Part 1: Theoretical Core of Image Processing that Interprets Drone Imagery

Interior Orientation

Interior Orientation

It is the internal geometry of a camera or sensor as it existed at the time of data capture. It is primarily used to transform the image pixel coordinate system or other image coordinate measurement system to the image space coordinate system(local pixel position to the global pix position system). It is the relation between the pixel coordinate system (x0,y0) and the image coordinate system(X, Y).

Internal Orientation is set up by measuring the fiducial mark. Data from the camera calibration is used to set up the camera file for the interior orientation. Fiducial marks are measured manually. The purpose of interior orientation is to establish a relationship between pixel coordinate system and the image coordinate system. The relation between pixel and image coordinates is almost constant. Fiducial mark is registered onto the film by projecting an image of the mark through a small lens.

Coordinate system transformation is the most elementary operation. From interior orientation to relative orientation, to absolute transformation is based on the coordinate system transformation. They are uniform, scale, rotation, reflection, stretch(non-uniform scale factors), etc. Coordinates are computed by 2D transformation, whose parameters are estimated using the measured and calibrated position of the fiducial marks.

The internal geometry is defined via terms:

Principal point

Focal length

Fiducial marks

Lens distortion

Principal Points

Object location with X0 and Y0.

Mathematically it is defined as the intersection of the perpendicular line through the perspective center of the image plane. It is the image position where the optical axis intersects the image plane. This is calibrated in two forms(to see the camera calibration report).

1. Principal point of autocollimation: The principal point is the principal point of autocollimation (PPA). It is defined as the image position where the optical axis intersects the image plane.
2. Principal point of symmetry: The principal point of symmetry (POS) is also known as the calibrated principal point. It is the point on the image where a ray of light traveling perpendicular to the image plane passes through the focal point of the lens and intersects the film.
3. The principal point of symmetry is used to compensate for the lens distortion.

Focal Length

The length from the principal point to the perspective center is called the focal length. The plane is commonly referred to as the focal plane. (Add the camera details) Prior to conducting any photogrammetry project (drone flight), the focal length is calibrated accurately.

Fiducial Marks

Marks at the corner of the imagery

It involves determining the image position of the principal point for each image in the project. The image position of the fiducial marks are measured on the image and subsequently compared to the calibrated coordinates of each fiducial mark. The measured image coordinates of the fiducial marks are referenced to pixel or file coordinate system. The pixel coordinated system has an x coordinate (column) and y coordinate (row). The origin of the pixel coordinate system is the upper left corner of the image.

The relationship between the pixel coordinate system and the image coordinate system is defined are as follows:

The coefficients required to transform pixel coordinate measurement to the image coordinates ie x and y image coordinate associated with the calibrated fiducial marks and the X and Y pixel coordinate of the measured fiducial marks are used to determine six affine transformation coefficients.

x = a1 + a2X + a3Y

y = b1 + b2X + b3Y

The quality of the two-dimensional affine transformation is represented using a root mean square error (RMSE) indicates poor correspondence. This can be attributed to film deformation, poor scanning quality, out-of-date calibration information or image mismeasurement.

Lens Distortion

Radial and Tangential Lens distortion in camera frame.

The position accuracy of the image points located on the image plane; the light rays passing through the lens are bent, thereby changing direction and intersecting the image plane at positions deviant from the normal. Lens distortion value is provided as a function of radial distance from the principal point or field angle.

1. Radial Lens distortion ⃤ r : Radial lens distortion causes images points to be distorted along radial lines from the principal points(it is also known as symmetric lens distortion).
2. Tangential Lens distortion ⃤ t : Distortion occurs at right angle to the radial line from the principal point.

Thank you, for reading the article. In my next article, I'll cover External Orientation which is another theoretical core part of image processing. Follow the publication for the updates. Also, benefit from the shared public projects on Indshine that you don’t have to log in to see and contribute to get yourself noticed among industry people