Watershed of a Continuous Function

Abstract : The notion of watershed, used in morphological segmentation, has only a digital definition. In this paper, we propose to extend this definition to the continuous plane. Using this continuous definition, we present the watershed differences with classical edge detectors. We then exhibit a metric in the plane for which the watershed is a skeleton by influence zones and show the lower semicontinuous behaviour of the associated skeleton. This theoretical approach suggests an algorithm for solving the eikonal equation: ‖∇ƒ‖ = g. Finally, we end with some new watershed algorithms, which present the advantage of allowing the use of markers and/or anchor points, thus opening the way towards grey-tone skeletons.
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Laurent Najman, Michel Schmitt. Watershed of a Continuous Function. Signal Processing, Elsevier, 1994, 38 (1), pp.99-112. 〈10.1016/0165-1684(94)90059-0〉. 〈hal-00622129〉

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