Region coloring using the Welsh Powell algorithm 62010

Region coloring using the Welsh -Powell algorithm 6/2010 Jacob D’Avy Slide 1

Region coloring • The output image from a segmentation method can be viewed as connected regions. • Coloring the regions can be used to help visualize the output. • The optimal coloring scheme would paint all adjacent regions in different colors and use the minimum required colors. D. Page, “Part decomposition of 3 D models, ” Ph. D. dissertation, University of Tennessee, Knoxville, TN 2003. Slide 2

Region coloring • There is no method that can find the optimal solution in a reasonable amount of time. (min colors) • Welsh and Powell created a method to approximate the optimal solution. • The Welsh-Powell method guarantees that no adjacent regions will be painted the same color. • The number of colors used is not guaranteed to be minimal, but it is usually close. D. J. A. Welsh and M. B. Powell, “An upper bound on the chromatic number of a graph and its application to timetabling problems", The Computer Journal, volume 10, no. 1, pp. 85 -86, 1967 Slide 3

Algorithm Definitions: Process: D. J. A. Welsh and M. B. Powell, “An upper bound on the chromatic number of a graph and its application to timetabling problems", The Computer Journal, volume 10, no. 1, pp. 85 -86, 1967 Slide 4

Results Mean-shift segmentation original image resolution: 240 x 240 Slide 5 segmentation region boundaries sb=8 rb=25. 6 min=128 Welsh-Powell coloring of segmentation 3 colors 5 regions

Results Mean-shift segmentation original image resolution: 376 x 490 Slide 6 segmentation region boundaries sb=8 rb=12. 8 min=32 Welsh-Powell coloring of segmentation 5 colors 127 regions

Results Comparison with random region color assignment: • A basic region coloring scheme would be to define a set of distinguishable colors. (~10) • Color the regions by assigning them a random color from the set. • The benefit is fast execution, but its possible that two adjacent regions are colored the same. • Random coloring will be used as a baseline for execution time. Slide 7

Results Comparison with random region color assignment: original image resolution 376 x 490 Slide 8 Welsh-Powell 5 colors 127 regions 45 secs runtime Random color 10 colors 127 regions 22 secs runtime

Results Comparison with random region color assignment: original image resolution: 240 x 240 Slide 9 Welsh-Powell Random color 3 colors 5 regions 17 secs runtime 5 colors 5 regions 10 secs runtime

Results Comparison with random region color assignment: original image Resolution: 240 x 240 Slide 10 segmented region boundaries Welsh-Powell 5 colors 3237 regions 100 secs runtime Random color 10 colors 3237 regions 5 secs runtime

Results This table shows the difference in execution time for the two methods. original image regions Welsh-Powell exec. time(s) Random color exec. time(s) seg 1 127 45 22 seg 2 5 17 10 seg 3 3237 100 5 seg 1 original seg 2 original seg 3 Execution time is for the whole process, from segmentation to final output. Slide 11

Conclusions • Using the Welsh-Powell method for coloring a segmentation output guarantees that adjacent regions will not be painted with the same color. • It also uses a near minimal amount of different colors which makes regions easier to distinguish. • Using Welsh-Powell does require additional computation time. • For a small number of regions, the increase in computation time is not large. As the number of regions increase, the required time increases substantially. Slide 12

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