In this paper, we prove that the scale-space of a onedimensional gray-scale signal based on morphological filterings satisfies the causality (no new feature points are created QS scale gets larger). For this we refine the standard definition of zero-crossing so QS to allow signals with certain discontinuity, and use them to define feature points. This new definition of zero-crossing agrees with the standard one in the case of functions with second order derivative. The previous work by Chen and Yan [l] used an inappropriate definition of feature points, which led them t o an incorrect proof of the causality. Our causality results, unfortunately, does not apply to Q more general two-dimensional gray scale image. Causality results on the standard morphological blurring [2], obtained as byproduct, are also included.

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