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Timed Fast Exact Euclidean Distance (tFEED) Maps

January 2005. Timed Fast Exact Euclidean Distance (tFEED) Maps. Theo Schouten Harco Kuppens Egon van den Broek. Distance transformation. distance map D(p) = min { dist(p,q), q  O }. Euclidean distance. not by local operations using scans approximations (city-block, chamfer)

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Timed Fast Exact Euclidean Distance (tFEED) Maps

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  1. January 2005 Timed Fast Exact Euclidean Distance (tFEED) Maps Theo Schouten Harco Kuppens Egon van den Broek

  2. Distance transformation • distance map D(p) = min { dist(p,q), q  O }

  3. Euclidean distance • not by local operations using scans • approximations (city-block, chamfer) • disconnected Voronoi tile • semi-exact ED often wright sometimes wrong

  4. Principle of FEED • D(p) = if (p  O) then 0 else  for each q  O for each p: D(p) = min ( D(p), ED(q,p)) • inverse of definition • reduce number of q  O to feed distances:only the border pixels of O, not the “inside” pixels • ED( (xq,yq),(xp,yp)) = M(|xq-xp|,|yq-yp|)M can contain any non-decreasing f(ED)square (ED), floating point, rounded integer

  5. Speed up, bisection lines • reduce number of p to update per B • search and bookkeeping<time gained

  6. Search optimization • 76800 pixels13942 object 1725 border • 86487 updates, 8.4 ms • 290771 updates, 5.7 ms • 179373 updates, 4.5 ms

  7. Results • FEED is about factor 2 faster than Shih & Wu 2-scan ED (CVIU 2004) • few % wrong, error 50% of chamfer 3,4 • FEED uses less memory • FEED is about factor 2 slower than Borgefors chamfer 3,4 (CVGIP, 1986) • FEED time depends more on content of image than the scan methods

  8. Video generation • generated with Macromedia Flash • vector oriented • preserve color maps

  9. tFEED video distance maps • Dfixed+moving = min { Dfixed, Dmoving } • FEED on fixed objects • per frame original FEED,but: • initialize with Dfixed • B  Omoving • up to dmax in Dfixedadditional object does not increase max distance

  10. Scan methods video distance maps • the scan methods need a rectangle: • bounding box of moving object, extended with dmax • moving object has no influence outside rectangle • in rectangle Dfixed+moving • copy with min operator intoDfixed

  11. Video results • tFEED factor 6 faster than FEED/frame • factor 3 - 4 faster than adapted Shih & Wu (semi) ED • 20-50% faster than adapted Borgefors chamfer 3,4 • which is often faster than the city-block which gets a larger rectangle

  12. Video example • further developments: • encoding fixed objects for faster search in FEED • faster locating the moving object • more effect on tFEED

  13. tFEED conclusions • DT’s (FEED, scan methods)adapted for fast generation of distance maps for video • tFEED: • gives exact ED • faster than city-block, chamfer 3,4 other (semi) ED • more complicated to implement

  14. The End

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