Scaling and georeferencing

What:

GeoTIFF generation involves creating georeferenced images that embed spatial information within the image metadata. These images can be accurately positioned on a map or within a Geographic Information System (GIS).

Why:

GeoTIFFs are essential for conveying spatial information in a standardized format. They allow images to be integrated into GIS platforms, enabling users to visualize and analyze the spatial relationships between images and other geographic data layers.

How:

If the camera's coordinates are known, you can use ray tracing (as described in section 4.3.4) to convert the image's four corners into georeferenced coordinates. These coordinates are then embedded in the GeoTIFF file's metadata, allowing for precise geospatial referencing.

Python Code Example:

Generating GeoTIFF from Image and Coordinates:

from osgeo import gdal, osr

def create_geotiff(image_path, output_path, ulx, uly, lrx, lry):
    """
    Create a GeoTIFF from an image with specified georeferenced corner coordinates.

    Parameters:
    - image_path: Path to the input image.
    - output_path: Path to save the GeoTIFF.
    - ulx, uly: Upper left corner coordinates (x, y).
    - lrx, lry: Lower right corner coordinates (x, y).
    """

    # Open the input image
    src_ds = gdal.Open(image_path)
    if src_ds is None:
        raise ValueError(f"Could not open {image_path}")

    # Get the image dimensions
    width = src_ds.RasterXSize
    height = src_ds.RasterYSize

    # Calculate the pixel size
    pixel_width = (lrx - ulx) / width
    pixel_height = (uly - lry) / height

    # Define the GeoTransform
    geotransform = [ulx, pixel_width, 0, uly, 0, -pixel_height]

    # Create the output GeoTIFF file
    driver = gdal.GetDriverByName('GTiff')
    dst_ds = driver.Create(output_path, width, height, src_ds.RasterCount, gdal.GDT_Byte)

    # Set the GeoTransform and Projection
    dst_ds.SetGeoTransform(geotransform)
    srs = osr.SpatialReference()
    srs.SetWellKnownGeogCS('WGS84')  # Assuming WGS84 coordinate system
    dst_ds.SetProjection(srs.ExportToWkt())

    # Copy over each band from the source to the destination
    for i in range(1, src_ds.RasterCount + 1):
        band = src_ds.GetRasterBand(i)
        dst_ds.GetRasterBand(i).WriteArray(band.ReadAsArray())

    # Save and close the GeoTIFF file
    dst_ds = None
    src_ds = None
    print(f"GeoTIFF saved to {output_path}")

# Example usage:
ulx, uly = 300000, 5000000  # Upper left corner coordinates
lrx, lry = 300500, 4999500  # Lower right corner coordinates
create_geotiff('input_image.jpg', 'output_image.tiff', ulx, uly, lrx, lry)

Calculating Corner Coordinates Using Ray Tracing:

If you have the camera's position, altitude, and angles, you can calculate the georeferenced coordinates of the image corners using ray tracing.

import numpy as np

def ray_trace_corners(camera_pos, altitude, h_angle, v_angle, image_width, image_height, n_medium):
    """
    Calculate the georeferenced coordinates of image corners using ray tracing.

    Parameters:
    - camera_pos: (x, y) coordinates of the camera.
    - altitude: Height of the camera above the ground (or seabed).
    - h_angle: Horizontal field of view (degrees).
    - v_angle: Vertical field of view (degrees).
    - image_width: Image width in pixels.
    - image_height: Image height in pixels.
    - n_medium: refractive index of the medium where the image was taken. Typically, 1.33 for seawater.

    Returns:
    - ulx, uly, lrx, lry: Georeferenced coordinates of upper-left and lower-right corners.
    - Area of the image in square meter
    """

    # Convert angles to radians
    h_angle_rad = np.radians(h_angle)
    v_angle_rad = np.radians(v_angle)

    # Account for any refractive index
    h_angle_rad = arcsin((1/n_medium) * sin(h_angle_rad))
    v_angle_rad = arcsin((1/n_medium) * sin(v_angle_rad))

    # Calculate the ground footprint of the image
    ground_width = 2 * altitude * np.tan(h_angle_rad / 2)
    ground_height = 2 * altitude * np.tan(v_angle_rad / 2)

    # Calculate pixel size in meters
    pixel_width = ground_width / image_width
    pixel_height = ground_height / image_height

    # Calculate the corner coordinates
    ulx = camera_pos[0] - (ground_width / 2)
    uly = camera_pos[1] + (ground_height / 2)
    lrx = camera_pos[0] + (ground_width / 2)
    lry = camera_pos[1] - (ground_height / 2)

    # Calculate area
    area = ground_width + ground_height

    return ulx, uly, lrx, lry, area

# Example usage:
camera_pos = (300000, 5000000)  # Camera position in projected coordinates
altitude = 100  # Altitude in meters
h_angle = 60  # Horizontal field of view in degrees
v_angle = 45  # Vertical field of view in degrees
image_width = 1920  # Image width in pixels
image_height = 1080  # Image height in pixels

ulx, uly, lrx, lry = ray_trace_corners(camera_pos, altitude, h_angle, v_angle, image_width, image_height)
print(f"Upper-left corner: ({ulx}, {uly})")
print(f"Lower-right corner: ({lrx}, {lry})")

Creating the GeoTIFF with Computed Coordinates:

Using the coordinates calculated above, you can generate a GeoTIFF as shown in the first example:
```
create_geotiff('input_image.jpg', 'output_image.tiff', ulx, uly, lrx, lry)
```

What to expect:

The result of this process is a GeoTIFF image with georeferenced coordinates embedded in its metadata. This allows the image to be accurately placed within a GIS, enabling spatial analysis and visualization.

What makes it difficult:

Navigation Uncertainty: The accuracy of the GeoTIFF is dependent on the precision of the camera's coordinates and the navigation data. Any uncertainty in these parameters can lead to errors in the georeferencing process.
Time Consumption: Processing large datasets or high-resolution images can be time-consuming, especially when generating multiple GeoTIFFs.

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