Conventional contrast enhancement algorithms use complicated nonlinear mapping functions with parameters specified manually. In this paper, a parameter-free piecewise linear transformation and monotone piecewise cubic interpolation are used for color image contrast enhancement. The Gaussian mixture model is used to divide luminance histogram of input color image into multiple sub-histograms. Each sub-histogram is mapped linearly or nonlinearly to a portion of available output dynamic range proportional to its extent and the number of its pixels. The proposed algorithm has more controlled contrast enhancement than conventional algorithms to preserve natural outlook and local details in the input color image. This is done by considering brightness histogram preservation of input image by proposed algorithm, due to considering extent of each sub-histogram for allocating a portion of output dynamic range to it. Experimental results show that the proposed algorithm produces better or comparable contrast-enhanced images with natural outlook than several conventional algorithms on various types of images.