Pinhole Camera Model

Definition

A pinhole camera (camera obscura) lets light through a single small hole onto an image plane. Every scene point is projected along a straight line through the pinhole, which gives a linear perspective image. In the equivalent model used in computer vision, the image plane is placed at distance $f$ in front of the camera center.

Perspective projection

$$x=f\frac{X}{Z}y=f\frac{Y}{Z}$$

Image size is inversely proportional to depth: twice as far, half as big.

A real pinhole is too dark, and a larger hole makes the image blurry. A lens solves this and still gives the same linear perspective: a lens with focal length $f$ focused at infinity is equivalent to a pinhole at distance $f$. That is why computer vision uses the pinhole model and ignores lenses unless images have to be undistorted.

Trap

The projection is not linear because of the division by $Z$. To write it as a matrix, we need homogeneous coordinates.

Appears in

• Lecture 2.1, Projection onto the picture plane: derivation with similar triangles
• Lecture 2.1, Pinhole camera: camera obscura, pinhole size trade-off
• Lecture 2.1, Pinhole vs. lens model
• Lecture 2.1, Worked Examples: exam-style calculations
• Lecture 1, Depth Ambiguity

Related concepts

• Focal Length
• Projection Matrix
• Orthographic Projection
• Depth Ambiguity