Disparity

Definition

The disparity is the horizontal displacement between a pair of corresponding pixels in the left and right image of a rectified stereo pair: $d=x_1-x_2$.

Depth from disparity

$$\frac{z-f}{b-d}=\frac{z}{b}⟹z=\frac{fb}{d}$$

$f$: focal length (px), $b$: baseline, $d$: disparity (px).

Intuition

Close objects shift a lot, far objects hardly move: $z\propto 1/d$. A small disparity error causes a depth error of roughly $\Delta z\approx \frac{z^2}{fb}\Delta d$, so a short baseline and far points give large errors.

Our brain uses the disparity between the two eyes to perceive depth. In the simple stereo system of Lecture 2.1 the disparity is $x_l-x_r=f\frac{T_x}{Z}$, the same formula.

Appears in

• Lecture 4, Disparity and Depth
• Lecture 4, Limitations: foreshortening
• Lecture 4, Worked Examples
• Lecture 2.1, Simple stereo system

Related concepts

• Image Rectification
• Stereo Matching
• Triangulation