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Otolith Shape Otolith Shape AnalysisAnalysisusing using
Wavelet TransfomsWavelet Transfomsandand
Curvature Scale Curvature Scale SpaceSpace
Vicenç Parisi Baradad, Joan Cabestany, Jaume Piera
Emili Garcia-Ladona, Toni Lombarte
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• Contour codingContour coding• Wavelet TransformWavelet Transform• Curvature Scale Space Curvature Scale Space representationrepresentation• Fourier TransformFourier Transform• Data base retrievalData base retrieval
INTRODUCTION – Contour – Wavelet – CSS – Fourier – Matching
IntroductionIntroduction
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• Coordinates (x,y)Coordinates (x,y)
Introduction – CONTOUR – Wavelet – CSS – Fourier– Matching
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• Equiangle coordinatesEquiangle coordinates
Introduction – CONTOUR – Wavelet – CSS – Fourier – Matching
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• Chain codeChain code
Introduction – CONTOUR – Wavelet – CSS – Fourier – Matching
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Wavelet TransformWavelet Transform
)(*)( 22 xfxfW jj
0)( dxx
s
x
sxs 1)(
22
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21 |)(||)(||)(| xfSxfWxfS Jj
J
j
Introduction – Contour – WAVELET – CSS – Fourier – Matching
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fS 22
fW 12
fS 32
fW 22
fS 12
fW 32
Introduction – Contour – WAVELET – CSS – Fourier – Matching
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• Mother wavelet: smoothing function second derivativeMother wavelet: smoothing function second derivative
22
2
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dx
dx
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))(*(2)(
22
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dx
dxfW jj
j
Introduction – Contour – WAVELET – CSS – Fourier – Matching
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Curvature Scale SpaceCurvature Scale Space
•Invariance to image translation, scale and rotation changes
•Robust to shear
•Good performance against high frequency noise
Introduction – Contour – Wavelet – CSS – Fourier– Matching
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Contour SmoothingContour Smoothing
Introduction – Contour – Wavelet – CSS – Fourier– Matching
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Curvature Inflection PointsCurvature Inflection Points
Introduction – Contour – Wavelet – CSS – Fourier– Matching
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Sampling InvarianceSampling Invariance150 samples 512 samples
CSS normalized
Introduction – Contour – Wavelet – CSS – Fourier– Matching
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Noise inmunityNoise inmunity
Low scales elimination increases noise inmunity
Introduction – Contour – Wavelet – CSS – Fourier– Matching
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Scaling invarianceScaling invariance
Introduction – Contour – Wavelet – CSS – Fourier– Matching
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Rotation invarianceRotation invariance
Rotation = Maxima translation
Introduction – Contour – Wavelet – CSS – Fourier– Matching
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Shear "invariance"Shear "invariance"
Shear produces slight changes
Introduction – Contour – Wavelet – CSS – Fourier– Matching
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Fourier TransformFourier Transform
Cosinus Sinus
• Integral covers whole contour
• Singularities not located
Introduction – Contour – Wavelet – CSS – FOURIER – Matching
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Data BaseData Base107 otoliths Wavelet
Fourier CSS
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Wavelet MatchingWavelet Matching• Energy conservationEnergy conservation
j
xfWf j2
2
2 |)(|||
• Wavelet distanceWavelet distance
j
gWfW (x)||||f(x) – g jj2
22
2 ||||
• Zero Crossing distanceZero Crossing distance
j
xgZxfZZgZfd jj2
22
2 ||)()(||),(
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
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Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
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Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
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Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
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Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
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CSS MatchingCSS Matching
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
Image Model
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Noise, Rotation and Shear
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
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Fourier MatchingFourier Matching|)()(|),(
1
n
jjCgjCfCgCfd
Introduction – Contour – Wavelet – CSS – Fourier– MATCHING
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Fourier Matching under Rotation
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
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Fourier Matching under Shear
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
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Fourier Matching under Noise
Introduction – Contour – Wavelet – CSS – Fourier– MATCHING
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ConclusionsConclusions
• (Wavelet + chain code) and CSS robust under (Wavelet + chain code) and CSS robust under affine transformations and Shearaffine transformations and Shear
• Wavelet and CSS locate SingularitiesWavelet and CSS locate Singularities• Wavelet + CSS allow database compressionWavelet + CSS allow database compression• Wavelet allows perfect contour reconstructionWavelet allows perfect contour reconstruction
Introduction – Contour – Wavelet – CSS – Fourier – Matching