Weighted Median Filtering for Terrain and Contour Generalization

Abstract. When working with terrain elevation data, as in image processing, it is often desirable to smooth the data, for purposes such as map generalization or removal of noise. Median filtering is one common technique that can be used for this purpose. It differs from linear filtering techniques like local averaging or Gaussian blurring by its ability to smooth while retaining sharp edges in an image. When applied to elevation data, this means that median filtering can better preserve steep slopes and cliffs while otherwise reducing noise or excessive detail in the terrain. However, median filtering as typically applied can also introduce new artifacts, such as lopping off the tops of peaks and ridges to create flat plateaus that don’t exist in the original landscape. A lesser known technique, a weighted median filter, can reduce or eliminate these artifacts. This method shows promise as a way to generalize digital elevation models, as well as their associated contour lines. It can also be used to smooth hillshaded images, preserving the sharp transition in shading that occurs across ridges. And due to its ability to retain discontinuities in the data, it can be used to locate latent terracing effects hidden in elevation data, which may represent real terrain features or may indicate artifacts of the processing methods used to generate the data.