© 2003 Rajesh Subbu sikes © 2003 Rajesh Subbu sikes Fall 2003 Fall 2003 11

CAP5416CAP5416Computer VisionComputer Vision

Level SetsLevel SetsFinal ProjectFinal Project

Rajesh PydipatiRajesh PydipatiArcot SubramanianArcot Subramanian

Jai SikesJai Sikes

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OverviewOverview

1.1. Results for running level set code for Results for running level set code for various input imagesvarious input images

2.2. Level set code modificationsLevel set code modifications

3.3. SummarySummary

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Results of Level Set MethodResults of Level Set Method

1.1. Noise analysis for a single contourNoise analysis for a single contour2.2. Multiple contours, spacing, and noise Multiple contours, spacing, and noise

analysis for four circles of various radiianalysis for four circles of various radii3.3. Multiple contours, spacing, and noise Multiple contours, spacing, and noise

analysis for two irregular abutting shapesanalysis for two irregular abutting shapes4.4. Multiple contours and noise analysis for Multiple contours and noise analysis for

multiple irregular shapesmultiple irregular shapes5.5. Multiple contours and noise analysis for Multiple contours and noise analysis for

intricate imageintricate image

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Noise analysis for a single contourNoise analysis for a single contour

Level set found for Level set found for SNR = 40, 32, SNR = 40, 32, and 26 dBand 26 dB

Failure occurred for Failure occurred for SNR = 26 dBSNR = 26 dB

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40 dB40 dB

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32 dB32 dB

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26 dB 26 dB –– FailureFailure

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Multiple contours, spacing, and noise Multiple contours, spacing, and noise analysis for four circles of various radiianalysis for four circles of various radii

Level set found for SNR = 40, 32, 26, and Level set found for SNR = 40, 32, 26, and 23 dB23 dB

For circle radius = 20, failure occurred at For circle radius = 20, failure occurred at 23 dB for both near and touching circles23 dB for both near and touching circles

For circle radius = 40, failure occurred at For circle radius = 40, failure occurred at 26 dB for both near and touching circles26 dB for both near and touching circles

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Radius = 20 Distance = 25 Radius = 40 Distance = 45

Radius = 40 Distance = 40Radius = 20 Distance = 20

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40 dB (radius = 20)40 dB (radius = 20)

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32 dB32 dB

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26 dB26 dB

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23 dB 23 dB –– Level set failureLevel set failure

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40 dB (radius = 40)40 dB (radius = 40)

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32 dB32 dB

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26 dB 26 dB –– Level set failureLevel set failure

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Multiple contours, spacing, and Multiple contours, spacing, and noise analysis for two irregular noise analysis for two irregular

abutting shapesabutting shapes

Level set found for SNR = 40, 32, 26, and 23 dBLevel set found for SNR = 40, 32, 26, and 23 dB

For near shapes, failure occurred for SNR = 26 dBFor near shapes, failure occurred for SNR = 26 dB

For far away shapes, failure occurred for SNR = 23 dBFor far away shapes, failure occurred for SNR = 23 dB

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40 dB40 dB

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32 dB32 dB

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26 dB 26 dB –– Failure for near shapesFailure for near shapes

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23 dB 23 dB –– Failure for far imagesFailure for far images

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Multiple contours and noise Multiple contours and noise analysis for multiple irregular analysis for multiple irregular

shapesshapes

Level set found for Level set found for SNR = 40, 32, 26, SNR = 40, 32, 26, and 23 dBand 23 dB

Failure occurred for Failure occurred for SNR = 23 dBSNR = 23 dB

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40 dB40 dB

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32 dB32 dB

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26 dB26 dB

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23 dB 23 dB –– Failure Failure

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Multiple contours and noise Multiple contours and noise analysis for intricate imageanalysis for intricate image

Level set found for Level set found for SNR = 40 and 32 dBSNR = 40 and 32 dB

Failure occurred for Failure occurred for SNR = 32 dBSNR = 32 dB

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40 dB40 dB

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32 dB32 dB

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DiscussionDiscussion

Occurrences of Level Set FailureOccurrences of Level Set FailureSimpler images: 26Simpler images: 26--23 dB23 dBMore complex images: 26More complex images: 26--23 dB23 dBMost complex image: 32 dBMost complex image: 32 dB

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DiscussionDiscussion

Effects of Size on CirclesEffects of Size on CirclesLarger circles exhibited greater SNRLarger circles exhibited greater SNR

Effects of Proximity of Neighboring ImagesEffects of Proximity of Neighboring ImagesFour similar circles: no observed effectFour similar circles: no observed effectIrregular shapes: Farther apart shapes Irregular shapes: Farther apart shapes had failure at lower SNRhad failure at lower SNR

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ConclusionsConclusionsGenerally, the level sets were able to split freely Generally, the level sets were able to split freely to represent each shape for SNR levels greater to represent each shape for SNR levels greater than 26 dB.than 26 dB.

Small object size and close proximity to other Small object size and close proximity to other objects increase the failure rate of the level sets.objects increase the failure rate of the level sets.

The level set method is a sound approach for The level set method is a sound approach for shape modeling when no shape modeling when no a prioria priori assumption assumption about the shape’s topology can be made.about the shape’s topology can be made.

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Level set code modificationsLevel set code modifications

1.1. Level set extractionLevel set extraction

2.2. Difference Equation in DeltaDifference Equation in Delta

3.3. Narrow Band InitializationNarrow Band Initialization

4.4. ΨΨ InitializationInitialization