A coseismic dislocation amount calculation method and system based on monocular monitoring video images

Abstract

The application discloses a coseismic dislocation amount calculation method and system based on monocular monitoring video images, belongs to the technical field of earthquake emergency monitoring and space geodetic survey, and sequentially completes video acquisition preprocessing, feature point partition, camera vibration correction and relative displacement calculation, sub-pixel displacement optimization, pixel-physical displacement conversion, coseismic dislocation parameter solving and sliding track reconstruction and result verification output. Image sequences are extracted from monocular monitoring video streams, tracking and correction windows are selected after distortion correction and scale calibration, the influence of camera shaking is eliminated, sub-pixel level displacement measurement is realized by combining a regularization algorithm, a mapping model is established by recalibrating objects to complete displacement conversion and component decomposition, sliding parameters are solved, and a track curve is drawn. The coseismic dislocation amount measurement is low in cost, high in precision and real-time, can capture complex fault sliding dynamics, and supplements a traditional measurement method, thereby providing key data support for earthquake emergency.

Description

Technical Field

[0001] This invention relates to the field of earthquake emergency monitoring and space geodesy technology, and in particular to a method and system for calculating coseismic displacement based on monocular monitoring video images. Background Technology

[0002] Coseismic displacement parameters, such as fault slip distance, slip direction, and slip velocity, are key parameters for understanding the earthquake rupture process and assessing seismic hazard. Accurate and real-time acquisition of coseismic displacement parameters is of great significance for earthquake emergency response, earthquake mechanism research, and seismic hazard assessment.

[0003] Currently, traditional methods for measuring coseismic displacement have many limitations:

[0004] Field measurement: The displacement on both sides of the fault is measured by field survey, ranging tools or GPS. However, the field survey period is long and it cannot obtain dynamic displacement information at the moment of the earthquake, which is difficult to meet the real-time requirements of earthquake emergency response.

[0005] Satellite remote sensing or drone aerial photography: can achieve wide-area displacement measurement, but it is limited by time resolution and weather conditions such as clouds and fog, making it difficult to obtain instantaneous displacement data of earthquakes, and the data processing cycle is relatively long;

[0006] Strong-motion seismographs / seismographs can record ground motion during earthquakes, but the distribution of stations is usually limited, the coverage is insufficient, and the displacement needs to be indirectly inverted through seismic wave analysis, which has uncertainties in accuracy and directionality, making it difficult to accurately characterize the actual slip state of the fault.

[0007] Daily surveillance cameras are widely distributed in urban and mountainous areas, offering low deployment costs and enabling continuous video image acquisition with high temporal resolution, capturing instantaneous dynamic information during earthquakes. Therefore, this paper proposes a method and system that utilizes widely distributed surveillance cameras to capture the entire process of coseismic displacement in a low-cost, high-precision, and real-time manner, overcoming the shortcomings of traditional measurement methods and possessing significant application value and practical significance. Summary of the Invention

[0008] This invention provides a method and system for calculating coseismic displacement based on monocular monitoring video images. It can automatically correct camera vibration, extract subpixel-level displacement time series of feature points on both sides of the fault, and then accurately calculate strike-slip and dip-slip components, reveal the dynamic trajectory of earthquake sliding, realize real-time and high-precision calculation of coseismic displacement, and provide data support for earthquake emergency monitoring.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] This invention provides a method for calculating coseismic dislocation based on monocular monitoring video images, including:

[0011] S1: Video image acquisition and preprocessing, acquiring monitoring video streams covering the seismogenic fault trace, extracting time-series image frames to establish an image sequence {I t |t=0,1,2,...,N}, where I0 is the initial frame before the arrival of the seismic wave. Lens distortion correction is performed on the image, and preliminary spatial scale calibration is completed using the known dimensions of ground features.

[0012] S2: Feature point selection and partitioning. In the initial frame I0, the image is divided into a near-field region and a far-field region according to the tomographic traces. In the near-field region, at least one target tracking window W containing clear texture is selected. obj At least one camera shake correction window W is selected in the far field region. ref ;

[0013] S3: Camera vibration correction and relative displacement calculation, using a normalized cross-correlation algorithm to track W. ref The position change is used to obtain the camera's motion trajectory, while simultaneously tracking W. obj The apparent displacement trajectory, through Calculate the true relative displacement time series on both sides of the fault to eliminate the influence of camera shake;

[0014] S4: Subpixel displacement optimization, introducing a regularized optimization algorithm and defining an energy function. Where C is the pixel matching cost, R is the smoothing constraint term, and λ is the weight coefficient. The sub-pixel level displacement field is obtained by minimizing this energy function.

[0015] S5: Conversion from pixel displacement to actual physical displacement. A pixel-distance mapping model is established using calibration objects with known spacing in the video. Combined with lens perspective and parallax effects, the pixel displacement is converted into actual ground displacement. Then, combined with the fault strike, the actual displacement is decomposed into strike-slip components D parallel to the fault. ss and the dip-slip or tension component D in the fault normal direction ds ;

[0016] S6: Coseismic dislocation parameter calculation and slip trajectory reconstruction for displacement time series D ss (t) and D ds Differentiating (t) yields the sliding velocity function V. ss (t) and V ds (t), calculate the sliding duration, peak sliding speed and total sliding amount, and plot the sliding trajectory curve with the slip component as the abscissa and the tilt component as the ordinate;

[0017] S7: Result verification and output. The calculated net slip is compared and verified with the coseismic displacement field obtained from the post-earthquake high-resolution satellite imagery. Key parameters such as fault slip time series, peak velocity, and slip trajectory map are output.

[0018] Furthermore, the known ground features in S1 are at least one of fences and road markings, and the target objects selected by the target tracking window and camera vibration correction window in S2 are objects with clear textures or structural features, such as fences, corners, and lampposts.

[0019] Furthermore, the regularization optimization algorithm in S4 is an energy minimization method in the semi-global matching algorithm, and the accuracy of the sub-pixel level displacement field can reach 0.1 pixels.

[0020] Furthermore, the markers mentioned in S5 are fence posts and road markings, and the fault orientation is obtained from regional geological data or post-earthquake satellite imagery.

[0021] Furthermore, the high-resolution satellite imagery mentioned in S7 is either optical satellite imagery or SAR imagery.

[0022] This invention also provides a coseismic dislocation calculation system based on monocular monitoring video images, comprising:

[0023] Image Acquisition and Preprocessing Module: Used for video image acquisition and preprocessing, obtaining monitoring video streams covering the seismogenic fault trace, extracting time-series image frames to establish image sequences {I t |t=0,1,2,...,N}, where I0 is the initial frame before the arrival of the seismic wave. Lens distortion correction is performed on the image, and preliminary spatial scale calibration is completed using the known dimensions of ground features.

[0024] Motion tracking module: used for feature point selection and partitioning. In the initial frame I0, the image is divided into near-field and far-field regions according to the tomographic traces. In the near-field region, at least one target tracking window W containing clear texture is selected. obj At least one camera shake correction window W is selected in the far field region. ref ;

[0025] Vibration correction module: used for camera vibration correction and relative displacement calculation, employing a normalized cross-correlation algorithm to track W. ref The position change is used to obtain the camera's motion trajectory, while simultaneously tracking W. obj The apparent displacement trajectory, through Calculate the true relative displacement time series on both sides of the fault to eliminate the influence of camera shake;

[0026] Sub-pixel optimization module: Used for sub-pixel displacement optimization, it introduces a regularization optimization algorithm and defines an energy function. Where C is the pixel matching cost, R is the smoothing constraint term, and λ is the weight coefficient. The sub-pixel level displacement field is obtained by minimizing this energy function.

[0027] Pixel displacement conversion module: Used to convert pixel displacement to actual physical displacement. It establishes a pixel-distance mapping model using calibration objects with known spacing in the video, and combines lens perspective and parallax effects to convert pixel displacement into actual ground displacement. Then, it decomposes the actual displacement into a strike-slip component D parallel to the fault line. ss and the dip-slip or tension component D in the fault normal direction ds ;

[0028] Solution module: Used for coseismic dislocation parameter calculation and slip trajectory reconstruction, for displacement time series D ss (t) and D ds Differentiating (t) yields the sliding velocity function V. ss (t) and V ds (t), calculate the sliding duration, peak sliding speed and total sliding amount, and plot the sliding trajectory curve with the slip component as the abscissa and the tilt component as the ordinate;

[0029] Output module: Used for result verification and output, it compares and verifies the calculated net slip with the coseismic displacement field obtained from post-earthquake high-resolution satellite imagery, and outputs key parameters such as fault slip time series, peak velocity, and slip trajectory map.

[0030] Compared with the prior art, the technical solution disclosed in this invention has the following beneficial effects:

[0031] The system achieves automatic camera vibration correction and real displacement extraction. By selecting a correction window to track the camera's motion trajectory, the influence of camera shaking is eliminated from the target displacement, and the real relative displacement time series on both sides of the fault is accurately obtained, thus achieving the core objective of accurate extraction of seismic dislocation dynamic data.

[0032] Achieving subpixel-level high-precision displacement measurement, minimizing the energy function through a regularization optimization algorithm, and combining perspective and parallax effects to complete the accurate conversion between pixel and physical displacement, accurately calculating strike-slip and tilt-slip components, thus meeting the invention's requirements for high-precision calculation of coseismic dislocation.

[0033] The invention fully reveals the dynamic trajectory of earthquake slip. By calculating parameters such as slip velocity and duration, the slip trajectory curve is plotted, which intuitively reflects the dynamic stress changes during the earthquake rupture process, thus achieving the invention objective of exploring the dynamic characteristics of earthquake slip.

[0034] Using a single-lens ordinary surveillance camera as the data acquisition carrier, it eliminates the need for multi-machine calibration and enables low-cost deployment by utilizing existing widely distributed surveillance equipment. It can also acquire and quickly process data in real time, achieving the goal of real-time capture of the entire coseismic displacement process and providing rapid data support for earthquake emergency response.

[0035] The calculation results can be compared and verified with traditional methods such as satellite remote sensing and strong earthquake records, complementing and integrating them to supplement the shortcomings of traditional measurement methods, further improving the overall accuracy and reliability of coseismic dislocation measurement, and helping to more comprehensively understand the earthquake rupture process, which is in line with the invention's deeper purpose of improving the coseismic dislocation measurement system. 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 embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a schematic diagram of the coseismic dislocation calculation method based on monocular monitoring video images provided in an embodiment of the present invention.

[0038] Figure 2 This is a schematic diagram illustrating the selection of target and reference objects in a video frame provided in an embodiment of the present invention. Detailed Implementation

[0039] 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.

[0040] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] This invention provides a method for calculating coseismic displacement based on monocular monitoring video images. It can automatically correct camera vibration, extract subpixel-level displacement time series of feature points on both sides of the fault, and then accurately calculate strike-slip and dip-slip components, revealing the dynamic trajectory of earthquake sliding. This enables real-time, high-precision calculation of coseismic displacement, providing data support for earthquake emergency monitoring.

[0042] like Figures 1-2 As shown, this embodiment of the invention provides a method for calculating coseismic dislocation based on monocular monitoring video images, including:

[0043] S1: Video Image Acquisition and Preprocessing

[0044] Acquire monitoring video streams covering the traces of the seismogenic fault.

[0045] Extract image frames from the video stream according to time sequence and establish an image sequence {I}. t |t=0,1,2,...,N}, where I0 is the initial frame before the arrival of the seismic wave.

[0046] Lens distortion correction is performed on the image, and preliminary spatial scale calibration is performed using the dimensions of known ground features (such as fences and road markings).

[0047] S2: Feature Point Selection and Partitioning

[0048] In the initial frame I0, the image is divided into two regions based on the fault traces: the near field region (e.g., the upper plate of the fault) and the far field region (e.g., the lower plate of the fault).

[0049] Select target objects with clear textures or structural features (such as fences, corners, lampposts, etc.) on both sides of the fault. Figure 2 As shown, at least one target tracking window W containing clear texture is selected in the near field region. obj Select at least one camera vibration correction window W in the far field region. ref .

[0050] S3: Camera Vibration Correction and Relative Displacement Calculation

[0051] The normalized cross-correlation algorithm is used to track W in the image sequence. ref The change in position is used to obtain the camera's own motion trajectory caused by ground vibration. .

[0052] Simultaneously track Wobj's view displacement trajectory .

[0053] pass The true relative displacement time series on both sides of the fault is calculated to eliminate the influence of camera shake.

[0054] S4: Subpixel displacement optimization

[0055] To improve the accuracy of displacement measurement, regularization optimization algorithms (such as the energy minimization method in the semi-global matching algorithm) are introduced.

[0056] Define the energy function , where C is the pixel matching cost (based on the correlation coefficient), R is the smoothing constraint term (regularization term), and λ is the weight coefficient.

[0057] By minimizing this energy function, a sub-pixel level displacement field can be obtained with an accuracy of 0.1 pixels or even higher.

[0058] S5: Conversion from pixel displacement to actual physical displacement

[0059] Utilizing known spacing of landmarks in the video (such as the spacing between fence posts and the length of road markings), a pixel-distance mapping model is established. Considering lens perspective and parallax effects, pixel displacements at different distances are converted into actual ground displacements (unit: meters).

[0060] Based on the fault strike (which can be obtained from regional geological data or post-earthquake satellite imagery), the actual displacement is decomposed into fault parallel components (strike-slip component D). ss ) and fault normal component (dip-slip or tension component D) ds ).

[0061] S6: Coseismic Dislocation Parameter Calculation and Slip Trajectory Reconstruction

[0062] For displacement time series D ss (t) and D ds Differentiating (t) yields the sliding velocity function V. ss (t) and V ds (t).

[0063] Calculate the sliding duration (rise time), peak sliding speed, and total sliding amount.

[0064] Plot the slip trajectory curve with the strike-slip component on the x-axis and the dip-slip component on the y-axis. The curvature and direction of this curve reflect the dynamic stress changes during the earthquake rupture process (such as the influence of the rupture direction on near-surface slip).

[0065] S7: Result Verification and Output

[0066] The calculated net slip (total displacement vector) is compared and verified with the coseismic displacement field obtained by correlating post-earthquake high-resolution satellite images (such as optical satellite or SAR images).

[0067] Output key parameters such as fault slip time series, peak velocity, and slip trajectory diagram.

[0068] Based on the same idea, embodiments of the present invention also provide a coseismic dislocation calculation system based on monocular monitoring video images, comprising:

[0069] Image Acquisition and Preprocessing Module: Used for video image acquisition and preprocessing, obtaining monitoring video streams covering the seismogenic fault trace, extracting time-series image frames to establish image sequences {I t|t=0,1,2,...,N}, where I0 is the initial frame before the arrival of the seismic wave. Lens distortion correction is performed on the image, and preliminary spatial scale calibration is completed using the known dimensions of ground features.

[0070] Motion tracking module: used for feature point selection and partitioning. In the initial frame I0, the image is divided into near-field and far-field regions according to the tomographic traces. In the near-field region, at least one target tracking window W containing clear texture is selected. obj At least one camera shake correction window W is selected in the far field region. ref ;

[0071] Vibration correction module: used for camera vibration correction and relative displacement calculation, employing a normalized cross-correlation algorithm to track W. ref The position change is used to obtain the camera's motion trajectory, while simultaneously tracking W. obj The apparent displacement trajectory, through Calculate the true relative displacement time series on both sides of the fault to eliminate the influence of camera shake;

[0072] Sub-pixel optimization module: Used for sub-pixel displacement optimization, it introduces a regularization optimization algorithm and defines an energy function. Where C is the pixel matching cost, R is the smoothing constraint term, and λ is the weight coefficient. The sub-pixel level displacement field is obtained by minimizing this energy function.

[0073] Pixel displacement conversion module: Used to convert pixel displacement to actual physical displacement. It establishes a pixel-distance mapping model using calibration objects with known spacing in the video, and combines lens perspective and parallax effects to convert pixel displacement into actual ground displacement. Then, it decomposes the actual displacement into a strike-slip component D parallel to the fault line. ss and the dip-slip or tension component D in the fault normal direction ds ;

[0074] Solution module: Used for coseismic dislocation parameter calculation and slip trajectory reconstruction, for displacement time series D ss (t) and D ds Differentiating (t) yields the sliding velocity function V. ss (t) and V ds (t), calculate the sliding duration, peak sliding speed and total sliding amount, and plot the sliding trajectory curve with the slip component as the abscissa and the tilt component as the ordinate;

[0075] Output module: Used for result verification and output, it compares and verifies the calculated net slip with the coseismic displacement field obtained from post-earthquake high-resolution satellite imagery, and outputs key parameters such as fault slip time series, peak velocity, and slip trajectory map.

[0076] The basic principles of the present invention have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in the present invention are merely examples and not limitations, and should not be considered as essential features of each embodiment of the present invention. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the present invention to the necessity of employing the aforementioned specific details.

[0077] The block diagrams of devices, apparatuses, devices, and systems involved in this invention are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0078] It should also be noted that in the apparatus, device, and method of the present invention, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered as equivalent solutions of the present invention.

[0079] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the invention. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of the invention. Therefore, the invention is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.

[0080] It should be understood that the qualifying terms "first", "second", "third", "fourth", "fifth" and "sixth" used in the description of the embodiments of the present invention are only used to more clearly illustrate the technical solutions and are not intended to limit the scope of protection of the present invention.

[0081] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of the invention to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations therein.

Claims

1. A method for calculating coseismic dislocation based on monocular monitoring video images, characterized in that, include: S1: Video image acquisition and preprocessing, acquiring monitoring video streams covering the seismogenic fault trace, extracting time-series image frames to establish an image sequence {I t |t=0,1,2,...,N}, where I0 is the initial frame before the arrival of the seismic wave. Lens distortion correction is performed on the image, and preliminary spatial scale calibration is completed using the known dimensions of ground features. S2: Feature point selection and partitioning. In the initial frame I0, the image is divided into a near-field region and a far-field region according to the tomographic traces. In the near-field region, at least one target tracking window W containing clear texture is selected. obj At least one camera shake correction window W is selected in the far field region. ref ; S3: Camera vibration correction and relative displacement calculation, using a normalized cross-correlation algorithm to track W. ref The position change is used to obtain the camera's motion trajectory, while simultaneously tracking W. obj The apparent displacement trajectory, through Calculate the true relative displacement time series on both sides of the fault to eliminate the influence of camera shake; S4: Subpixel displacement optimization, introducing a regularized optimization algorithm and defining an energy function. Where C is the pixel matching cost, R is the smoothing constraint term, and λ is the weight coefficient. The sub-pixel level displacement field is obtained by minimizing this energy function. S5: Conversion from pixel displacement to actual physical displacement. A pixel-distance mapping model is established using calibration objects with known spacing in the video. Combined with lens perspective and parallax effects, pixel displacement is converted into actual ground displacement. Then, considering the fault strike direction, the actual displacement is decomposed into a strike-slip component D parallel to the fault. ss and the dip-slip or tension component D in the fault normal direction ds ; S6: Coseismic dislocation parameter calculation and slip trajectory reconstruction for displacement time series D ss (t) and D ds Differentiating (t) yields the sliding velocity function V. ss (t) and V ds (t), calculate the sliding duration, peak sliding speed and total sliding amount, and plot the sliding trajectory curve with the slip component as the abscissa and the tilt component as the ordinate; S7: Result verification and output. The calculated net slip is compared and verified with the coseismic displacement field obtained from the post-earthquake high-resolution satellite imagery. Key parameters such as fault slip time series, peak velocity, and slip trajectory map are output.

2. The method for calculating coseismic dislocation based on monocular monitoring video images according to claim 1, characterized in that, The known ground features mentioned in S1 are at least one of fences and road markings, and the target objects selected by the target tracking window and camera vibration correction window in S2 are objects with clear textures or structural features, such as fences, corners, and lampposts.

3. The method for calculating coseismic dislocation based on monocular monitoring video images according to claim 1, characterized in that, The regularization optimization algorithm in S4 is an energy minimization method in the semi-global matching algorithm, and the accuracy of the sub-pixel level displacement field can reach 0.1 pixels.

4. The method for calculating coseismic dislocation based on monocular monitoring video images according to claim 1, characterized in that, The markers mentioned in S5 are fence posts and road markings, and the fault orientation is obtained from regional geological data or post-earthquake satellite imagery.

5. The method for calculating coseismic dislocation based on monocular monitoring video images according to claim 1, characterized in that, The high-resolution satellite imagery mentioned in S7 is optical satellite imagery or SAR imagery.

6. A coseismic dislocation calculation system based on monocular monitoring video images, characterized in that, include: Image Acquisition and Preprocessing Module: Used for video image acquisition and preprocessing, obtaining monitoring video streams covering the seismogenic fault trace, extracting time-series image frames to establish image sequences {I t |t=0,1,2,...,N}, where I0 is the initial frame before the arrival of the seismic wave. Lens distortion correction is performed on the image, and preliminary spatial scale calibration is completed using the known dimensions of ground features. Motion tracking module: used for feature point selection and partitioning. In the initial frame I0, the image is divided into near-field and far-field regions according to the tomographic traces. In the near-field region, at least one target tracking window W containing clear texture is selected. obj At least one camera shake correction window W is selected in the far field region. ref ; Vibration correction module: used for camera vibration correction and relative displacement calculation, employing a normalized cross-correlation algorithm to track W. ref The position change is used to obtain the camera's motion trajectory, while simultaneously tracking W. obj The apparent displacement trajectory, through Calculate the true relative displacement time series on both sides of the fault to eliminate the influence of camera shake; Sub-pixel optimization module: Used for sub-pixel displacement optimization, it introduces a regularization optimization algorithm and defines an energy function. Where C is the pixel matching cost, R is the smoothing constraint term, and λ is the weight coefficient. The sub-pixel level displacement field is obtained by minimizing this energy function. Pixel displacement conversion module: Used to convert pixel displacement to actual physical displacement. It establishes a pixel-distance mapping model using calibration objects with known spacing in the video, and combines lens perspective and parallax effects to convert pixel displacement into actual ground displacement. Then, it decomposes the actual displacement into a strike-slip component D parallel to the fault line. ss and the dip-slip or tension component D in the fault normal direction ds ; Solution module: Used for coseismic dislocation parameter calculation and slip trajectory reconstruction, for displacement time series D ss (t) and D ds Differentiating (t) yields the sliding velocity function V. ss (t) and V ds (t), calculate the sliding duration, peak sliding speed and total sliding amount, and plot the sliding trajectory curve with the slip component as the abscissa and the tilt component as the ordinate; Output module: Used for result verification and output, it compares and verifies the calculated net slip with the coseismic displacement field obtained from post-earthquake high-resolution satellite imagery, and outputs key parameters such as fault slip time series, peak velocity, and slip trajectory map.

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