Fast Exact Euclidean Distance (FEED) Transformation

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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 &amp; Pfaltz local, parallel or sequential Borgefors

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Fast Exact Euclidean Distance (FEED)Transformation

Theo Schouten

Egon van den Broek

FEED

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

Cuisenaire & Macq

CVIU 76 (1999)

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
• 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
• 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
• reduce p  O to update per B

FEED

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

FEED

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

FEED

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