Projective Geometry
Definition
The mathematical framework describing how 3D points are mapped to 2D image coordinates through the camera model. Lines remain lines, but distances and angles are not generally preserved. Parallel lines meet at a vanishing point.
- Field
- Photogrammetry / image-based measurement
- Preserves
- Straight lines
- Does not preserve
- Distances, angles in general
- Key feature
- Vanishing point for parallel lines
Common questions
Why does projective geometry matter for measuring objects from crime scene photographs?+
A camera's perspective projection distorts distances and angles unless corrected, so an analyst cannot simply measure lengths directly off an uncalibrated photograph. Projective geometry provides the mathematical model needed to relate 2D pixel positions back to real 3D measurements, typically using known reference points or camera calibration.
What is a vanishing point and why is it useful in forensic photogrammetry?+
A vanishing point is where a set of parallel lines in the real world appear to converge in the 2D image due to perspective. Because its location depends on the camera's orientation, identifying vanishing points from scene features such as building edges lets an analyst recover camera geometry even without a physical calibration target.
Related terms
- Camera Calibration
- The process of determining the camera's intrinsic parameters: focal length, principal point, and lens distortion coefficients. Calibration can be done from a...
- Homography
- A 3x3 projective transformation matrix that maps one plane to another. For a flat scene (a floor, a wall, a road surface),...
- Structure-from-Motion (SfM)
- A photogrammetric technique in which overlapping images from a drone or camera, processed by software, generate a three-dimensional point cloud and textured...
- Uncertainty Propagation
- The mathematical process of carrying measurement errors through a calculation to estimate the error in the final result. For photogrammetric measurements, it...
- Vanishing Point
- The image point where a set of parallel real-world lines converges due to perspective. Identifying vanishing points for multiple sets of parallel...