A Linear System Form Solution to Compute the Local Space Average Color

Joaquín Salas

Carlo Tomasi

Instituto Politécnico Nacional


Duke University




We present an alternative to the iterative method for computing the local space average color introduced by Ebner[1]. We show that when the problem is framed as a linear system and the resulting series is solved, there is a solution based on LU decomposition that reduces the computing time by   at least an order of magnitude.



The gray-world is too bold an assumption about how the world looks in general. However, there may be the need to make assumptions to gain intuition in order to build more comprehensive models. In this document, we present an alternative form solution to Ebner's iteration scheme [1]. In our proposal, we formulate the problem as a linear system and solve the resulting series. We show that the resulting matrices are sparse and hence admit a compact representation and a fast solution via LU factorization. Furthermore, we show that the computing requirements are reduced at least by an order of magnitude. Also, in this document we are only concerned with the computational aspects of the problem. A method to compute a constant descriptor for color, including chroma and lightness, is out of the scope of the present research, and it is still one of the most fascinating open problems in the field of Computer Vision. Here are the MATLAB [Code] and the [Paper].

Joaquin Salas and Carlo Tomasi. A Linear System Form Solution to Compute the Local Space Average Color. Machine Vision and Applications. No. 138. 2013 [PDF].










Office Environment. Results of the algorithm for the same set of images used by Ebner [1]. The columns show the original, the local space color average, and the corrected image. With kind permission from Springer Science and Marc Ebner.