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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) - PowerPoint PPT Presentation
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Timed Fast Exact Euclidean Distance (tFEED) Maps
January 2005
Theo SchoutenHarco 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( (xq,yq),(xp,yp)) = M(|xq-xp|,|yq-yp|)
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
• 76800 pixels13942 object 1725 border
• 86487 updates, 8.4 ms• 290771 updates, 5.7 ms• 179373 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 imagethan the scan methods
tFEED
Video generation
• generated with Macromedia Flash– vector oriented– preserve color maps
tFEED
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 Dfixed
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 dmax
– moving object has no influence outside rectangle
• in rectangle Dfixed+moving
• copy with min operator into Dfixed
tFEED
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
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