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

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

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

tFEED 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( (x q,y q ),(x p,y p )) = M(|x q -x p |,|y q -y p |) M can contain any non-decreasing f(ED) square (ED), floating point, rounded integer

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

tFEED Search optimization pixels object 1725 border updates, 8.4 ms updates, 5.7 ms updates, 4.5 ms

tFEED 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

tFEED Video generation generated with Macromedia Flash –vector oriented –preserve color maps

tFEED tFEED video distance maps D fixed+moving = min { D fixed, D moving } FEED on fixed objects per frame original FEED, but: –initialize with D fixed –B  O moving –up to d max in D fixed additional object does not increase max distance

tFEED Scan methods video distance maps the scan methods need a rectangle: –bounding box of moving object, extended with d max –moving object has no influence outside rectangle in rectangle D fixed+moving copy with min operator into D fixed

tFEED Video results tFEED factor 6 faster than FEED/frame factor 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

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

tFEED 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

tFEED The End