Abstract: Split-beam sonar binary images are inherently noisy and have large quantities of shot noise as well as many missing data points. We address the problem of their restoration via mathematical morphology. Conventional restoration techniques for these types of images do not make use of any of the spatial relationships between data points, such as a qualitative observation that outliers tend to have much larger distances to neighboring pixels. We first define an explicit noise model that characterizes the image degradation process for split-beam sonar images. A key feature of the model is that the degradation is split into two parts, a foreground component and a background component. The amount of noise occurring in the background decreases with distance from the underlying signal object. Thus outliers in the model have the same statistical properties as those observed in training data. Next we propose two different restoration algorithms for these kinds of images based respectively on morphological distance transforms and dilation with a toroid shaped structuring element followed by intersection. Finally we generalize to processing other kinds of imagery where applicable. !27
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