A method for active vision calibration of baseline direction in biplane observation
By using a dual-plane observation method to constrain the baseline direction, and utilizing rank-one decomposition and collinearity constraints to recover the baseline direction, the difficulty of baseline calibration in active vision systems is solved, achieving efficient and robust baseline direction estimation, which is applicable to real-world active vision systems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUILIN UNIV OF AEROSPACE TECH
- Filing Date
- 2026-03-09
- Publication Date
- 2026-06-09
AI Technical Summary
In active vision systems, accurate calibration of the baseline orientation is difficult, especially when the emission and imaging units cannot directly observe the same area or are limited by physical layout. Existing methods usually require multiple poses, many images, or high computational costs. Furthermore, the baseline orientation, as a simpler but highly influential component among extrinsic parameters, is rarely studied as a quantity that can be recovered from a minimum number of observations.
A dual-plane observation method is adopted to constrain the baseline direction. By constructing an optical active vision system, the external parameters of the emission and imaging device are described by the rotation matrix and the baseline vector. The planar constraints are derived by combining reference plane images at different depths. The baseline direction is directly recovered by rank-one decomposition and collinearity constraints, avoiding the prior requirements for the plane normal or distance.
It achieves efficient and robust baseline orientation recovery without the need for plane normals or distance priors, simplifies experimental setup, is applicable to real-world active vision systems, and improves system stability and applicability, especially in terms of accuracy when using arbitrary planes or with minute geometric perturbations.
Smart Images
Figure CN122176065A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of optical active vision, and more specifically to an active vision calibration method for constrained baseline directions in dual-plane observation. Background Technology
[0002] Active vision systems combine emission / illumination modules with sensing / imaging modules, playing a crucial role in computer vision, robot perception, industrial inspection, and augmented reality. Compared to purely passive imaging, active systems can provide reliable geometric information even in textureless areas or under varying lighting conditions because the emitted light provides controllable textures and corresponding cues. For these systems, accurate geometric calibration between the emission and imaging units is critical, determining the alignment between virtual and physical spaces in mixed reality environments. Among all parameters, the baseline direction (defined as the direction of the translation vector between two units) is particularly critical, as it directly affects the stability of triangulation geometry and spatial registration.
[0003] However, the calibration of such active devices faces unique challenges: the illumination unit does not capture scene images, so the correspondence between the two devices must be established indirectly. Classic camera-to-camera calibration methods cannot be applied directly without modification, which has prompted researchers to propose a large number of calibration strategies for active vision systems.
[0004] Traditional photogrammetry and computer vision calibration techniques rely on known geometric targets to recover intrinsic and extrinsic parameters through 2D–3D correspondence. Widely used planar calibration methods estimate the homography between the calibration plane and the image to solve for camera intrinsic parameters, followed by nonlinear optimization refinement. While highly accurate, these methods typically assume that both devices can observe the same calibration pattern, which is not applicable to active vision systems.
[0005] In transmitter-based systems, the transmitting unit is often modeled as an "inverse camera," projecting structured light rays into the scene. The calibration task can be reformulated as a stereo correspondence problem, i.e., establishing a relationship between a projected pattern and an acquired image. Among various techniques, planar calibration methods are dominant due to their simplicity and ease of use. They typically require only a planar target; the system projects an coded pattern (such as Gray code or manually marked symbols) onto the plane, often combined with a printed checkerboard pattern to extract correspondences.
[0006] To enhance robustness, many studies have introduced nonlinear optimization or bundle adjustment to jointly estimate intrinsic and extrinsic parameters while compensating for calibration plate misalignment and lens distortion. Some work has also been extended to multi-emitter-camera systems to handle larger or more complex configurations. Other studies have focused on reducing the number of poses or images required without sacrificing accuracy, for example, by projecting the pattern only once per plate position, thus significantly reducing acquisition time and operational complexity.
[0007] In recent years, the calibration problem has also been extended to more complex or flexible geometries, such as non-overlapping fields of view, mirror transitions, and multi-sensor fusion systems with auxiliary cameras. These methods are particularly useful when two devices cannot directly observe the same area or are constrained by physical layout.
[0008] Despite a significant amount of existing work, most methods still aim to recover complete extrinsic parameters (rotation and translation), typically requiring multiple poses, numerous images, or computationally expensive optimization processes. Baseline orientation, as a simpler yet highly influential component of the extrinsic parameters, is rarely studied as a quantity that can be recovered independently with minimal observations.
[0009] The direction of the translation vector between the emitting and imaging units directly controls the epipolar geometry and measurement sensitivity. In many optical active vision systems, emitting unit rotation is not critical because the emitting unit can be modeled as a ray source. Therefore, geometric reconstruction only requires the emitting unit's center position in the camera coordinate system, i.e., the baseline direction.
[0010] In augmented reality and transmitter-based applications, accurate baseline calibration is crucial for precise registration of virtual and real spaces. This calibration directly impacts depth estimation and extrinsic alignment between the display (or transmitter) and the imaging unit. Inaccurate baseline orientation can cause parallax inconsistencies or inaccurate digital content overlay, thus reducing geometric accuracy and user experience. In robotics and metrology scenarios, baseline inaccuracy can also affect the repeatability of geometric measurements and may propagate and amplify subsequent localization and mapping errors in multi-sensor fusion pipelines.
[0011] Furthermore, the impact of baseline orientation error is non-linear: for near planes, small angular deviations may cause minimal depth changes; however, for distant or tilted surfaces, they can lead to significant depth errors. This sensitivity makes baseline orientation estimation particularly critical in high-precision optical metrology, industrial inspection, and long-distance reconstruction tasks. Therefore, a reliable, lightweight, and mathematically robust baseline orientation retrieval method can significantly improve the stability and portability of active vision systems. Summary of the Invention
[0012] In view of this, the present invention provides an active visual calibration method for constrained baseline directions by dual-plane observation.
[0013] To achieve the above objectives, the present invention adopts the following technical solution: An active visual calibration method for constrained baseline directions based on dual-plane observations includes the following steps: Constructing an optical active vision system, including a transmitter and an imaging device, wherein the extrinsic parameters between the transmitter and the imaging device are determined by a rotation matrix. With baseline vector describe; The transmitting and imaging equipment are placed on reference planes at different depths. Planar homography is derived from the images of the reference planes at different depths, and planar constraints are constructed. The planar constraints link the unknown baseline direction with the observed homography and the planar parameters. The planar constraint relationship couples the baseline vector b with the planar parameters of two reference planes at different depths. The rank-one decomposition of the scaled homography difference yields the quadratic constraint. The baseline direction can be directly obtained by selecting the physically feasible root.
[0014] Optionally, the intrinsic parameters of the transmitting device and the imaging device are respectively denoted as the sensor's... With the transmitter .
[0015] Optionally, the expressions for reference planes at different depths are as follows:
[0016] in, For unit normal vector, This corresponds to the signed distance.
[0017] Optionally, the planar homography derived from the image for reference planes at different depths is expressed as follows: ; in, and Through planar position and The homotopy transformation caused between the projector (emitter) and the camera is explained in the following notation: in, : Normalized homotopic transformation between the projector and camera images, with a size of 3x3. : 3x3 identity matrix. : Baseline translation vector from the transmitter to the camera (direction is the primary consideration). :flat and The unit normal vector, expressed in the selected coordinate system, has a size of 3x1. This corresponds to the signed distance.
[0018] Optionally, planar homography is derived from the image for reference planes at different depths, and the homography ratio of the reference planes at different depths is used to eliminate scale ambiguity, as shown in the following expression: .
[0019] Optionally, the expression for the planar constraint is as follows: ; H: The measurable homography ratio obtained from two planar observations (also ).
[0020] This can usually be understood as:
[0021] in, For unit normal vector, For the corresponding signed distance, s is a scalar.
[0022] Optionally, the planar constraint relationship couples the baseline vector b with the planar parameters of two reference planes at different depths. A rank-one decomposition of the scaled homography is then performed to obtain a quadratic constraint. The baseline direction can be directly obtained by selecting a physically feasible root, specifically including the following steps: Applying the Sherman–Morrison identities to the inverses of the planar constraints yields a compact rank-one decomposition:
[0023] in For global scale, and
[0024] r: one Vector (right-hand factor vector).
[0025] The derivation will yield similar results.
[0026] so: It is the "left vector" of the rank-one decomposition, corresponding to the baseline direction; It is a composite expression that includes plane parameters (normal and distance, etc.).
[0027] : A dimensionless scalar quantity representing the ratio of "the projection of the baseline onto the plane's normal direction" to "the distance to the plane". It is usually written as: Baseline In legal direction Components in direction (scalar projection).
[0028] Divide by The dimensionless quantity was then obtained. .
[0029] The matrix is as follows in the noise-free case:
[0030] It is rank 1, and its column space is composed of Zhang Cheng; From the formula For any vector The collinearity condition is obtained as follows:
[0031] By selecting vectors, collinear constraints can be constructed, thereby obtaining information about... The quadratic equation:
[0032] The coefficients depend only on With the selected vector ;Pick The physically feasible real roots of the quadratic equation are obtained by a unique metric. .
[0033] get Afterwards, the baseline direction was changed from The left factor is given directly:
[0034] As can be seen from the above technical solution, compared with the prior art, the present invention discloses an active visual calibration method for baseline direction constraint by dual-plane observation, which does not require prior knowledge of plane normal or distance to recover the baseline direction. In fact, decomposition show Completely decoupled from planar information: the baseline appears only in the left factor, while all information about the plane is completely decoupled. All dependencies were absorbed Therefore, even if the plane orientation is unknown, the baseline direction can be determined solely by homography measurements.
[0035] This property significantly enhances the method's applicability. In real-world scenarios, especially when using arbitrary planes or when there are minute perturbations in the geometry, accurately measuring the plane normal is often difficult. Avoiding this requirement simplifies experimental setup and allows for the use of flexible planar targets. Planar parameters are only important when absolute depth information needs to be recovered; homography observations are sufficient for baseline orientation estimation. This robustness and flexibility make it suitable for real-world active vision systems. Attached Figure Description
[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0037] Figure 1This is a schematic diagram of the calibration system of the present invention; Figure 2 This is a schematic diagram of the method flow of the present invention. Detailed Implementation
[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0039] This invention discloses an active visual calibration method for constrained baseline directions based on dual-plane observations, such as... Figures 1-2 As shown, it includes the following steps: Constructing an optical active vision system, including a transmitter and an imaging device, wherein the extrinsic parameters between the transmitter and the imaging device are determined by a rotation matrix. With baseline vector describe; The transmitting and imaging equipment are placed on reference planes at different depths. Planar homography is derived from the images of the reference planes at different depths, and planar constraints are constructed. The planar constraints link the unknown baseline direction with the observed homography and the planar parameters. The planar constraint relationship couples the baseline vector b with the planar parameters of two reference planes at different depths. The rank-one decomposition of the scaled homography difference yields the quadratic constraint. The baseline direction can be directly obtained by selecting the physically feasible root.
[0040] Specifically, in this embodiment, the active vision system is modeled as two pinhole devices: a transmitter and an imaging sensor. The extrinsic parameters between the two devices are determined by a rotation matrix. With baseline vector Description. The intrinsic parameters of the two devices are denoted as those of the imaging sensor. With the transmitter To simplify the analysis, a reference plane is introduced as an auxiliary constraint, thereby restoring the baseline in a closed loop. The direction.
[0041] To derive the constraints, a reference plane is introduced that can be placed at different depths relative to the two devices. After normalizing the image coordinates, the influence of intrinsic parameters is eliminated, and relative rotation can be compensated for or assumed to be an identity matrix. Under this setting, the relative geometry is determined only by the translation direction. Decision. Since only direction is of concern, a unit norm constraint is imposed. .
[0042] Assume the plane is placed twice.
[0043] in For unit normal vector, This corresponds to the signed distance. The two planes do not need to be parallel, therefore this formula applies to general configurations.
[0044] According to standard two-view geometry, the mapping from transmitter coordinates to camera coordinates derived from the plane is equivalent to the following homography:
[0045] This indicates that the plane will produce a rank-1 update to the identity matrix, directly relating the baseline direction to the plane geometry.
[0046] For the two placements, there are
[0047] Since homography can only be observed at the global scale, their ratios are considered to eliminate scale ambiguity:
[0048] Let the measurable homography ratio be... and absorb all scales into a scalar In this process, planar constraints are obtained:
[0049] This equation will determine the unknown baseline direction. With observation single response And this is related to planar parameters. In practice, once the corresponding values are estimated from the image... This relation can provide closed algebraic conditions for simultaneously estimating the unknown depth. and projection scale Solve under the following circumstances Compared to traditional calibration, this formula can be extended to any planar direction and allows for the use of flexible planar patterns.
[0050] Equation (1) defines the baseline direction With plane parameters , Coupling. Utilizing its algebraic structure, the unknown baseline can be recovered in a closed-form manner. Applying the Sherman–Morrison identity to the inverse term in equation (1) yields a compact rank-one decomposition:
[0051] in For global scale, and
[0052] This form implies that the matrix is in noise-free condition.
[0053] It should be rank 1, and its column space is composed of... Zhang Cheng.
[0054] From equation (2) for any vector The collinearity condition can be obtained as follows:
[0055] By choosing appropriate vectors, collinearity constraints can be constructed, thereby obtaining information about... The quadratic equation:
[0056] Where the coefficient Only depend on With the selected vector Taking the physically feasible real root of equation (4) yields the unique scale. .
[0057] get Afterwards, the baseline direction can be determined by... The left factor is given directly:
[0058] This closed-loop recovery avoids iterative optimization and relies solely on homography. .
[0059] A significant advantage of this method is that recovering the baseline direction does not require prior knowledge of the plane normal or distance. In fact, decomposition show Completely decoupled from planar information: the baseline appears only in the left factor, while all information about the plane is completely decoupled. All dependencies were absorbed Therefore, even if the plane orientation is unknown, the baseline direction can be determined solely by homography measurements.
[0060] This property significantly enhances the method's applicability. In real-world scenarios, especially when using arbitrary planes or when there are minute perturbations in the geometry, accurately measuring the plane normal is often difficult. Avoiding this requirement simplifies experimental setup and allows for the use of flexible planar targets. Planar parameters are only important when absolute depth information needs to be recovered; homography observations are sufficient for baseline orientation estimation. This robustness and flexibility make it suitable for real-world active vision systems.
Claims
1. An active visual calibration method for constrained baseline directions based on dual-plane observation, characterized in that, Includes the following steps: Constructing an optical active vision system, including a transmitter and an imaging device, wherein the extrinsic parameters between the transmitter and the imaging device are determined by a rotation matrix. With baseline vector describe; The transmitting and imaging equipment are placed on reference planes at different depths. Image-induced plane homography is performed on the reference planes at different depths, and plane constraints are constructed. The plane constraints link the unknown baseline direction with the observed homography and plane parameters. The planar constraint relationship couples the baseline vector b with the planar parameters of two reference planes at different depths. The rank-one decomposition of the scaled homography difference yields the quadratic constraint. The baseline direction can be directly obtained by selecting the physically feasible root.
2. The active visual calibration method for constrained baseline direction based on dual-plane observation as described in claim 1, characterized in that, The intrinsic parameters of the transmitting device and the imaging device are respectively denoted as the sensor's intrinsic parameters. With the transmitter .
3. The active visual calibration method for constrained baseline direction based on dual-plane observation as described in claim 1, characterized in that, The plane homography derived from the image of reference planes at different depths is expressed as follows: ； The homotopic transformation between the normalized projector and camera images represents the planar homotopy transformation. Represents the identity matrix. Represents the baseline translation vector from the transmitter to the camera, where, For unit normal vector, This corresponds to the signed distance.
4. The active visual calibration method for constrained baseline direction based on dual-plane observation as described in claim 3, characterized in that, Planar homography is derived from reference planes at different depths, and scale ambiguity is eliminated based on the homography ratio of reference planes at different depths, as expressed below: 。 5. The active visual calibration method for constrained baseline direction based on dual-plane observation as described in claim 1, characterized in that, The planar constraint relationship couples the baseline vector b with the planar parameters of two reference planes at different depths. A rank-one decomposition of the scaled homography yields a quadratic constraint. The baseline direction can be directly obtained by selecting the physically feasible root, specifically including the following steps: Applying the Sherman–Morrison identities to the inverses of the planar constraints yields a compact rank-one decomposition: in For global scale, and It is the "left vector" of the rank-one decomposition, corresponding to the baseline direction; It is a composite expression that includes planar parameters; The ratio of "the projection of the baseline onto the plane normal" to "the distance to the plane" is represented as: Representing the baseline In legal direction Components in direction, divided by The dimensionless quantity was then obtained. ; From the formula For any vector The collinearity condition is obtained as follows: Choosing a vector involves constructing collinear constraints, thereby obtaining information about... The quadratic equation: Where the coefficient Only depend on With the selected vector ;Pick The physically feasible real roots of the quadratic equation are obtained by a unique metric. ; get Afterwards, the baseline direction was changed from The left factor is given directly: 。