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

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