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The camera baseline is the separation between the camera centers of two views. For centers $C_L,C_R$, its length is $B=\Vert C_R-C_L\Vert$. It measures translation, so turning a stationary camera without moving its camera center does not create a nonzero camera baseline. A known camera baseline supplies the length scale in stereoscopic triangulation.^[ref]

In the ideal aligned model with matched coordinate origins, stereo disparity satisfies $d=fB/Z$. For focal length 800 pixels and depth 5 metres, a camera baseline 0.10 metres gives 16 pixels; doubling the camera baseline gives 32 pixels. With unchanged disparity precision, the larger separation improves depth sensitivity. It can also increase occlusion in stereo vision and reduce overlap of the views. Finally, multiplying both $B$ and all reconstructed lengths by the same factor leaves the projections unchanged: a small reprojection error alone cannot certify the metric scale.

The camera center is the center of projection in an ideal perspective camera model: the common origin of its viewing rays. It is a point in scene space, distinct from a principal point, which is an image-plane coordinate. Two distinct camera centers define the camera baseline used by stereoscopy.

For the calibrated perspective projection model $q\sim K(RP+t)$, where $R$ is a rotation matrix, the camera center $C$ satisfies $RC+t=0$. HenceThis follows by applying the inverse rotation to the zero camera-space position.^[ref] For $R=I$ and $t=(-0.1,0,0)$ metres, $C=(0.1,0,0)$ metres: the translation parameter is not directly the world-space camera center. Rotating about that center changes viewing directions without creating a new triangulation baseline.

A depth map assigns a distance-related value to each accepted image location. The geometry must specify whether this means depth along the camera axis or Euclidean distance along the viewing ray. Units, missing values and the coordinate frame are also part of the representation. In calibrated stereoscopy, converting a disparity map through the camera geometry produces depth estimates.^[ref]

For an ideal camera, suppose a point has coordinates $(X,Y,Z)=(1,0,2)$ metres. Its axial depth is two metres, but its Euclidean distance from the camera center is $\sqrt{5}$ metres. The same scene can thus yield different valid numerical maps under different conventions. A missing stereo correspondence requires an invalid-location marker rather than a fabricated depth. Camera calibration and measurement uncertainty determine how confidently accepted values describe the scene.

Epipolar geometry describes the projective relationship between two camera views. A scene point away from the camera baseline and the two camera centers determine an epipolar plane. Its intersections with the image planes are corresponding epipolar lines. Knowing one image point therefore constrains its partner to a line rather than the whole second image.^[ref]

With image points in homogeneous coordinates, a fundamental matrix $F$ expresses the constraintFor an ideal horizontally rectified pair this reduces to equality of image-row coordinates, while horizontal displacement remains free and carries stereo disparity. A line constraint does not determine depth: many scene points along one viewing ray satisfy the geometry. Correct stereo correspondence selects a partner, and camera calibration then supports metric stereoscopic triangulation.

An epipolar plane contains both camera centers and a scene point. For a scene point away from the camera baseline, these three points determine a unique plane. Its intersection with each image plane is an epipolar line, so corresponding image points lie on the two traces of the same plane.^[ref]

To see the geometry directly, take camera centers $C_L=(0,0,0)$ and $C_R=(B,0,0)$, and a scene point $P=(X,Y,Z)$. The plane they span satisfies $Zy-Yz=0$. For parallel forward-facing image planes at common focal length $f$, its traces have $y=fY/Z$ in both views. This is why an ideal horizontal stereo pair places corresponding image points on the same row.

Moving the scene point within that plane leaves its epipolar lines unchanged. A single trace therefore cannot recover depth. If the scene point lies on the baseline, the three defining points are collinear and no unique epipolar plane is determined. These degeneracies explain both the usefulness and the limits of line-based stereo correspondence.

The fundamental matrix $F$ encodes the epipolar geometry of two distinct camera centers using image homogeneous coordinates. For matching image points $x_L,x_R$, the ideal constraint isThus $F{x}_L$ is an epipolar line in the right image, while $F^{\mathsf{T}}{x}_R$ is an epipolar line in the left image. A nondegenerate fundamental matrix has matrix rank two and is defined only up to nonzero scale.^[ref]

For an ideal horizontally aligned stereo pair with matched image coordinate origins, one possible scale convention isPutting $x_L=(20,50,1{)}^{\mathsf{T}}$ gives $F{x}_L=(0,-1,50{)}^{\mathsf{T}}$, so the right point must satisfy $v_R=50$. Its horizontal coordinate remains free: the constraint reduces the search to a line but does not determine stereo disparity or depth. Repeated texture can still make stereo correspondence ambiguous.

With camera calibration matrices $K_L,K_R$ and relative pose $(R,t)$ under the convention $X_R=R{X}_L+t$, the relation is $F=K_R^{-\mathsf{T}}[t{]}_{\times }R{K}_L^{-1}$, where $[t{]}_{\times }v=t\times v$. Translation direction affects the geometry, but multiplying $t$ by a scalar only rescales $F$: the fundamental matrix alone cannot establish a metric camera baseline. Pure rotation has $t=0$ and requires a different geometric description.^[ref]