Photometric calibration

Geometric calibration: This corresponds to mapping a scene point \({\bf x} \in \mathbb{R}^3\) onto the image plane \({\bf u} \in \Omega\). Most widely used being pinhole camera model

Photometric calibration: This calibration takes into account the actual image formation pipeline at the image plane. i.e, this calibration mathematically formulates right from irradiance recieved at a photon receptor on the camera pixel sensor to the corresponding observed pixel intensity.

If \({B}\) denotes irradiance, \(t\) denotes exposure time of shutter, \({V}\) denotes lens attenuation (vignetting) then we have and \(G\) denotes non-linear response function:

\[I({\bf x}) = G(t {V}({\bf x}) {B}({\bf x}))\]

where \(I({\bf x})\) is the pixel intensity value at pixel location \({\bf x} \in \Omega\). Denote \(I’({\bf x}) := t {B}({\bf x}) = \frac{G^{-1}(I({\bf x}))}{V({\bf x})}\). Using naming convention as in [1], \(I’\) is the photometrically corrected image. Also, note that inverse of \(G\) is well defined since, \(G\) is a monotonically increasing function.