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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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