Understanding Parallax in Photogrammetry: Principles and Methods
Parallax in Photogrammetry
Parallax: Displacement apparent at the position of an object with respect to a reference system, due to a change in the point of observation. This is a change in the position of an object in an image due to motion. For example, the change in position of a point in a picture due to the motion of an aircraft. Parallax exists because images taken from different locations will show longitudinal overlap.
Parallax Formula
[pa / B = f / (H-ha)]
[pa = (Bf) / (H-ha)]
Where:
- B = Distance of effect shots
- H = Height datum
- ha = Height of point A
- f = Focal length
The parallax is directly related to altitude. Greater altitude corresponds to greater parallax. If ha > hb, then pa > pb. Parallaxes are produced parallel to the flight path for each pair of frames.
Monoscopic Methods
- Direct measurement of dx and dy in the left and right frames (estimate of pa = x – x’).
- Two measurements for each pair, identifying conjugate points and their principals, and aligning the flight axes.
Coordinate System of the Flight Axis
The xx’ axis is the photographic flight axis, the line that contains the main points and their conjugates. Each frame (except the ends) should have two coordinate systems for measuring parallaxes. If the two pictures match w1 with w2 and x -> x’, y -> y’, parallaxes occur parallel to the axis of flight for each pair of frames.
General Photogrammetric Method
- Determining the shape of the beams from prospective internal data (internal focus).
- Determination of position in space of the beams from the prospective internal data (External Orientation). (Relative and Absolute Orientation).
- Identification of homologous ray couples (stereoscopic vision).
- Locate and materialize the intersection of the pairs of homologous rays (restitution).
Direct Determination
The exterior orientation parameters are determined at the time of taking the view.
Indirect Determination
The exterior orientation parameters are determined from other data that can be acquired before or after the time of making views (Coordinates of Support points).
Relative Orientation Analysis
Photo-coordinates are measured for 5 or more points in an analytic or digital restorer, refined, and conditions or coplanarity/collinearity are applied, obtaining the values of the guidance elements that make up the analytical model.
Analytical Photogrammetry
- Simultaneously with the registration of the terrain image, fiducial marks are recorded, which can be measured (Comparator System: xy) (pixel system: cf).
- Internal orientation, bilinear coordinate transformation: coordinate system measures -> Calibration System. Refinement of coordinates: systematic corrections.
- External orientation: Condition of collinearity.
- Relative orientation to coplanarity.
- Absolute orientation: Transfer of similarity.
- 3D Restitution: XYZ coordinates of points in the Object Reference System adopted.
Orientation
(Formation of the model.)
Absolute Orientation
(Adjustment to the reference model.)
Internal Data
Determined through the calibration process: focal length, principal point position with respect to fiducial marks, radial and tangential distortion, separating power, flatness of the focal plane, relative position between fiducial marks.
Terrestrial Sphere
Through the frames, we are looking for a flat representation of the Earth’s surface. The sphericity of the land grows radially with the decrease of focal distance. Negative distortion.
Atmospheric Refraction
Pressure decreases with H > 10 km (photograph). The rays are arcs of a curve, which moves the points away from their theoretical positions. Positive distortion. (Ar = Aresf-Arref).
Reconstructing the Beam
Each beam reconstruction must be done individually, its position in space homologous. The ray intersection problem is to reconstruct its current position in space against a certain system of reference. This is achieved through 3 displacements of the beams (in x, y, z) and 3 rotations: azimuthal (around z axis), broken length (y axis), transverse (x axis).