Ron Goldberg Yulia Turovski Supervisor: Arie Nakhmani Winter 2011 Date: 07.05.2012 Technion –...
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Transcript of Ron Goldberg Yulia Turovski Supervisor: Arie Nakhmani Winter 2011 Date: 07.05.2012 Technion –...
Modeling of visual form and motion of nano-particles drifting in a polymeric fluid
Ron Goldberg
Yulia Turovski
Supervisor: Arie Nakhmani
Winter 2011
Date: 07.05.2012
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Technion – Israel Institute of TechnologyFaculty of Electrical EngineeringControl & Robotics Laboratory
• Motivation & Goals• Previous work on the subject• System description• Modules• Example• Results• Future work
Outline
• Active and controllable drug transport– Few and isolated damaged cells– Healthy tissue unaffected
• Super paramagnetic nanoplatforms– Control of platforms via magnetic field
• Improve control of nanoplatforms motion– Automatic platforms characteristics and motion
analysis
Motivation
• Automatic analysis of platforms motion and characteristics:– Static noisy background subtraction– Dynamic noise filtering– Platforms detection– Platforms modeling and reconstruction– Motion analysis
• MATLAB Environment• Non real time• Short processing time (~minutes)
Goals
Input movies
• Microscope generated movies• Diffraction patterns• Polymeric fluid• 15 seconds
Example
• Previous solution (Nakhmani et al., 2010)– Static noisy background subtraction– Dynamic noise filtering– Platforms detection– Platforms modeling and reconstruction– Motion analysis
• Background subtraction: classic & advanced• Unique problem
– Collection of issues– Unrelated & uncommon solutions
Previous Works
• Noise cleaning–Static noise (background subtraction)–Dynamic noise (optional)
• Particles modeling
System Description
Block DiagramBackgroun
d subtraction
Marking suspicious sub frames
Gaussian fitting
process
Per frame
Circles detection
Particles reconstruction
Sorting Algorithm
Original movie Cleaned movie
Fitting errors
Sub frames locations
Circles parameters
Sorting results & parameters
Reconstructed movie
• Based on Stauffer & Grimson GMM algorithm• GMM – Gaussian Mixture Model
– Linear superposition– Different expectations, variances and weights
Module:Background Subtraction
• Stauffer & Grimson– Threshold operation– Pixel wise analysis– Mixture of Gaussians PDF– Multiple background objects– Continuously updating model’s parameters
Module:Background Subtraction
• Improved Implementation– External source– Dynamic number of Gaussians– Results & run time improved
Module:Background Subtraction
• Improvement– Merging regular and reversed movies– Learning process– Later frames better cleaned– Linear weight:
Module:Background Subtraction
1 1
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forward backwardn n n N n N n
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Background Subtraction:Example
Original frame Cleaned frameOriginal frame
• Particles’ diffraction patterns– Theoretically: Bessel functions– Practically: Bessel functions & Gaussians
• Initial detection– Sub frames – Gaussian fitting– Revaluation error
Module:Particles Detection I
• Gaussian fitting– Least squares
• Linearization of Gaussian model• Pseudo Inverse
– Mean Square Error• Normalized to revaluated amplitude
Module:Particles Detection I
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• Improved disadvantages– Sensitivity to zeros & low intensities– Saturation– Pseudo inverse
• Perfect revaluation for ideal Gaussians• Impressive revaluation & detection capabilities• Excellent reliability
– Thousands sub frames per frame– Numbered error messages
Module:Particles Detection I
Particles Detection I:Example (I)
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Particles Detection I:Example (II)
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• Particles detection in frames– Uniform sub frames ( )– Overlap (50% in each axis)– Filtering out hopeless sub frames– Negative revaluation error image
Module:Particles Detection I
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Particles Detection I:Example (III)
frame1 frame2
fitting error - frame 1 fitting error - frame 2
Frame 1 Frame 2
Fitting error - frame 1 Fitting error - frame 2
• Sub frames matching– For circle detection– Sub frames depend on suspicious areas
• Revaluation error based algorithm– Clear distinction– Suspicious areas– Size of sub frames
Module:Particles Detection II
• Chosen method– Lower threshold– Square sub frame– Exponential formula for area:
Module:Particles Detection II
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– : Revaluation error– : Lower threshold– : Sub frame’s maximum area– : Sub frame’s minimum area– : Curvature of exponential function
• , descending function• Spans sub frames sizes
Module:Particles Detection II
min min
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Particles Detection II:Example
frame1 frame2Frame 1 Frame 2
Calculated frames of frame 1 Calculated frames of frame 2calculated frames of frame 1 calculated frames of frame 2
• Good compatibility with particles– Size– Location
• Multiple sub frames dealt by sorting algorithm
Module:Particles Detection II
• Centers and radii• Basis for particles modeling• Popular problem
– Many circles detection algorithms exist– Chosen solution from external source
• Chosen algorithm– Gray scale input images– Based on circular Hough transform
Module:Circles Detection
• Circular Hough transform– Method for detecting shapes in images– Basic transform detects straight lines
• Generalization to circles & ellipses• Further Generalization to any parametric shape
– Shapes detected in parameter space
• Chosen algorithm enables control of:– Allowed asymmetry– Sensitivity to concentric circles
Module:Circles Detection
• Suitable solution– Revaluation error based detection– Sub frames matching for suspicious areas– On each sub frame
• Chosen algorithm is performed• Uniform parameters set
– Circles data is accumulated
Module:Circles Detection
Circles Detection:Example
Frame 1 Frame 2
• Overlap causes need to cross data from different structures
Module:Sorting Algorithm
Original frameReconstructed frame
• Sorts to Gaussians and Besselians• Considers all circles detected
I. Handles structures separately• Each structure can contain several particles• Initial & temporary sorting
II. Crosses data from different structures• Filtering out resembling circles• Final sorting
Module:Sorting Algorithm
• Determines equivalent centers for Besselians– Based on two largest radii– Linear weight– Bigger weight for larger circle
Module:Sorting Algorithm
Sorting Algorithm:Example (I)
Circles frame Sorted circles frame
Circles frame Sorted circles frame
Sorting Algorithm:Example (II)
Sorting Algorithm:Example (II)
Original frameReconstructed frame
Sorting Algorithm:Example (III)
Frame 1 Frame 2
• Based on sorted circles• Gaussian particles
– Least squares Gaussian fitting– Same algorithm used for particles detection– Selected sub frames– Sub frames’ sizes determined by circles data
Module:Particles Reconstruction
• Besselian particles– Sub frames’ sizes determined by circles data– Besselian formula:
– Needed parameters: &
Module:Particles Reconstruction
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• :– Zeros of Besselian known– Detected circles are zero contours– computed using smallest circle’s radius
• :– Common Besselians:
• Truncated main lobe • Just one ring
Module:Particles Reconstruction
0r
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Normalized Particle - first ring
• :– Reconstruction based on first ring:
• Analytic function’s mean known• First ring’s mean computed• Comparison of both gives
Module:Particles Reconstruction
A
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Normalized ParticleAnalytic Function First ring
Particles Reconstruction:Example (I)Original particleOriginal particle with its detected circles
Original particle - first ringReconstructed particle
Original particle Detected circles
Original particle’s first ring Reconstructed particle
Original frameReconstructed frame
Particles Reconstruction:Example (II)
Example
• System’s products– Reconstructed movie– Circles’ data
• Limited quantitative analysis• Qualitative analysis
– Satisfactory results– Unsatisfactory results
Results
frame 1 frame 2
Quantitative analysis
Frame 2Frame 1
frame1 reconstructed with original particles areas marked frame2 reconstructed with original particles areas marked
Quantitative analysisFrame 2Frame 1
frame1 with manually marked particles frame2 with manually marked particles
Frame 1 reconstructed Frame 2 reconstructed
Quantitative analysis
• Frame 1:– 16 particles– 9 correct detections – 7 misses– 6 false detections– Mean distance: 1.32– Distance standard
deviation: 0.96
• Frame 2:– 13 particles– 12 correct detections – 1 miss– 1 false detection– Mean distance: 2.75– Distance standard
deviation: 2.16
• Centers of mass• Manual radii calculation
• Satisfactory results
Qualitative analysisexample 1 - original
example 1 - reconstructedexample 1 - background subtracted
Original Frame
Cleaned Frame Reconstructed Frame
• Impressive reconstruction• Conspicuous & small particles• Inconspicuous & weak particles• Asymmetric & imperfect particles• Particles in noisy environment• Reconstruction algorithm corrects detection
algorithm’s faults.
Qualitative analysis
• Unsatisfactory results
Qualitative analysisOriginal Frame
Cleaned Frame Reconstructed Frame
example 4 - original
example 4 - background subtracted example 4 - reconstructed
• False detections– Prominent in final movies– Reconstruction of large & bright particles
• Multiple detections per particle– Result of sub frames matching
• Extremely bright particles• False detections rejection capabilities
– Deficient for Besselians
Qualitative analysis
• Big blurry particles• Difficulty detecting Besselian particles• Noise
– Damages detection & reconstruction– Increases false detections
• Independent frames– Various results in adjacent frames
Qualitative analysis
• Particles reconstruction: Impressive & unique results
• Complementary modules improve results• Limited theoretical model• Significant disadvantage: false detections
– Flickering– Exceptionally large particles
• Independent frame analysis– Various results in adjacent frames– Incapability of handling flickering
Conclusions
• Motion analysis– Reduced false detections and miss rates– Consistent reconstructed movie
• Additional system products– Types of particles– Particles’ characteristics
• Extension of the theoretical model• Re-examination of dynamic noise reduction• Further exploration of edge detection
Future Work
References• [1] Q.Wu, F.A.Merchant, K.R.Castelman, ”Microscope Image Processing,” Academic Press,
2008.• [2] A. Nakhmani, L. Etgar, A. Tannenbaum, E. Lifshitz, R. Tannenbaum, "Visual Motion
Analysis of Nanoplatforms Flow under an External Magnetic Field",NSTI – Nanotech 2010, Vol 2, chapter 8, Pp.504-507.
• [3] A. Nakhmani, L. Etgar, A. Tannenbaum, E. Lifshitz, R. Tannenbaum, "Trajectory control of nanoplatforms under viscous flow and an external magnetic field", 2010.
• [4] M. Piccardi, "Background subtraction techniques: a review".• [5] Z. Zivkovic. Improved adaptive Gaussian mixture model for background subtraction.
International Conference Pattern Recognition, Vol. 2, 2004, Pp.28-31.• [6] Z. Zivkovic, "Efficient adaptive density estimation per image pixel for the task of
background subtraction", Pattern Recognition Letters 27, 7/2006, Pp.773–780.• [7] Kenneth R. Castelman, "Digital Image Processing",Prentice Hall, 1979, Chap. 19, Sec. 5.• [8] E. Trucco, A. Verri, "Introductory Techniques For 3-D Computer Vision", Prentice Hall,
1998, Pp. 86-87.• [9] J.W. Goodman, "Introduction to Fourier Optics", Third Edition, Roberts and Company,
2005.• [10] C.A. Balanis, "Antenna Theory: Analysis and Design". 3rd Ed. Wiley, 2005.
The End…