The camera characterization procedure has been recognized as a convenient methodology to correct color recordings in cultural heritage documentation and preservation tasks. Instead of using a whole color checker as a training sample set, in this paper, we introduce a novel framework named the Patch Adaptive Selection with K-Means (P-ASK) to extract a subset of dominant colors from a digital image and automatically identify their corresponding chips in the color chart used as characterizing colorimetric reference. We tested the methodology on a set of rock art painting images captured with a number of digital cameras. The characterization approach based on the P-ASK framework allows the reduction of the training sample size and a better color adjustment to the chromatic range of the input scene. In addition, the computing time required for model training is less than in the regular approach with all color chips, and obtained average color differences $\Delta E_{ab}^{*}$ lower than two CIELAB units. Furthermore, the graphic and numeric results obtained for the characterized images are encouraging and confirms that the P-ASK framework based on the K-means algorithm is suitable for automatic patch selection for camera characterization purposes.