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Computer vision infers information about a scene from digital images or video. Tasks include recognizing objects, image segmentation and estimating three-dimensional geometry. A digital image records pixel measurements after image formation; lighting, viewpoint and occlusion therefore affect what can be inferred. A dark pixel can indicate a dark surface, a shadow or a surface facing away from the light.

For example, in rectified stereo vision with parallel cameras, horizontal disparity $d$ is related to depth by $Z=fB/d$, where $f$ is focal length in pixel units and $B$ is camera separation. similar triangles give the relation; a smaller disparity means greater distance. The relation requires corresponding scene points and calibrated geometry. Since $|dZ/dd|=fB/d^2$, a fixed disparity error produces much greater depth error for distant points. Camera calibration, correspondence and uncertainty are thus part of the computation, rather than details that can be ignored after acquiring a picture.

Jean Gallier is a computer scientist whose research connects mathematical foundations with computer programming and geometric applications. His earlier work includes formal verification, automated deduction and unification; his later interests include computer graphics, computer vision, robotics and the geometry of curves and surfaces.^[ref]

His Curves and Surfaces in Geometric Modeling: Theory and Algorithms by Jean Gallier develops geometric constructions with explicit mathematical foundations. For example, its account of affine maps separates the geometry of points from the linear maps acting on displacement vectors, a distinction useful when describing transformations in computer graphics.^[ref]

Homepage: www.cis.upenn.edu/~jean/

OpenCV is a software library for computer vision and image processing. Its camera-geometry tools connect observed pixel coordinates to models of imaging, including camera calibration, correction of lens distortion, stereo rectification and three-dimensional reconstruction.^[ref]

A checkerboard calibration target supplies known geometry that can be observed from several camera positions. Fitting the model compares detected image points with projected target points. The resulting reprojection error measures agreement in the image, rather than independently confirming every physical dimension of the reconstructed scene.

A simple perspective projection illustrates the distinction: in $u=fX/Z$, replacing $X$ and $Z$ by $kX$ and $kZ$ for $k>0$ leaves $u$ unchanged. This scale ambiguity of perspective projection means that image agreement alone cannot verify a chosen unit of length. A camera baseline or a target of known size supplies additional metric information. Using the library well therefore includes checking geometric assumptions and units, alongside the numerical fit.