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This paper deals with connected operators based on reconstruction process. Connected operators are filtering tools that act on the connected components of the space where the image is constant, the so-called “flat zones”. Intuitively, connected operators can remove boundaries between flat zones but cannot add new boundaries nor shift existing contours. After reviewing the filtering strategy, new operators are proposed to perform size and motion simplification. In the case of size simplification, the proposed approach allows a better preservation the contrast of maxima or minima that have not been totally simplified by the filtering process. In the case of motion simplification, two applications are presented: motion detection for maxima/minima and sequence simplification to improve the coding efficiency of standard encoders.