Gray-level co-occurrence matrix (GLCM) is one of the most used methods for texture representation. As it can be computed only from gray-level images, a significant amount of information that could be provided by color is totally ignored. We propose a generalization of GLCM from gray level to hue saturation value color space, which we refer to as modified integrative color intensity co-occurrence matrix (MICICM). To reach such a generalization, a mapping function, which determines for each pixel value the bin it falls into, is needed. In many previous studies, this function uses a hard mapping where all pixel values that fall in a bin are considered as the same, regardless of their values. This presents a number of drawbacks. To fix them, we introduce a color and gray-level mapping scheme based on a set of weight assignment functions we propose. In our scheme, each pixel is mapped to more than one possible color (and gray-level) bin, to avoid the drawbacks of hard mapping. Although a fuzzy-based scheme has been recently proposed, our MICICM has successfully outperformed it and those of the state of the art. Our findings make several noteworthy contributions to image representation.