accuracy.

[0034] The three-dimensional coordinates of discrete points on a sphere are defined using longitude and latitude in a geographic coordinate system. A rectangular coordinate system is established with the center of the sphere as the origin of the three-dimensional spatial coordinate system, and the line connecting the origin to the equator and the prime meridian (i.e., 0 longitude and 0 latitude) as the positive x-axis. The longitude and latitude coordinates of discrete points on the three-dimensional sphere can then be derived. The transformation relationship between Cartesian coordinates (x, y, z) and spatial coordinates is as follows:

[0035]

[0036] Where r is the radius of the three-dimensional sphere.

[0037] Next, the representation of latitude and longitude is standardized, uniformly using (0,-90) and (0,90) to represent the North and South Poles, and uniformly using 180° longitude instead of -180° longitude. This establishes a one-to-one mapping relationship between the three-dimensional information of any discrete point on the sphere and the three-dimensional coordinates defined by latitude and longitude. Furthermore, two-dimensional rectangular coordinates (x, y) are used to define the coordinates of the projected points on the projected plane.

[0038] Angular distance is introduced to quantify the relative positional relationship between discrete points on a sphere. Angular distance is the angle between a vector formed by a third point outside the two points and the two lines connecting the third point to the two points. Based on this concept, the angle between the lines connecting the center of the sphere to the two discrete points on the sphere is defined as the three-dimensional angular distance d3 between the discrete points. After projection onto a plane, the planar angular distance Δ2 is defined as the angle between the vector formed by the lines connecting the center of the unit sphere and the projection points of these two points onto the plane. The angular distance information extracted from the projected reference map, i.e., the two-dimensional angular distance d2 between the discrete points on the sphere corresponding to the planar projection points, is calculated using a formula based on the planar angular distance Δ2.

[0039] The accuracy of the planar representation of angular distance information is defined as the difference between the three-dimensional angular distance d3 and the two-dimensional angular distance d2, called the angular distance difference, denoted by the letter δ, and calculated using the following formula:

[0040] δ=d3-d2

[0041] In this invention, the angular distance information extracted from discrete points on the sphere and planar projection points in the reference map is represented using the aforementioned angular distance information definitions (three-dimensional angular distance d3 and two-dimensional angular distance d2) and projection accuracy quantization methods. The angular distance difference quantization method is used to quantify the representation accuracy of the angular distance information of discrete points on the sphere.

[0042] Step 2: Obtain the reference map after projecting the global discrete points of the sphere.

[0043] Perspective center-of-sphere projection is a perspective projection of a viewpoint at the center of a sphere, as illustrated in the diagram. Figure 2As shown. A scale factor k is introduced during the calculation process to establish a one-to-one correspondence between the entire sphere and the plane, ensuring that all discrete points on the sphere can be projected onto the plane with high precision, thus obtaining a reference map for image matching. The projection center of the sphere is defined as the sphere's center P, and the direction from the projection center to O' is called the viewing axis. The projection plane can intersect, be tangent to, or be separate from the sphere.

[0044] Reference diagram for the calculation formula of perspective projection of the sphere's center of gravity. Figure 3 The projection formula is as follows:

[0045]

[0046]

[0047] Where, λ i , These are the longitude and latitude of a discrete point A on the sphere, λ0, d3 is the longitude and latitude of the spherical projection point O' of the plane origin, i.e., the longitude and latitude of the viewing axis; d3 is the three-dimensional angular distance between A and O', and pa is the spherical angle AO'Z. d3 and pa are calculated from the longitude and latitude of the viewing axis and the discrete point A on the sphere, yielding the x and y coordinates of the corresponding projection point. The drawback of this method is that the three-dimensional angular distance between discrete points on the sphere is equal to the planar angular distance between the projection points on the plane. The selectable range of the spherical angular distance exceeds the representation range of the planar angular distance, causing this method to only project local discrete points on the sphere. To solve this problem, we introduce the concept of angular distance scaling, scaling the projected planar angular distance so that the improved projection method can overcome the limitation of the original perspective spherical center azimuth projection on the spherical projection range. Dividing the three-dimensional angular distance d3 by the scaling factor k (k can be arbitrarily chosen, but k needs to be greater than 2 to project all discrete points on the sphere onto the plane at once) yields the x and y coordinates of the corresponding projection point, obtaining a two-dimensional planar reference map. The projection point obtained by the improved perspective spherical center azimuth projection combined with angular distance scaling is then represented as:

[0048]

[0049] Where d is the projection distance from the projection center to the projection plane, which can be any distance. The value of d only affects the values ​​of x and y, and does not affect the angular distance between the projection points. This formula can project discrete points of the sphere onto a two-dimensional plane at equal angular intervals, with any direction as the viewing axis.

[0050] Step 3: Extract the angular distance information from the reference map.

[0051] The formula for calculating the two-dimensional angular distance is derived using the cosine theorem of spherical triangles. Angular distance information of corresponding discrete points on the sphere is extracted from the projected reference image. The difference in angular distance before and after projection is then calculated, quantifying the representation accuracy of the angular distance information before and after projection, ensuring that the method of this invention can achieve the required accuracy. The two-dimensional angular distance extracted from the reference image is used as a feature quantity for subsequent image matching.

[0052] The reference map needs to extract feature information for image matching, specifically angular distance information. In the reference map obtained by the improved perspective sphere center azimuth projection algorithm, the two-dimensional angular distance d2 of the spherical discrete points corresponding to the planar projection points needs to be calculated based on the horizontal and vertical coordinates of the planar projection points. In the first case, when one of the two projection points is the origin of the plane, the two-dimensional angular distance of the corresponding spherical discrete points is equal to the planar angular distance Δ2 between the projection points multiplied by the scaling factor k, d2 = kΔ2. In the second case, when the planar projection points are any two points on the plane, the above method is no longer applicable. This is because the projection method only performs radial scaling of the angular distance, without horizontal scaling. This means that when there is a horizontal difference between the two points, it is not possible to simply multiply the planar angular distance between the two points on the plane by the scaling factor k. Therefore, it is proposed to use the cosine theorem of spherical triangles to calculate the two-dimensional angular distance of the spherical discrete points.

[0053] Suppose that the two projection points on the plane are a and b, and their corresponding discrete points on the sphere are A and B, respectively. The origin of the plane is O, and the spherical projection point of the origin is O'. Points A, B, and O' on the sphere form a spherical triangle. Let the center of the sphere be P. From the projection plane, the angular distance Δ between points a and O can be obtained. aO And the angular distance Δ between points b and O bO Multiplying both by the scaling factor k yields the three-dimensional angular distance d between discrete points A and O' on the sphere. AO’ And the three-dimensional angular distance d between points B and O' on the sphere. BO’ That is, ∠APO' and ∠BPO'. According to Δ... aO Δ bO Given the planar coordinates of projection points a and b, the azimuth angles pa and pb can be calculated in reverse. Here, pa is the spherical angle formed by the discrete point A, the spherical projection point O' of the plane origin, and the North Pole Z, i.e., pa = ∠AO'Z. Similarly, the spherical angle pb = ∠BO'Z, thus ∠AO'B = pa - pb (when A and B are on the same side of O', pa and pb have the same sign; when they are on opposite sides of O', pa and pb have opposite signs). Given ∠APO', ∠BPO', and ∠AO'B, the two-dimensional angular distance between discrete points A and B can be obtained using the cosine theorem of spherical triangles. For a reference map obtained from the improved perspective spherical center azimuth projection, the formula for calculating the two-dimensional angular distance d2 between any two planar projection points corresponding to discrete points on the spherical surface is as follows:

[0054] cos(d2)=cos(d AO' )*cos(d BO' )+sin(d AO' )*sin(d BO' )*cos(pa-pb)

[0055] Where, d AO’ It is ∠APO', d BO’ It is ∠BPO', and pa–pb is ∠AO'B. This formula also holds true in the first case.

[0056] In this way, the present invention can extract the two-dimensional angular distance information between discrete spherical points corresponding to any two planar projection points in the projected reference image, and use it as a feature information for subsequent image matching.

[0057] By randomly generating 1000 discrete points on the entire sphere and combining them with an improved perspective sphere-center azimuth projection using angular distance scaling, we obtain... Figure 4 The image shown is a high-precision planar representation of the three-dimensional angular distance information of discrete points on a sphere. The latitude and longitude of 1000 discrete points on the sphere, along with the coordinates of their planar projection points, are recorded. Then, two discrete points are randomly selected each time, and their three-dimensional angular distance d3, two-dimensional angular distance d2, and angular distance difference δ are calculated. This operation is repeated 100 times for each group. Finally, the mean and standard deviation of the 100 angular distance differences are calculated. This operation is repeated 10 times to obtain a mean-variance plot of the 10 angular distance differences, as shown below. Figure 5 As shown. From Figure 5 The data shows that by randomly selecting two discrete points each time and calculating the angular distance difference, the average angular distance difference obtained after repeating this process 100 times is 10. -12 The accuracy is on the order of degrees, and the average angular distance difference obtained from 10 repeated experiments all meet the high precision requirement of 1 arcsecond.

[0058] This method demonstrates that it can accurately project globally discrete points on a three-dimensional sphere onto a two-dimensional plane to create a reference map for image matching. Furthermore, it can extract the angular distance information between the corresponding discrete points on the sphere from the reference map as feature values ​​for subsequent image matching. The error between the angular distance information extracted from the reference map (two-dimensional angular distance) and the actual angular distance between the discrete points on the sphere (three-dimensional angular distance) is less than 1 arcsecond, meeting the high-precision requirement for angular distance in the reference map.

[0059] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for preparing a reference map containing angular distance information for image matching, characterized in that, The method includes the following steps: A camera is used to acquire a 3D image of the object, which is then used to establish spherical coordinates, determine the North Pole Z, obtain all discrete points on the sphere, and then perform planar projection. Establish a one-to-one mapping relationship between the three-dimensional information of any discrete point on the sphere and the three-dimensional coordinates defined by latitude and longitude, and define the angle between the lines connecting the center of the sphere to the two discrete points on the sphere as the three-dimensional angular distance between the discrete points on the sphere. d 3 ; A scale factor is introduced into the calculation formula for perspective sphere center azimuth projection. k The angular distance of the projected plane is scaled to establish a one-to-one correspondence between the entire sphere and the plane, and to meet the requirement that all discrete points of the sphere can be projected onto the plane with high precision. The horizontal and vertical coordinates of the corresponding projection points are obtained, and then the reference map after the global discrete points of the sphere are projected is obtained. After obtaining the x and y coordinates of the corresponding projection points, define a and b as two projection points on the plane, and their corresponding discrete points on the sphere as A and B, respectively. O is the origin of the plane, then the projection point of the origin on the sphere is O', and P is the center of the sphere. d AO’ It is the three-dimensional angular distance between discrete points A and O' on the sphere, expressed as... express; d BO’ It is the spherical projection point of the discrete point B on the sphere and the origin of the plane. The three-dimensional angular distance between them is used express; pa – pb yes , pa Discrete points on a sphere A spherical projection point of the origin of the plane and the North Pole Z The spherical angle formed by them pb The spherical projection point of discrete point B on the sphere and the origin of the plane. and the North Pole Z The spherical angle formed by the two projection points a and b is obtained from the planar coordinates of the corresponding projection points; then the two-dimensional angular distance between the discrete spherical points corresponding to the two planar projection points a and b is... d 2 Calculated using the following formula: ； The two-dimensional angular distance between discrete spherical points corresponding to any two plane projection points in the reference map obtained by projection is calculated according to the above formula. A reference map containing the two-dimensional angular distance is obtained, and the two-dimensional angular distance extracted from the reference map is used as a feature quantity for subsequent image matching.

2. The method for preparing a reference map containing angular distance information for image matching according to claim 1, characterized in that, The process of establishing a one-to-one mapping relationship between the three-dimensional information of any discrete point on the sphere and the three-dimensional coordinates defined by latitude and longitude is as follows: taking the center of the sphere as the origin of the three-dimensional spatial coordinate system, and taking the line connecting the origin with the intersection of the equator and the prime meridian (i.e., 0 longitude and 0 latitude) as... x Establish a spatial rectangular coordinate system along the positive axis, then the latitude and longitude coordinates of discrete points on the three-dimensional sphere are... Rectangular coordinates The conversion relationship between them is ， in, r Let be the radius of the three-dimensional sphere; The North and South Poles are uniformly represented by (0, -90) and (0, 90), and 180° longitude is used instead of -180° longitude. The latitude and longitude are standardized, and a one-to-one mapping relationship is established between the three-dimensional information of any discrete point on the sphere and the three-dimensional coordinates defined by latitude and longitude.

3. The method for preparing a reference map containing angular distance information for image matching according to claim 1, characterized in that, The k is greater than 2.

4. The method for preparing a reference map containing angular distance information for image matching according to claim 1, characterized in that, The preparation method is used in image matching for ground scene matching and star navigation.

5. A computer-readable medium storing a computer program that causes a computer to perform processing, characterized in that, The computer program executes the reference map preparation method containing angular distance information for image matching as described in claim 1 when running on a computer.

6. An apparatus comprising a data acquisition module, a data storage module, a display unit, and a processing unit, wherein the processing unit performs the reference map preparation method including angular distance information for image matching as described in claim 1, wherein the acquisition module is used to acquire three-dimensional image data of an object; the data storage module is used to store relevant data; and the display unit is used to display the image matching process and related parameters.

Images