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