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Technion – Israel Institute of Technology Faculty of Electrical Engineering Control & 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.

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modeling of visual form and motion of nano particles drifting in a polymeric fluid
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
Outline
  • Motivation & Goals
  • Previous work on the subject
  • System description
  • Modules
  • Example
  • Results
  • Future work
slide3
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
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
Input movies
  • Microscope generated movies
  • Diffraction patterns
  • Polymeric fluid
  • 15 seconds
previous works
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
System Description
  • Noise cleaning
    • Static noise (background subtraction)
    • Dynamic noise (optional)
  • Particles modeling
block diagram
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
Module:Background Subtraction
  • Based on Stauffer & GrimsonGMM algorithm
  • GMM – Gaussian Mixture Model
  • Linear superposition
  • Different expectations, variances and weights
module background subtraction1
Module:Background Subtraction
  • Stauffer & Grimson
  • Threshold operation
  • Pixel wise analysis
  • Mixture of Gaussians PDF
  • Multiple background objects
  • Continuously updating model’s parameters
module background subtraction2
Module:Background Subtraction
  • Improved Implementation
    • External source
    • Dynamic number of Gaussians
    • Results & run time improved
module background subtraction3
Module:Background Subtraction
  • Improvement
    • Merging regular and reversed movies
    • Learning process
    • Later frames better cleaned
    • Linear weight:
background subtraction example
Background Subtraction:Example

Original frame

Cleaned frame

module particles detection i
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 i1
Module:Particles Detection I
  • Gaussian fitting
    • Least squares
      • Linearization of Gaussian model
      • Pseudo Inverse
    • Mean Square Error
      • Normalized to revaluated amplitude
module particles detection i2
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 i3
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
particles detection i example iii
Particles Detection I:Example (III)

Frame 1

Frame 2

Fitting error - frame 2

Fitting error - frame 1

module particles detection ii
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 ii1
Module:Particles Detection II
  • Chosen method
    • Lower threshold
    • Square sub frame
    • Exponential formula for area:
module particles detection ii2
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
Particles Detection II:Example

Frame 1

Frame 2

Calculated frames of frame 2

Calculated frames of frame 1

module particles detection ii3
Module:Particles Detection II
  • Good compatibility with particles
    • Size
    • Location
  • Multiple sub frames dealt by sorting algorithm
module circles detection
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 detection1
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 detection2
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
Module:Sorting Algorithm
  • Overlap causes need to cross data from different structures

Reconstructed frame

Original frame

module sorting algorithm1
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 algorithm2
Module:Sorting Algorithm
  • Determines equivalent centers for Besselians
    • Based on two largest radii
    • Linear weight
    • Bigger weight for larger circle
sorting algorithm example i
Sorting Algorithm:Example (I)

Circles frame

Sorted circles frame

sorting algorithm example ii
Sorting Algorithm:Example (II)

Circles frame

Sorted circles frame

sorting algorithm example ii1
Sorting Algorithm:Example (II)

Reconstructed frame

Original frame

module particles reconstruction
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 reconstruction1
Module:Particles Reconstruction
  • Besselian particles
    • Sub frames’ sizes determined by circles data
    • Besselian formula:
    • Needed parameters: &
module particles reconstruction2
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 reconstruction3
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
Particles Reconstruction:Example (I)

Original particle

Detected circles

Original particle’s first ring

Reconstructed particle

particles reconstruction example ii
Particles Reconstruction:Example (II)

Reconstructed frame

Original frame

results
Results
  • System’s products
    • Reconstructed movie
    • Circles’ data
  • Limited quantitative analysis
  • Qualitative analysis
    • Satisfactory results
    • Unsatisfactory results
quantitative analysis
Quantitative analysis

Frame 1

Frame 2

quantitative analysis1
Quantitative analysis

Frame 1

Frame 2

Frame 1 reconstructed

Frame 2 reconstructed

quantitative analysis2
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
Qualitative analysis

Original Frame

  • Satisfactory results

Cleaned Frame

Reconstructed Frame

qualitative analysis1
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 analysis2
Qualitative analysis

Original Frame

  • Unsatisfactory results

Cleaned Frame

Reconstructed Frame

qualitative analysis3
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 analysis4
Qualitative analysis
  • Big blurry particles
  • Difficulty detecting Besselian particles
  • Noise
    • Damages detection & reconstruction
    • Increases false detections
  • Independent frames
    • Various results in adjacent frames
conclusions
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
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
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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