A Linear System Form Solution to Compute the Local Space Average Color
Joaquín Salas 
Carlo Tomasi 
Instituto Politécnico Nacional jsalasr@ipn.mx 
Duke University tomasi@cs.duke.edu 
Abstract:
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.
Description:
The grayworld 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].
Gallery:



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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. 