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Fast Exact Euclidean Distance (FEED) Transformation. Theo Schouten Egon van den Broek Radboud University Nijmegen. Distance transformation. distance map D(p) = min { dist(p,q), q  O } approximation of Euclidean Rosenfeld & Pfaltz local, parallel or sequential Borgefors

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fast exact euclidean distance feed transformation
Fast Exact Euclidean Distance (FEED)Transformation

Theo Schouten

Egon van den Broek

Radboud University Nijmegen

FEED

distance transformation
Distance transformation
  • distance map D(p) = min { dist(p,q), q  O }
  • approximation of Euclidean
  • Rosenfeld & Pfaltz
    • local, parallel or sequential
  • Borgefors
    • chamfer, weighted distances

FEED

euclidean distance
Euclidean distance
  • not by local operations
  • disconnected Voronoi tile
  • often right, sometimes wrong ED
  • correction

Cuisenaire & Macq

CVIU 76 (1999)

FEED

principle of feed
Principle of FEED
  • D(p) = if (p  O) then 0 else 

for each q  O

for each p  O

D(p) = min ( D(p), ED(q,p))

  • inverse of definition
  • correct, terrible slow

FEED

speed up step 1
Speed up, step 1
  • reduce q  O to consider
  • only the border pixels of O

x Border: q  O

x x x at least 1 4-conn p  O

x

FEED

speed up step 2
Speed up, step 2
  • pre-computation of ED(q,p)
  • matrix, size of image translation, reflection invariant
  • M = fnon-decr( ED), like square
  • size can be reduced
    • in case max. dist. is known
    • only up to a maximum is interesting

FEED

speed up step 3
Speed up, step 3
  • reduce p  O to update per B

FEED

balance
Balance
  • time lost:
    • searching object pixels
    • administration bisection line
  • against time gained:
    • not updating certain p  O
  • optimum, distribution object pixels

FEED

results
Results
  • Shih & Liu 4-scan ED (PR 31, 1998)
    • not their correction method
  • test images, object-like images
  • FEED is faster, up to 2.7
    • up to 4.5 reduced M
  • random dot images, faster < 15%
  • FEED uses less memory

FEED

applications
Applications
  • human color categories
    • black, white, gray, red, green, blue, yellow, brown, purple, pink, orange
  • 216 web-safe colors
  • classify 2563 colors
  • RGB->HSI, SI: 3 /8, 3, HI: 8
  • content based image retieval, texture

a

FEED

further developments
Further developments
  • step 3: faster, simpler
  • formal proofs
  • partial maps, fixed objects + moving objects in video
  • color space applications

FEED

feed conclusions
FEED conclusions
  • EDT inverse definition
  • simple, correct, slow
  • 3 speed up approaches
  • faster than 4-scan method
  • up to maximum, partial maps
  • human-centered color space

FEED

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