3D Computer Vision

Classical and neural 3D computer vision — learned from scratch, derived from geometry. Cameras, epipolar geometry, structure from motion, point clouds, and neural scene representations.

3D computer vision from first principles — Part 1

Homogeneous coordinates and the projective plane derived via Gaussian elimination

Homogeneous coordinates and the projective plane derived from Gaussian elimination — no prior projective geometry assumed.

Jul 7, 2026

Madhav Prashanth Ramachandran

3D Computer Vision from First Principles — Part 2

Projective Duality and Conics in \(\mathbb{P}^2\)

Projective duality derived from the symmetry of the incidence condition, and an introduction to conics in the projective plane.

Jul 13, 2026

Madhav Prashanth Ramachandran

3D Computer Vision from First Principles Part 3

The Camera Matrix \(P = K[R \mid \mathbf{t}]\)

Deriving the camera matrix from similar triangles to \(P = K[R \mid \mathbf{t}]\), stage by stage from first principles.

Jul 15, 2026

Madhav Prashanth Ramachandran

3D Computer Vision from First Principles — Part 4

Homographies

Homographies derived from the camera matrix restricted to a plane — what they preserve, how to estimate them, and why they are everywhere in computer vision.

Jul 20, 2026

Madhav Prashanth Ramachandran

3D Computer Vision from First Principles — Part 5

Projective Three-Space \(\mathbb{P}^3\)

Points, lines, planes, and incidence in projective three-space — derived from linear algebra, no prior projective geometry assumed.

Jul 21, 2026

Madhav Prashanth Ramachandran

3D Computer Vision from First Principles — Part 6

Camera Calibration

Estimating a camera’s intrinsic parameters from images of a known planar pattern.

Jul 24, 2026

Madhav Prashanth Ramachandran