Segmentation is a key stage in dermoscopic image processing, where the accuracy of the border line that defines skin lesions is of utmost importance for subsequent algorithms (e.g., classification) and computer-aided early diagnosis of serious medical conditions. This paper proposes a novel segmentation method based on Local Binary Patterns (LBP), where LBP and K-Means clustering are combined to achieve a detailed delineation in dermoscopic images. In comparison with usual dermatologist-like segmentation (i.e., the available ground-truth), the proposed method is capable of finding more realistic borders of skin lesions, i.e., with much more detail. The results also exhibit reduced variability amongst different performance measures and they are consistent across different images. The proposed method can be applied for cell-based like segmentation adapted to the lesion border growing specificities. Hence, the method is suitable to follow the growth dynamics associated with the lesion border geometry in skin melanocytic images.