Decolorization is to convert a color image into a gray scale image while preserve image features like salient structure and chrominance contrast. The sign of the color contrast is crucial for the decolorization algorithm and is usually determined in existing works by giving a strict defined color order or twomode weak order. In this paper, a fast computation on color order is achieved via a simple global mapping which is introduced in a linear parametric model using an extended structure transfer filter. The values of the parameters are obtained via an elegant approximation method. A local decolorization algorithm is finally designed on basis of the global linear mapping so that both color and spatial information are preserved robustly and accurately. Experimental results show that the proposed decolorization algorithms obtain a good performance among existing quality metrics for the decolorization. In addition, the proposed global decolorization algorithm is friendly to mobile devices with limited computational resource.