The Hopfield network model associates an input pattern with trained patterns and is generally considered to be a pattern recognition system that completes missing pieces of the input image. In this paper the Morphological Hopfield Net associates segments in input patterns with trained pattern segments and is used to reconstruct known patterns degraded by noise by reconstructing the individual segments. A very simple Hopfield model is defined over an image space and consists of a large number of identical Hopfield networks, one about each pixel site, each with a local connectivity to a neighborhood of pixels. The weights are all 1 and the thresholds are adjusted to extreme values (max or min). It is shown that this Hopfield model is equivalent to a union of openings. Convergence occurs in only one iteration since the union of openings is idempotent.