Let the measured colour of channel i that the camera of the kth view receives be denoted as Mi(k). Suppose that we want to correct the colour of jth view into the colour of kth view. It can be proven [12] that there exists a 3x3 transformation matrix Tj->k that converts the colour of one view to the other:
For the evaluation of Tj->k colour correspondences between the two images are needed. We will use the registered range views that the images correspond to in order to get these correspondences. Specifically we calculate the points (Xj, Xk) that overlap in the two range views. With the registration algorithm [1] we then compute the pixels that these points are projected in the images, (Pj, Pk), |Pj| = |Pk|. We expand each of these pixels in a neighbourhood (e.g. 5x5) in order to enrich our selection because the spatial resolution is usually smaller than the pixel resolution. This enriches the selection of pixels for the calculation of the matrix.
The two images corresponding to two different views.
The
correspondences and their expansions are marked by black
The model after global correction. In circle is the area
where there are still visible some small artefacts at the boundary of the images