This paper introduces an image decomposition and simplification method based on the constrained connectivity paradigm. According to this paradigm, two pixels are said to be connected if they comply to a series of constraints defined in terms of simple measures such as the maximum grey level differences over well-defined pixel paths and regions. The resulting connectivity relation generates a unique partition of the image definition domain. The simplification of the image is then achieved by setting each segment of the partition to the mean value of the pixels falling within this segment. Fine to coarse partition hierarchies (and therefore images of increasing degree of simplification) are produced by varying the threshold value associated with each connectivity constraint. The paper also includes a generalisation to multichannel images, applications, a review of related image segmentation techniques, and pseudo-code for an implementation based on queue and stack data structures.