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

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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


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

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


Example

Example


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


Particles detection i example i

Particles Detection I:Example (I)


Particles detection i example ii

Particles Detection I:Example (II)


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


Circles detection example

Circles Detection:Example

Frame 1

Frame 2


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


    Sorting algorithm example iii

    Sorting Algorithm:Example (III)

    Frame 1

    Frame 2


    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


    Example1

    Example


    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.


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

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