Projective Geometry & the Camera Model
Why a camera is a linear map, once you stop insisting on Euclidean coordinates.
A camera turns a 3D world into a 2D array of numbers, and the transformation is almost linear. The "almost" is the division by depth, and the whole apparatus of projective geometry exists to absorb it.
Most people meet this material as a sequence of matrices to memorise — , , — and come away able to write the pipeline without being able to say what any single symbol does. This topic is built the other way round: each concept isolates one operation, gives you a control to move it, and only then names the matrix that packages it.
- 01 Why homogeneous coordinates Foundation 1 interactive 9′ One extra number turns projection, translation and points at infinity into linear algebra. Repairs The belief that homogeneous coordinates are a notational trick for "adding a 1", rather than a change of space with real consequences.
- 02 The pinhole model Foundation 1 interactive 10′ Similar triangles, one division, and the reason depth is unrecoverable from one view. Repairs Treating projection as "the camera matrix" rather than as a division by depth that destroys exactly one degree of freedom per pixel.
- 03 Intrinsics: from metres to pixels Core 1 interactive 11′ K is an affine map applied after the division. Each entry is a fact about a sensor. Repairs Reading $K$ as "the camera matrix" without being able to say which entry changes when you crop, resize, or switch to a different lens.
- 04 Lens distortion Core 1 interactive 8′ The pinhole model is a lie about real lenses, and the correction is not invertible in closed form. Repairs Assuming distortion is a small cosmetic effect, and that "undistort" and "distort" are the same operation run backwards.