In this paper, different texture descriptors are proposed for the automatic classification of skin lesions from dermoscopic images. They are based on color texture analysis obtained from (1) color mathematical morphology (MM) and Kohonen Self-Organizing Maps (SOM) or (2) Local Binary Patterns (LBPs), computed with the use of local adaptive neighborhoods of the image. Neither of these two approaches need a previous segmentation process. In the first proposed descriptor, the adaptive neighborhoods are used as structuring elements to carry out adaptive mathematical morphology operations which are further combined by using Kohonen SOM, and it has been compared with a non-adaptive version. In the second one, the adaptive neighborhoods enable geometrical feature maps to be defined, from which Local Binary Patterns (LBP) histograms are computed. Also, it has been compared with a classical LBP approach. A ROC analysis of the experimental results shows that the adaptive neighborhood-based LBP approach yields the best results. It outperforms the non-adaptive versions of the proposed descriptors and the dermatologists' visual predictions.