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We devise a new fusion technique for single-channel SAR images and optical images. First, a statistical model for both individual and joint distribution of SAR and optical images is provided. Then the corresponding maximum likelihood (ML) classifier is derived, and lower and upper bounds to classification performance are introduced. An optimised technique for ML joint segmentation and classification is proposed, showing results close to the upper bound. Finally, the effectiveness of the fusion of SAR and optical images is investigated quantitatively, showing the performance improvement with respect to using either sensor alone.