To improve the performance of pixel-wise classification results for remotely sensed imagery, several contextual classification schemes have been proposed that aim at avoiding classification noise by local averaging. These algorithms, however, bear the serious disadvantage of smoothing the segment boundaries and producing rounded segments that hardly match the true shapes. In this contribution, we present a novel contextual classification algorithm that overcomes these shortcomings. Using a hierarchical approach for generating a triangular mesh, it decomposes the image into a set of polygons that, in our application, represent individual land-cover types. Compared to classical contextual classification approaches, this method has the advantage of generating output that matches the intuitively expected type of segmentation. Besides, it achieves excellent classification results.