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With the development of novel parallel architectures for image processing, the implementation of well-known image operators needs to be reformulated to take advantage of the so-called massive parallelism. In this work, we propose a general algorithm that implements a large class of nonlinear filters, called stack filters, with a 2D-array processor. The proposed method consists of decomposing an image into bitplanes with the bitwise decomposition, and then process every bitplane hierarchically. The filtered image is reconstructed by simply stacking the filtered bitplanes according to their order of significance. Owing to its hierarchical structure, our algorithm allows us to trade-off between image quality and processing time, and to significantly reduce the computation time of low-entropy images. Also, experimental tests show that the processing time of our method is substantially lower than that of classical methods when using large structuring elements. All these features are of interest to a variety of real-time applications based on morphological operations such as video segmentation and video enhancement.