Depth Ambiguity

Definition

Depth ambiguity: during image formation, depth information is lost. From a single image we can’t tell if an object is small or just far away. This makes 3D reconstruction from one image ill-posed.

Formula

$$x=f\frac{X}{Z}=f\frac{kX}{kZ}\text{for any }k>0$$

An object $k$ times larger and $k$ times further away projects to the same image point.

Intuition

Every pixel corresponds to a whole viewing ray from the camera center. All 3D points on that ray land on the same pixel.

Ways around it:

• More views: stereo, Multi-View Stereo and Structure from Motion recover depth by triangulation.
• Learned priors: monocular depth estimation learns depth from visual cues in large datasets. It still fails on illusions like the Ames room.

Appears in

• Lecture 1, Challenges: Depth Anything V2 on the Ames room illusion
• Lecture 1, Stereo and depth: triangulation vs. monocular depth
• Lecture 2.1, Imaging geometry: camera → film is the only step that loses information
• Lecture 2.1, Worked Examples: a pixel without depth is only a ray
• Lecture 4, Recovering 3D: why two views are needed
• Lecture 4, Monocular depth: scale-invariant loss
• Lecture 3, Challenges: SfM is scale ambiguous, $u\simeq ({\alpha }^{-1}P)(\alpha X)$
• Lecture 10, Motivation: ill-posed single-view reconstruction calls for generative models

Related concepts

• Disparity
• Monocular Depth Estimation
• Triangulation
• Structure from Motion
• Pinhole Camera Model
• Projection Matrix
• Inverse Rendering
• Point Cloud