Hermitian Curvature Flow and Curvature Positivity Conditions
Otolith Shape Analysis using Wavelet Transfoms and Curvature Scale Space
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Analysis Analysis using using Wavelet Transfoms Wavelet Transfoms and and Curvature Scale Curvature Scale Space Space Vicenç Parisi Baradad, Joan Cabestany, Jaume Piera Emili Garcia-Ladona, Toni Lombarte
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Otolith Shape Analysis using Wavelet Transfoms and Curvature Scale Space. Vicenç Parisi Baradad, Joan Cabestany, Jaume Piera Emili Garcia-Ladona, Toni Lombarte. INTRODUCTION – Contour – Wavelet – CSS – Fourier – Matching. Introduction. Contour coding Wavelet Transform - PowerPoint PPT Presentation
Transcript of Otolith Shape Analysis using Wavelet Transfoms and Curvature Scale Space
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
• 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
• Coordinates (x,y)Coordinates (x,y)
Introduction – CONTOUR – Wavelet – CSS – Fourier– Matching
• Equiangle coordinatesEquiangle coordinates
Introduction – CONTOUR – Wavelet – CSS – Fourier – Matching
• Chain codeChain code
Introduction – CONTOUR – Wavelet – CSS – Fourier – Matching
Wavelet TransformWavelet Transform
)(*)( 22 xfxfW jj
0)( dxx
s
x
sxs 1)(
22
2
12
21 |)(||)(||)(| xfSxfWxfS Jj
J
j
Introduction – Contour – WAVELET – CSS – Fourier – Matching
fS 22
fW 12
fS 32
fW 22
fS 12
fW 32
Introduction – Contour – WAVELET – CSS – Fourier – Matching
• Mother wavelet: smoothing function second derivativeMother wavelet: smoothing function second derivative
22
2
2)(
dx
dx
j
j
))(*(2)(
22
22
2xf
dx
dxfW jj
j
Introduction – Contour – WAVELET – CSS – Fourier – Matching
2
32.2.
......
)),(),((
),(),(),(),(),(
uYuX
uYuXuYuXuk
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
Contour SmoothingContour Smoothing
Introduction – Contour – Wavelet – CSS – Fourier– Matching
Curvature Inflection PointsCurvature Inflection Points
Introduction – Contour – Wavelet – CSS – Fourier– Matching
Sampling InvarianceSampling Invariance150 samples 512 samples
CSS normalized
Introduction – Contour – Wavelet – CSS – Fourier– Matching
Noise inmunityNoise inmunity
Low scales elimination increases noise inmunity
Introduction – Contour – Wavelet – CSS – Fourier– Matching
Scaling invarianceScaling invariance
Introduction – Contour – Wavelet – CSS – Fourier– Matching
Rotation invarianceRotation invariance
Rotation = Maxima translation
Introduction – Contour – Wavelet – CSS – Fourier– Matching
Shear "invariance"Shear "invariance"
Shear produces slight changes
Introduction – Contour – Wavelet – CSS – Fourier– Matching
Fourier TransformFourier Transform
Cosinus Sinus
• Integral covers whole contour
• Singularities not located
Introduction – Contour – Wavelet – CSS – FOURIER – Matching
Data BaseData Base107 otoliths Wavelet
Fourier CSS
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
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
CSS MatchingCSS Matching
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
Image Model
Noise, Rotation and Shear
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
Fourier MatchingFourier Matching|)()(|),(
1
n
jjCgjCfCgCfd
Introduction – Contour – Wavelet – CSS – Fourier– MATCHING
Fourier Matching under Rotation
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
Fourier Matching under Shear
Introduction – Contour – Wavelet – CSS – Fourier – MATCHING
Fourier Matching under Noise
Introduction – Contour – Wavelet – CSS – Fourier– MATCHING
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
