Post on 15-Jan-2016
description
transcript
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
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1
0.5
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Min Filling
Method
1
2
3
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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?