Perceptual grouping: Curvature enhanced closure of elongated

structures

ByGijs Huisman

Committee:

prof. dr. ir. B.M. ter Haar Romenyprof. dr. ir. P. Hilbersdr. L.M.J. Florackdr. ir. R. Duitsir. E.M. Franken

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Content

1. Introduction

2. Orientation scores• Cake kernels

3. G-convolution• Stochastic completion

kernel• Adaptive G-Convolution

4. Mode line extraction• Theory

5. Non-linear operations• Advection based

enhancement• 3 non-linear operations

6. Curvature estimation• 4 methods• Test results

7. Experiments• Mode line extraction• Increased gap filling• Improved smoothness• Adaptive shooting• Examples medical images

8. Conclusion• Conclusions• Recommendations

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Introduction

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Orientation score

An orientation score has 2 spatial dimensions and 1 orientation dimension

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Orientation Score

An orientation score is obtained by wavelet transformation of an image

Where and

Reconstruction of an image is possible

by an inverse wavelet transform

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Orientation scoreCake Kernels

The wavelet is defined by:

The function is defined by B-splines:

Main advantage is easily adaptive kernels with good reconstruction properties

is defined by a 2D gauss

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G-convolution

Normal convolution

G-convolution

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Stochastic Completion Kernel

G-convolution

The used kernel depicts a probability density function for the continuation of a line kernel in an orientation score.

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G-convolutionStochastic Completion Kernel

Gap closing operation with the stochastic completion kernel

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G-convolution

Making the G-convolution adaptive means that the kernel properties change with the position in the orientation score.

Kernels are adapted to fit the local curvature

Adaptive

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Mode line extraction

Very often the lines itself are demanded instead of an enhanced image.

Any point is part of a local mode line if and at the point

Lines in the spatial plane are 3D ridges in an orientation score.

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Non-Linear Operations

Enhancement can be done before and after an G-convolution

Non ideal cake kernel response:

•DC-extraction

•MIN-Extraction

•Erosion

•Advection

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Non-Linear Operations

•DC-Extraction

•MIN-Extraction

•Erosion

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Non-Linear OperationsAdvection

A force field directed towards the local mode lines:

By means of advection the score can now be sharpened

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Non-Linear OperationsResults ErosionDC-extraction

MIN-extraction

Straight

Curved

Advection

Intensity

No preprocessing

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Curvature estimation

1. Inner product stochastic completion kernel

2. Inner product Gaussian based kernel

3. Region estimation

4. Hessian based method

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Curvature estimationResults

Stochastic Gaussian

Region Hessian

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Curvature estimationResults

Curvature measurement on a cross section of the circle line

Stochastic Gaussian

Region Hessian

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Curvature estimationResults

Stochastic Gaussian

Region Hessian

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ExperimentsMode line extraction

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ExperimentsMode line extraction

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ExperimentsMode line extraction

Mode line extraction on artificial image

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ExperimentsIncreased gap filling

Plane DC Min Plane DC Min

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ExperimentsImproved smoothness

Straight

Curved

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ExperimentsAdaptive shooting

Original image

Orientation scoreStraight shooting result

Curvature estimate

Enhanced image

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ExperimentsAdaptive shooting

Original Straight shooting (1)

Curved Shooting (2)

Curved Shooting (3)

Mean Filling

Method

1.5

1

0.5

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Min Filling

Method

1

2

3

02 31

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ExperimentsExamples Medical images

Blood vessel extraction on images of the human retina

Original Threshold Straight shooting

Blood vessels

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ExperimentsExamples Medical images

Straight shooting Adaptive shooting

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Conclusion

•Curvature enhanced shooting does improve the gap filling

•Successful method of curve extraction

•Good method to estimate the curvature

•Improve the accuracy of the curve extraction method

•Better numerical implementation advection enhancement

•Devise a method to extract the correct curves (e.g. fast marching)

•Better tuning of the cake kernel parameters

Conclusions

Recommendations

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Questions?