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# Fast Exact Euclidean Distance (FEED) Transformation - PowerPoint PPT Presentation

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

Theo Schouten

Egon van den Broek

FEED

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

• approximation of Euclidean

• Rosenfeld & Pfaltz

• local, parallel or sequential

• Borgefors

• chamfer, weighted distances

FEED

• not by local operations

• disconnected Voronoi tile

• often right, sometimes wrong ED

• correction

Cuisenaire & Macq

CVIU 76 (1999)

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

• 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

• 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

• reduce p  O to update per B

FEED

• time lost:

• searching object pixels

• against time gained:

• not updating certain p  O

• optimum, distribution object pixels

FEED

• 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

• 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

• step 3: faster, simpler

• formal proofs

• partial maps, fixed objects + moving objects in video

• color space applications

FEED

• 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