ter haar romeny, icpr 2010 mathematical models of contextual operators eindhoven university of...
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ter Haar Romeny, ICPR 2010
Mathematical Models
ofContextual Operators
Eindhoven University of Technology
Department of Biomedical Engineering
Markus van Almsick, Remco Duits, Erik Franken
Bart ter Haar Romeny
ter Haar Romeny, ICPR 2010
Context: the Idea
What a local filter sees:What a context filter sees:
ter Haar Romeny, ICPR 2010
Perceptual grouping (Gestalt) from orientations: robust detection
Gestalt laws
ter Haar Romeny, ICPR 2010
IntroductionProblem: segmentation of curves, contours, surfaces,
etc.
Methods can be distinguished by (spatial) ‘locality’
Local Global
Pixelwise Local filters
/derivativesContext operators Active contours,
ASM, etc.
E.g. threshold on pixel values
Pro: computationally efficientCon: only applicable on very ‘clean’ images
E.g. Gaussian derivatives+threshold/local max
Pro: pretty efficientCon: sensitive to noise or inconsistent data if features “live” at low scale in scale-space
Optimization of global cost functional based on smoothness constraints (+ shape/texture knowledge)
Pro: effective and stable on specific class of objectsCon: needs initial estimate, (prior shape knowledge)
Operators that take a “larger context” into account, by enhancing local features using context model.
Pro: noise-robust, limited amount of prior knowledgeCon: computational expensive
ter Haar Romeny, ICPR 2010
Context: the Empirics
Angular specifity in the striate cortex: voltage sensitive dye recording of cortical colums. Similar orientations are connected (even over great distances) – “probability voting”.
“Orientation selectivity and the arrangement of
horizontal connections in tree shrew striate cortex”
W.H.Bosking, Y Zhang, Y.Schofield, D.Fitzpatrick
(1997) J. Neuroscience 17:2112-2127
ter Haar Romeny, ICPR 2010
Goal: Extracting Edges, Lines and Surfacesfrom noisy, low dose, or fastly acquired medical
images
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Overview
• Invertible Orientation Bundle
TransformationThe output of the oriented filters spans a new transformed
space, like the Fourier transform. An inverse transform can be
found!
• Tensor Voting
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Template Matching
imagekernelresponse
Classical filters
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G-Convolution
symmetry transformation g
g dependence
Classical filters
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Linear Convolution Filter
translation by b
Classical filters
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Wavelet Transform
dilation a translation b
Classical filters
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Orientation Bundle Transform
rotation α translation b
New filter family
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Orientation Bundle Transform
QuickTime™ and aAnimation decompressor
are needed to see this picture.
ter Haar Romeny, ICPR 2010
Measures
L2 inner product by Euclidean measure
L2 inner product by Haar measure
image response
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Inverse Transformation
Kernel Constraint
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Gaussian Orientation Bundle
Harmonic amplitudes are constructed from the local Gaussian derivative jet
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ter Haar Romeny, ICPR 2010
RemcoDuits:
InvertibleOrientationWaveletTransform[Siam2004]
Best paperaward atPRIA 2004
ter Haar Romeny, ICPR 2010
Strong non-linear filtering in orientation spacegives a much better detection of very dim lines in noise
{x,y} OS
OS OS6
OS6 {x,y}
ter Haar Romeny, ICPR 2010
Finding the very thin Adamkiewiczvessel in aorta reconstructive surgery:Not reconnecting may give spinal lesion.
3D waveletfor invertibleorientationtransform
Noisy original Denoised vessel
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Orientation Bundle Transform• invertible
• isometric
• variety of admissible kernels
This gives a new ‘space’ for geometricreasoning
ter Haar Romeny, ICPR 2010
Context: Autocorrelation of Luminosity
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Autocorrelation of Edges
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Autocorrelation of Lines
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Autocorrelation of Lines
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Tensor voting
Voting kernel
ter Haar Romeny, ICPR 2010
Steerable Tensor Voting
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Context filters for dim and broken contour detection
Ultrasound kidney Context-enhanced
Contour extraction
Local
Contour extraction
ter Haar Romeny, ICPR 2010
Vessel detectionfor ComputerAided Diagnosisin mammography
E. Franken, M. van Almsick
ter Haar Romeny, ICPR 2010
Application: Cardiac ElectrophysiologyTreatment of heart rhythm disorders
1. Insertion of EP catheters
2. Recording of intracardiac electrograms
3. Ablation of problematic spot, or blocking undesired conduction path
Erik Franken, 2006
ter Haar Romeny, ICPR 2010
Example - input
Source image
Local ridgeness
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ter Haar Romeny, ICPR 2010
Example - result
Context enhanced ridgeness
*
*
*
*
*
+
+
+
+
U2(x,y)=|U2|
Erik Franken, 2006
ter Haar Romeny, ICPR 2010
Repeated tensor voting
Tensor voting thinning tensor voting
Result after first step Result after second step
Erik Franken, 2006
ter Haar Romeny, ICPR 2010
Fluoroscopyat 1/50 of theregular dose
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Extracted most salient paths
Extraction of paths
Extracted catheter tips
Erik Franken, 2006
ter Haar Romeny, ICPR 2010
Extension of catheter tips
Selection of the best extension candidate for each
tip.
Result:
Erik Franken, 2006
ter Haar Romeny, ICPR 2010
Evaluation of extraction results
20
40
60
80
100%
Low noise High noise
TV
No TV
TV
No TV
%entire
%tip
Erik Franken, 2006
ter Haar Romeny, ICPR 2010
Sarcomers – bands of overlappingactine – myosine molecules inmuscle fibres
Orientation score - nonlinar diffusion