Modeling method of camera point target smear image center trajectory

Abstract

The application provides a modeling method for a center track of a point target trail image of a camera. The method first integrates three-axis angular velocities of the camera into a total angular velocity vector; constructs a cone with a unit vector of the total angular velocity as a main axis, and a point target incident light ray sweeps around the main axis to form a conical surface; establishes a conic surface equation of the conical surface; establishes an image array plane equation in a same reference coordinate system as that of the angular velocity unit vector; and obtains an intersection line equation of the conic surface and the image array plane, which is a center track of the point target trail image of the point target. According to different distribution conditions of a point target line-of-sight direction and an angular velocity vector direction relative to the camera, possible dynamic trail tracks are listed as four kinds of geometric descriptions, i.e., a circular arc, a trail circular arc, a parabola and a hyperbola. The application correctly reveals a geometric mechanism of the trail track, the model is complete in an analytical form, and theoretically solves an accurate modeling problem of the point target trail image track under a dynamic imaging working condition.

Description

Technical Field

[0001] This invention relates to the field of dynamic imaging technology for optical devices, and more specifically to a method for modeling the center trajectory of a camera point target trailing image. Background Technology

[0002] A star sensor is a high-precision attitude measurement instrument that observes stars in the night sky. It is a type of space camera and is widely used in the field of astronomical navigation. The optimal operating condition for a star sensor is a stable attitude at a low angular rate. When the strapdown carrier is in a high dynamic range, the accuracy of the star sensor's output attitude deteriorates significantly or it fails to output the attitude correctly. The high dynamic range of the strapdown carrier is currently a bottleneck restricting the engineering application of star sensors.

[0003] For a typical camera, if strapdown mounted to a carrier, and the carrier is stationary or moving at a constant speed in a straight line without any attitude maneuvers, no trailing will occur, and the image of a point target will be close to a circle. This speckled image is usually modeled as a two-dimensional Gaussian distribution model in the industry. When the carrier performs attitude maneuvers, the imaging point will move on the sensor target surface for a duration equal to the exposure time, eventually forming a trailing image diffused along the trailing trajectory on the sensor target surface. The longer the light integration time and the greater the angular velocity, the greater the degree of image trailing. The trailing of point target imaging will cause the energy of the image point to diverge, significantly reducing the signal-to-noise ratio. Originally darker image points may be submerged in noise and become undetectable. At the same time, the trailing will elongate the target image. The greater the angular velocity, the greater the elongation. Once it touches the image array boundary, it will cause image information defects and unreliable results in the extraction of the centroid of the trailing image. For star sensors, this will lead to insufficient number of effective star points extracted and failure in matching and attitude determination.

[0004] Existing methods for modeling the center trajectory of dynamic point target trailing images (see comparative document: ZL201310038713.2) are based on the superposition of the trailing linear velocity components generated on the sensor target surface by the transverse axis angular rate and the optical axis angular rate, respectively. Under the condition that the dynamic imaging model is a nonlinear system, this superposition lacks theoretical rationality. This invention proposes a novel method for modeling the center trajectory of camera point target trailing images. This method reveals the geometric mechanism that the trailing trajectory is a conic section, and its analytical function form is complete, which helps to establish more reasonable processing techniques for dynamic trailing images of point targets. Summary of the Invention

[0005] The purpose of this invention is to provide a method for modeling the center trajectory of a camera point target trailing image. This objective is achieved through the following technical solution:

[0006] The formation mechanism of point target image trailing is the camera attitude maneuver during the exposure period. The three-axis angular velocities of the attitude measurement are synthesized into a total angular rate vector in the camera body coordinate system. According to the principle of relative motion, the camera's attitude maneuver relative to a fixed point target can be considered as the point target rotating in the opposite direction around a fixed axis of the total angular rate vector. The incident ray from the point target passing through the optical center performs a conical sweep motion around the angular rate vector, forming a partial conical surface during the exposure period. This forms the center trajectory of the camera point target trailing image on the imaging plane, which is a conic curve, an arc segment formed by the intersection of the conical surface and the imaging plane during the exposure period. The geometric construction of the cone is as follows: the lens optical center is the cone point, the principal axis of the cone is collinear with the total angular rate vector, and the incident ray from the point target passing through the lens optical center is the generatrix of the cone. The acute angle between the principal axis and the incident ray from the point target is defined as the semi-apex angle α of the cone, and the acute angle between the principal axis and the lens optical axis is defined as θ. The type of the center trajectory of the camera point target trailing image is related to α and θ as follows:

[0007] (1) When θ = 0, the total angular velocity vector is collinear with the optical axis, and the center trajectory of the point target trailing image is a circular arc;

[0008] (2) When α + θ < π / 2, the center trajectory of the trailing image of the point target is an elliptical arc;

[0009] (3) When α + θ = π / 2, the image plane is parallel to a generatrix of the cone, and the trajectory of the center of the trailing image of the point target is a parabola;

[0010] (4) When α + θ > π / 2, the center trajectory of the trailing image of the point target is a hyperbola.

[0011] The beneficial effects of this invention are explained as follows:

[0012] This invention establishes an analytical mathematical model of the center trajectory of a camera point target trailing image based on geometric principles. The model is theoretically sound, incorporating complete parameters such as the camera's three-axis angular rate, the incident direction of the point target light rays, the lens optical axis, and the camera's optical integral, strictly conforming to the physical mechanism of dynamic trailing imaging of camera point targets. It abandons numerical integration methods such as Longorkotta based on the trailing plane velocity vector, which helps improve the realism of simulating dynamic trailing imaging of point targets. Attached Figure Description

[0013] Figure 1 This describes the modeling steps for the center trajectory of a camera point target trailing image as described in this invention.

[0014] Figure 2 A physical schematic diagram for imaging a point target trailing image. Detailed Implementation

[0015] To better understand the present invention, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0016] like Figure 2 As shown, a camera body coordinate system OX is established with the camera optical center O as the origin. c Y c Z c Z c The axis is along the optical axis of the camera, X c / Y c The axes are parallel to the row and column directions of the pixel array on the imaging plane. Let the focal length of the lens be f, then the image array plane A lies at z... c = -f on the surface.

[0017] The camera's attitude change during the exposure period can be described by its three-axis angular rate, which is then combined into a total angular rate vector. Its unit direction vector in the camera's body coordinate system is denoted as:

[0018]

[0019] Figure 2 The position of the point target shown is S, and the line of sight is... Direction of total angular velocity The acute angle between them is defined as the semi-apex angle α of the cone. According to the geometric definition of a conic surface, with the optical center O as the apex of the cone... Let α be the direction of the principal axis of the cone and α be the semi-apex angle. When the point target moves at a constant angular velocity... Around the principal axis During rotation, the trajectory of motion in space lies on the rotating conic surface with O as the vertex.

[0020] Let the position vector of an arbitrary point Q on the cone surface in the camera's body coordinate system be:

[0021]

[0022] Then the position vector and the principal axis direction vector Let the included angle be α, then:

[0023]

[0024] Squaring and rearranging both sides, we can obtain the coordinates of the revolved conic surface in the camera's body coordinate system OX. c Y c Z c The general equation below:

[0025]

[0026] At any given moment, the image point of the target on the image array plane A is the intersection of the spatial line OS and the plane Z. c The intersection point of = -f, denoted as P, neglecting the distortion of the imaging system, is the intersection point of the extension of SO and the image array plane A. During the exposure period, OS rotates around the principal axis. As the image rotates, the position P of the imaging point moves along a certain trajectory on the image array plane A, forming the motion trajectory of the center of the trailing image.

[0027] z c = -f Substitution formula This yields the equation of the intersection line between the conic surface and the image array plane A, which is the expression for the trajectory of the center of the point target's trailing image on the imaging plane:

[0028]

[0029] spindle direction relative to the camera's optical axis Z c The acute angle is denoted as θ, which is the angle between the principal axis of the cone and the normal to the image plane. Combining the geometric relationship between the cone and the plane section, we know that the trajectory of point P is a conic section located on the image plane A, and the shape of the curve is related to the relationship between the magnitudes of α and θ.

[0030] The trajectory of point P may fall into the following four categories:

[0031] (1) When θ = 0, the total angular velocity vector is collinear with the optical axis, and the center trajectory of the point target trailing image is a circular arc;

[0032] (2) When α + θ < π / 2, the center trajectory of the trailing image of the point target is an elliptical arc;

[0033] (3) When α + θ = π / 2, the image plane is parallel to a generatrix of the cone, and the center trajectory of the trailing image of the point target is a parabola;

[0034] (4) When α + θ > π / 2, the center trajectory of the trailing image of the point target is a hyperbola.

[0035] In the actual dynamic imaging process of the camera, the trajectory of the center of the trailing image during the light integration time T appears as an arc segment of a conic curve, such as... Figure 2 The red arc in the middle is shown. The angle of this arc is determined by the total angular velocity ω and the light integration time T, and its magnitude is Δφ = ωT.

[0036] As a specific embodiment of the present invention, a method for modeling and simulating the center trajectory of a camera point target trailing image based on the above-mentioned conic section geometric mechanism, the specific programming steps are as follows:

[0037] Step 1: Camera parameter initialization and coordinate system definition

[0038] Set the camera focal length f, principal point coordinates (u0, v0), pixel size, and array size (PixX, PixY). Define the camera light integration time as T. intg The Gaussian radius of the Gaussian diffuse spot distribution is set to σ. The coverage area of ​​the Gaussian diffuse spot can be considered to be 6σ × 6σ.

[0039] Step 2: Angular velocity vector synthesis

[0040] The three-axis angular rate ω output by attitude measurement x , ω y , ω z Combined into a total angular velocity vector = (ω x ,ω y , ω z ) T And calculate the angular velocity modulus ω = | If ω is less than a preset small threshold, the state is determined to be stationary; otherwise, the unit angular velocity vector is calculated. = / ω, this vector is the direction of the principal axis of the cone.

[0041] Step 3: Calculate the global adaptive discretization step size

[0042] To digitally simulate a trailing image, the optical integration time needs to be discretized. The maximum value v of the moving velocity of the image point on the two-dimensional image plane within the field of view needs to be calculated. max If v max If the displacement is small and insufficient to reach the Gaussian radius σ within half an integration time, then the time step h is set to T. intg / 2. In a highly dynamic situation, the time step is calculated based on σ_dynamic: h = σ / v max Then the number of discrete points num during the light integration time can be determined as ceil(T) intg Since the distance between any two adjacent discrete points is no greater than σ, the smoothness of the outline of the superimposed dynamic trailing image can be ensured.

[0043] Step 4: Calculation of image plane trajectory points based on the cone rotation vector

[0044] Based on the conical geometric model proposed in this invention, discrete points on the trailing trajectory are calculated using the Rodriguez rotation formula. Let the initial star vector be S0, and the rotation angle increment be... For a time series i = 1, 2, ..., num, calculate the three-dimensional vector S at each time point on the trajectory. i :

[0045]

[0046] Using the pinhole imaging model, the three-dimensional vector S i = (s xi , s yi , s zi ) T Projecting onto a two-dimensional image plane yields the coordinate sequence of the center of the trailing trajectory (x... i , y i ):

[0047]

[0048] Step 5: Grayscale energy diffusion and trailing star image generation

[0049] Based on the calculated trajectory center point sequence (x) i , y i (i = 1, 2, ..., num), firstly, a two-dimensional Gaussian distribution model is used to generate Gaussian grayscale values ​​centered at each discrete point. The formula for assigning pixel grayscale values ​​within a 3σ neighborhood in all directions is as follows:

[0050]

[0051] In the formula, F is the energy coefficient of static Gaussian dispersion of the point target, reflecting the amplitude of the energy; num-1 is the number of equal parts of the energy; and (r, c) represents the energy around the discrete point (x). i , y i The pixel coordinates in the neighborhood of the Gaussian image point are obtained by summing the pixel gray levels of the Gaussian image points at different discrete points, thus obtaining a realistic, frozen dynamic trailing image with a conic curve as the center trajectory.

Claims

1. A method for modeling the center trajectory of a camera point target trailing image, characterized in that, The method includes the following steps: combining the three-axis angular velocities of the camera into a total angular rate vector, and calculating the unit vector of the total angular rate vector; constructing a cone with the angular rate unit vector pointing to the principal axis, and performing a conical sweep around the principal axis to form a conical surface; establishing the conical surface equation of the conical surface; establishing the image array plane equation in the same reference coordinate system as the one describing the angular rate unit vector; and simultaneously solving the conical surface equation and the image array plane equation to obtain the intersection equation of the conical surface and the image array plane, where the intersection line is a conic curve, which is the center trajectory of the trailing image of the point target.

2. The method according to claim 1, characterized in that, By combining the equations of the conic surface and the image array plane, the equation of the intersection line between the conic surface and the image array plane is obtained, which is the model of the center trajectory of the camera point target trailing image.

3. The method according to claim 1, characterized in that, The acute angle between the line of sight of the point target and the direction of the total angular rate is defined as the semi-apex angle of the cone, denoted as α. The acute angle between the principal axis of the cone and the normal to the image plane is denoted as θ. The imaging trailing motion trajectory during the light integration period is described in the following four cases: (1) When θ = 0, the total angular velocity vector is collinear with the optical axis, and the center trajectory of the point target trailing image is a circular arc; (2) When α + θ < π / 2, the center trajectory of the trailing image of the point target is an elliptical arc; (3) When α + θ = π / 2, the image plane is parallel to a generatrix of the cone, and the center trajectory of the trailing image of the point target is a parabola; (4) When α + θ > π / 2, the center trajectory of the trailing image of the point target is a hyperbola.

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