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Modeling of visual form and motion of nano -particles drifting in a polymeric fluid

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Technion – Israel InstituteofTechnologyFacultyofElectricalEngineeringControl & Robotics Laboratory### 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

Outline

- Motivation & Goals
- Previous work on the subject
- System description
- Modules
- Example
- Results
- Future work

Motivation

- 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

Goals

- 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)

Input movies

- Microscope generated movies
- Diffraction patterns
- Polymeric fluid
- 15 seconds

Previous Works

- 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

System Description

- Noise cleaning
- Static noise (background subtraction)
- Dynamic noise (optional)
- Particles modeling

Block Diagram

Background subtraction

Original movie

Cleaned movie

Per frame

- Gaussian fitting process

Marking suspicious sub frames

- Circles detection

Fitting

errors

Sub frames locations

- Particles reconstruction

- Sorting Algorithm

Sorting results & parameters

Circles

parameters

Reconstructed movie

Module:Background Subtraction

- Based on Stauffer & GrimsonGMM 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:Particles Detection I

- 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

- 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 in frames
- Uniform sub frames ( )
- Overlap (50% in each axis)
- Filtering out hopeless sub frames
- Negative revaluation error image

Module:Particles Detection II

- 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

- : Revaluation error
- : Lower threshold
- : Sub frame’s maximum area
- : Sub frame’s minimum area
- : Curvature of exponential function
- , descending function
- Spans sub frames sizes

Particles Detection II:Example

Frame 1

Frame 2

Calculated frames of frame 2

Calculated frames of frame 1

Module:Particles Detection II

- Good compatibility with particles
- Size
- Location
- Multiple sub frames dealt by sorting algorithm

Module:Circles Detection

- 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:Sorting Algorithm

- Overlap causes need to cross data from different structures

Reconstructed frame

Original frame

Module:Sorting Algorithm

- Sorts to Gaussians and Besselians
- Considers all circles detected
- Handles structures separately
- Each structure can contain several particles
- Initial & temporary sorting
- 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:Particles Reconstruction

- 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

- :
- 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

- :
- Reconstruction based on first ring:
- Analytic function’s mean known
- First ring’s mean computed
- Comparison of both gives

Analytic Function

First ring

Particles Reconstruction:Example (I)

Original particle

Detected circles

Original particle’s first ring

Reconstructed particle

Results

- System’s products
- Reconstructed movie
- Circles’ data
- Limited quantitative analysis
- Qualitative analysis
- Satisfactory results
- Unsatisfactory results

Quantitative analysis

- Centers of mass
- Manual radii calculation

- 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

Qualitative analysis

- Impressive reconstruction
- Conspicuous & small particles
- Inconspicuous & weak particles
- Asymmetric & imperfect particles
- Particles in noisy environment
- Reconstruction algorithm corrects detection algorithm’s faults.

Qualitative analysis

- 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

Conclusions

- 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

Future Work

- 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

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.

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