The paper makes a survey of the morphological tools which are useful for image simplification and segmentation. It starts presenting the connected filters, which have the unique feature to simplify the images without blurring the contours of the remaining objects. Such filters may be constructed on several criteria : size, contrast, complexity or type of motion. In the case where geometric criteria are used, it is possible to base a scale-space description of the images on a series of increasing filters. This is most useful when applied to a gradient image : successive filters will progressively fill the valleys of the gradient image and a watershed transform applied on these images will produce segmentations which are coarser and coarser. These segmentations have a tree structure : from a finer level to a coarser level, only fusions take place.

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