Fast Multi Class Distance Transforms for Video Surveillance

January 2008

Theo SchoutenEgon van den Broek

Fast Multi Class DT for Video

Distance Transformation

•distance map D(p) = min { dist(p,q), q O }

Fast Multi Class DT for Video

Multi Class DT

•class map C(p) = C(q), q O, dist(p,q) == D(p)

Fast Multi Class DT for Video

Used original distance transformation

• CH11: city-block DT of Rosenfeld and Pfaltz• CH34: chamfer 3,4 of Borgefors• EDT4: 4-scan semi-exact EDT of Shih and Liu• EDT2: 2-scan semi-exact EDT of Shih and Wu• EDLT: EDT method of Maurer, Qi and Raghavan

– based on dimension reduction– proces first rows then columns– partial Voronoi diagram for each row, column

• FEED: or own EDT

Fast Multi Class DT for Video

Fast Exact Euclidean Distance (FEED)

• each q O

feeds its ED to all p:D(p) = min ( D(p), ED(q,p))

border pixels bisection lines precalculate ED

•Faster than EDLT, EDT4, EDT2•More implementation effort

•more lines of code•parameters and strategies

Fast Multi Class DT for Video

Multi class extension

• scan methods (CH11, CH34, EDT4, EDT2):– compare d(p) with d’s of neighbours– add compare c(p) with c’s of neighbours

• EDLT:– add extra vector to contain class of Voronoi points– used to set class of filled-in points on row, column

• FEED:– change update step D(p) = min ( D(p), ED(q,p))– if( ED(q,p) < D(p) ) D(p) = ED(q,p), C(p)=C(q)

Fast Multi Class DT for Video

Timing Multi Class DT

time in s/pixel

P-4 3 GHz 1024 MB

12 KuOps, 16KB; 2048 KB

P-M 1.6 GHZ 512 MB

32 KB, 32 KB ; 2048 KB

image size

640 x 480

1280 x 960

2560 x 1920

640 x 480

1280 x 960

2560 x 1920

FEED 0.033 0.037 0.045 0.036 0.048 0.119

EDLT 0.066 0.076 0.195 0.101 0.116 0.317

EDT2 0.059 0.060 0.066 0.100 0.104 0.111

CH11 0.013 0.013 0.014 0.018 0.023 0.025

Fast Multi Class DT for Video

Video frames

D fixed+mov (p) = if( D fixed (p) < D mov (p) )

then Dfixed+mov(p) = Dfixed(p) , Cfixed+mov(p) = Cfixed(p)

else Dfixed+mov(p) = Dmov(p) , Cfixed+mov(p) = Cmov(p)

Fast Multi Class DT for Video

Fast moving part calculation

• fast location moving object– sequence of refining scans over the image– using RLE encoding of fixed objects

• use dmax = max ( Dfixed(p) ) to calculate D (C ) mov

– only over part of the frame

– bounding box of moving object extended by dmax

• combining fixed and moving D (C ) only for part

• same memory locations for D fixed and D fixed+mov

Fast Multi Class DT for Video

Extra speed-up for FEED

• merge the application of FEED on the moving object– with combining fixed and moving D (C ):– replace initialization D(p)= if( p O ) 0 else – by D(p) = D fixed (p)

• not possible for other methods– only partial evaluations of D during scans

• further the RLE encoding is used to speed-up FEED

Fast Multi Class DT for Video

Timing video Multi Class DT

time in s/pixel

P-4 3 GHz 1024 MB

12 KuOps, 16KB; 2048 KB

P-M 1.6 GHZ 512 MB

32 KB, 32 KB ; 2048 KB

640 x 480

7 fixed

full fixed video full fixed video

FEED 0.035 0.039 0.003 0.041 0.045 0.004

EDLT 0.066 0.070 0.025 0.102 0.105 0.037

EDT2 0.060 0.064 0.026 0.102 0.106 0.040

CH11 0.012 0.017 0.013 0.018 0.023 0.019

Fast Multi Class DT for Video

Timing video MCDT

time in s/pixel

P-4 3 GHz 1024 MB

12 KuOps, 16KB; 2048 KB

P-M 1.6 GHZ 512 MB

32 KB, 32 KB ; 2048 KB

640 x 480

13 fixed

full fixed video full fixed video

FEED 0.033 0.037 0.002 0.038 0.043 0.002

EDLT 0.058 0.062 0.012 0.091 0.095 0.019

EDT2 0.061 0.066 0.013 0.104 0.109 0.020

CH11 0.012 0.017 0.007 0.018 0.023 0.009

Fast Multi Class DT for Video

Examples

Fast Multi Class DT for Video

Conclusion

• extended several DT’s to– handle images with multi class objects– and to faster processing of video frames

with fixed and one moving multi class objects• extension methods applicable to all scans based DT’s• our Fast Exact Euclidean Distance transformation

– is faster (6-10) than other MC (semi-)exact EDT’s– on video frames even faster than city-block

• more implementation effort– tune to cache-systems, image characteristics