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Multi-track fusion 3D Deformation processing functions

Multi-track fusion in 3D deformation processing refers to the combination of multiple data sources or sensor streams to enhance the accuracy and resolution of deformation analysis. These data sources could include:

  • LiDAR data
  • Stereo cameras
  • 3D scanners
  • Deformation sensors (strain gauges, accelerometers)
  • Simulated models (e.g., finite element simulations)

The goal is to merge these inputs into a unified representation of the deforming 3D object or structure.

Key Functions in Multi-Track Fusion 3D Deformation Processing

  1. Preprocessing Functions These functions ensure that data from different tracks are standardized and cleaned before fusion.

  • Data Synchronization

    • Aligns timestamps from multiple tracks for time-series consistency.
    • Handles different sampling rates and delays using interpolation or extrapolation.
    def synchronize_tracks(track_data, timestamps):
# Input: track_data (list of datasets), timestamps (list of time arrays)
# Output: synchronized datasets
aligned_data = []
ref_time = min([ts[0] for ts in timestamps])
for track, ts in zip(track_data, timestamps):
    aligned = interpolate_to_ref_time(track, ts, ref_time)
    aligned_data.append(aligned)
return aligned_data

  • Noise Reduction

    • Applies filters like Gaussian smoothing or median filtering to reduce sensor noise.
    • Removes outliers using statistical methods (e.g., Z-scores).
    def denoise_data(data, method="gaussian", **params):
if method == "gaussian":
    return gaussian_filter(data, **params)
elif method == "median":
    return median_filter(data, **params)
  1. Registration Functions Aligns the spatial data from multiple tracks into a common coordinate system.

  • Point Cloud Registration

    • Uses algorithms like Iterative Closest Point (ICP) or deep learning-based approaches.
    def register_point_clouds(cloud_a, cloud_b, init_transform=None):
# Input: Two 3D point clouds, initial transform
# Output: Aligned point cloud and transform
result = icp_algorithm(cloud_a, cloud_b, init_transform)
return result.transformed_cloud, result.transform

  • Coordinate Transformation

    • Converts data between coordinate systems (e.g., local to global).
    def transform_coordinates(data, transformation_matrix):
return np.dot(transformation_matrix, data.T).T
  1. Fusion Functions Combine data streams into a unified model.

  • Weighted Fusion

    • Assigns weights to different data tracks based on reliability or precision.
    def weighted_fusion(data_tracks, weights):
fused_data = np.zeros_like(data_tracks[0])
for data, weight in zip(data_tracks, weights):
    fused_data += weight * data
return fused_data / sum(weights)

  • Probabilistic Fusion

    • Combines data using probabilistic methods (e.g., Kalman filtering or Bayesian inference).
    def probabilistic_fusion(data_tracks, variances):
inverse_variances = 1 / variances
weighted_sum = sum(d * iv for d, iv in zip(data_tracks, inverse_variances))
total_weight = sum(inverse_variances)
return weighted_sum / total_weight
  1. Deformation Analysis Functions Processes the fused data to compute 3D deformation metrics.

  • Strain and Stress Estimation

    • Uses deformation gradients to compute strain and stress tensors.
    def compute_strain(displacement_field):
gradient = np.gradient(displacement_field)
strain_tensor = 0.5 * (gradient + gradient.T)
return strain_tensor

  • Surface Deformation

    • Tracks changes in surface geometry using curvature or point displacement.
    def surface_deformation(original_surface, deformed_surface):
displacement = np.linalg.norm(original_surface - deformed_surface, axis=1)
return displacement
  1. Visualization Functions Provides tools for 3D visualization of deformation results.

  • Point Cloud Visualization

    • Renders fused point clouds in 3D space.
    def visualize_point_cloud(point_cloud, color_map=None):
import open3d as o3d
cloud = o3d.geometry.PointCloud()
cloud.points = o3d.utility.Vector3dVector(point_cloud)
if color_map:
    cloud.colors = o3d.utility.Vector3dVector(color_map)
o3d.visualization.draw_geometries([cloud])

  • Mesh Deformation

    • Displays the deformation of a 3D mesh with color-coded metrics like displacement magnitude.
    def visualize_mesh_deformation(original_mesh, deformed_mesh, displacement_field):
# Apply color to represent deformation magnitude
colors = map_displacement_to_color(displacement_field)
deformed_mesh.paint_uniform_color(colors)
o3d.visualization.draw_geometries([deformed_mesh])
  1. Validation Functions Ensures the fused deformation model is accurate.

  • Error Metrics

    • Compares the fused model with ground truth data.
    def compute_rmse(predicted, ground_truth):
return np.sqrt(np.mean((predicted - ground_truth) ** 2))

  • Stability Check

    • Verifies if the deformation results are physically consistent.
    def check_physical_consistency(strain_tensor, material_properties):
# Example: Ensure strain tensor obeys material laws
is_valid = validate_tensor_with_material_model(strain_tensor, material_properties)
return is_valid

Workflow

  • Input data: Gather raw data from multiple tracks.
  • Preprocessing: Synchronize, denoise, and standardize the input.
  • Registration: Align all datasets into a unified spatial-temporal frame.
  • Fusion: Combine data streams using weighted or probabilistic methods.
  • Analysis: Extract deformation parameters (e.g., strain, displacement).
  • Visualization: Render the results for analysis or reporting.
  • Validation: Ensure the results are accurate and consistent.

What is Multi-Track in Satellite Context?

In satellite remote sensing, tracks refer to the ground paths that satellites follow as they orbit the Earth. Different satellite tracks provide different perspectives or angles for observing the Earth's surface. Multi-track data means data collected from multiple such paths, which can enhance the analysis of deformation.

This multi-track concept is especially useful in Interferometric Synthetic Aperture Radar (InSAR) and optical imaging for detecting and analyzing 3D deformations such as:

Ground movement (subsidence, uplift, or faulting). Changes due to earthquakes, landslides, or volcanic activity.

Types of Multi-Track Data in Satellites

  • Multiple Tracks from the Same Satellite:

    • A single satellite revisits the same area from slightly shifted orbits over time.
    • Example: Sentinel-1 has an orbital configuration that allows it to collect ascending and descending tracks.
      • Ascending Track: When the satellite moves from south to north.
      • Descending Track: When the satellite moves from north to south.

  • Tracks from Different Satellites:

    • Data from multiple satellites observing the same area.
    • Example: Combining data from Sentinel-1 and RADARSAT-2.
    • This helps mitigate gaps in observation or improve temporal resolution.

  • Cross-Track and Along-Track:

    • Cross-Track Observations: Data collected perpendicular to the satellite's motion (side-looking radar or imaging).
    • Along-Track Observations: Data collected in the same direction as the satellite's motion.

Why Use Multi-Track Data for 3D Deformation?

Single-track data often provides only 2D information, such as:

+ Vertical displacement (e.g., land subsidence).
+ Relative displacement between two points.

Multi-track data allows for:

  • Full 3D Deformation Analysis:

    • Combining ascending and descending track data provides vertical and horizontal deformation components.
    • Adding data from other directions (e.g., oblique views) further enhances this.

  • Improved Accuracy:

    • Using multiple perspectives reduces errors caused by noise, atmospheric effects, or limited viewing geometry.

  • Redundancy and Temporal Coverage:

    • Multi-track data ensures more frequent observations, especially in areas with long revisit times for a single satellite.

How Multi-Track Data is Used for Deformation Processing

    1. Data Collection
    • Collect satellite imagery or radar data from multiple tracks over time.
    • Examples:
      • InSAR data from ascending and descending passes.
      • Optical images from satellites with slightly shifted tracks (e.g., SPOT, Landsat).
    1. Co-Registration and Alignment
    • Align the data to a common coordinate system.
    • Challenges:
      • Different viewing angles cause geometric distortions.
      • Orbital errors require correction.
    1. Data Fusion
    • Combine the tracks to enhance deformation measurements.
    • InSAR Example:
      • Ascending track gives east-west displacement.
      • Descending track gives north-south displacement.
    • Together, they enable computation of vertical and horizontal deformations.
    1. Deformation Modeling
    • Use fused data to compute 3D deformation fields.
    • Integration with external data (e.g., GPS or ground-based sensors) improves accuracy.
    1. Validation
    • Compare deformation results with independent datasets or simulations.

Resources : [ Forum : Combining Ascending/Desceding Order ]