“…In the first case, all boundary end points with an empirically determined maximum distance of d = 20 pixels are linked to close gaps in between. In the second case, we apply a Euclidean distance transformation to the binary image, followed by a watershed transformation on the distance image using the implementation available in ImageJ according to Leymarie and Levine (1992). To remove implausible boundaries resulting from oversegmentation of the watershed segmentation, we apply a combination of different criteria for filtering boundary segments.…”
Section: Cell Boundary Segmentation and Region Filteringmentioning
“…In the first case, all boundary end points with an empirically determined maximum distance of d = 20 pixels are linked to close gaps in between. In the second case, we apply a Euclidean distance transformation to the binary image, followed by a watershed transformation on the distance image using the implementation available in ImageJ according to Leymarie and Levine (1992). To remove implausible boundaries resulting from oversegmentation of the watershed segmentation, we apply a combination of different criteria for filtering boundary segments.…”
Section: Cell Boundary Segmentation and Region Filteringmentioning
“…Borgefors proposes a chamfer DT using two raster scans, but only provides a much coarser approximation of the Euclidean metric. Leymarie [13] showed that, if implemented carefully, both approximations have similar computational cost. Ragnemalm [14] proposed an ordered propagation version of Danielsson's algorithm, as well as a raster scan implementation [17] using a minimal number of scans.…”
Section: D( P) = Min{dist( P Q) Q ∈ O}mentioning
confidence: 99%
“…In other words, belonging to a given Voronoi tile is not a local property: the tile to which a pixel belongs cannot always be deduced from the tiles to which its neighbors belong. Because they propagate the information locally from neighbor to neighbor, both raster scanning and propagation DT algorithms [2,13,14,17] will provide a wrong value for D(q) at Fig. 1.…”
Section: Voronoi Diagrams and Distance Transformationsmentioning
confidence: 99%
“…Leymarie [13] recommends dist E (dp + n) = dist E (dp) + 2 · dp x + 1 if n = (1, 0), dist E (dp + n) = dist E (dp) + 2 · dp y + 1 if n = (0, 1), etc. which only requires using additions, one shift and one increment.…”
Section: Iterationsmentioning
confidence: 99%
“…For n × n images, simple approximate algorithms such as Danielsson [2], chamfer DT [3] or Leymarie [13] have a fixed o(n 2 ) cost, regardless of the image content. Yamada's parallel algorithm [4] has a o(d · n 2 ) cost proportional to the maximum distance d found in the image.…”
Section: Complexity and Computational Costmentioning
We propose a new exact Euclidean distance transformation (DT) by propagation, using bucket sorting. A fast but approximate DT is first computed using a coarse neighborhood. A sequence of larger neighborhoods is then used to gradually improve this approximation. Computations are kept short by restricting the use of these large neighborhoods to the tile borders in the Voronoi diagram of the image. We assess the computational cost of this new algorithm and show that it is both smaller and less image-dependent than all other DTs recently proposed. Contrary to all other propagation DTs, it appears to remain o(n 2 ) even in the worst-case scenario.
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