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