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In this work, we treat the problem of combined classification of a high spatial resolution color image and a lower spatial resolution hyperspectral image of the same scene. The problem is particularly challenging, since we aim for classification maps at the spatial resolution of the color image. Contextual information is obtained from the color image by introducing Color Attribute Profiles (CAPs). Instead of treating the `R', `G', and `B' bands separately, the color image is transformed into CIE-Lab space. In this color space, attribute profiles are extracted from the `L' band, which corresponds to the Luminance, while the `a' and `b' bands, which contain the color information, are kept intact, and the resulting images are transformed back into RGB space. The spectral information is obtained from the hyperspectral image. A Composite Decision Fusion (CDF) strategy is proposed, combining a state-of-the-art kernel-based decision fusion technique with the popular composite kernel classification approach. Experiments are conducted, using simulated data and a real multisource dataset containing airborne hyperspectral data and orthophotographic data from a suburban area in Belgium. These experiments show that our CAPs perform well with respect to other approaches for extracting attribute profiles from high resolution color images, and that the proposed CDF strategy produces meaningful results with respect to concatenation and the highlighted state-of-the-art approaches for combining multisource data.