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Linear Color: Applying the Forward Matrix

Now that we know how to create a 3×3 linear matrix to convert white balanced and demosaiced raw data into XYZ_{D50}  connection space – and where to obtain the 3×3 linear matrix to then convert it to a standard output color space like sRGB – we can take a closer look at the matrices and apply them to a real world capture chosen for its wide range of chromaticities.

Figure 1. Image with color converted using the forward linear matrix discussed in the article.

Continue reading Linear Color: Applying the Forward Matrix

Color: Determining a Forward Matrix for Your Camera

We understand from the previous article that rendering color with Adobe DNG raw conversion essentially means mapping raw data in the form of rgb triplets into a standard color space via a Profile Connection Space in a two step process

    \[ Raw Data \rightarrow  XYZ_{D50} \rightarrow RGB_{standard} \]

The first step white balances and demosaics the raw data, which at that stage we will refer to as rgb, followed by converting it to XYZ_{D50} Profile Connection Space through linear projection by an unknown ‘Forward Matrix’ (as DNG calls it) of the form

(1)   \begin{equation*} \left[ \begin{array}{c} X_{D50} \\ Y_{D50} \\ Z_{D50} \end{array} \right] = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix} \left[ \begin{array}{c} r \\ g \\ b \end{array} \right] \end{equation*}

with data as column-vectors in a 3xN array.  Determining the nine a coefficients of this matrix M is the main subject of this article[1]. Continue reading Color: Determining a Forward Matrix for Your Camera