Automated quantitative analysis of locomotory behavior Of C. elegans populations

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Automated quantitative analysis of locomotory behavior Of C. elegans populations R1 R2 Fundamental Science Validating TestBEDs L1 L2 L3 R3 S1 S4 S5 S3 S2 Bio-Med Enviro- Civil 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 Fig 1: Contour modeling through B-spline An automated image analysis system has been constructed to perform quantitative morphometry and locomotory behavior analysis of C. elegans populations from time-lapse wide-field microscope imagery. Multiple worms of varying size, age, sex, and morphology, such as would be found in typical cultures, can be analyzed simultaneously. Each worm is uniquely numbered, and its associated measurements are stored in a spreadsheet. The analysis results are also displayed in a color-coded manner for visual inspection. The system makes explicit use of flexible and detailed geometric worm models in combination with cluster analysis algorithms to achieve reliable identification, classification, and tracking, even when dealing with dense, highly entangled populations. Both short-term (frame to frame) as well as longer term (over multiple frames) movements are analyzed. When available, fluorescent marker expression can be scored in a region or organ-specific manner for each worm as long as sufficient spatial detail is available. Experimental results demonstrate robust automation of this currently tedious and subjective task. In addition to the higher throughput implied by reliable automation, it is expected that this system can also provide verifiable and objective classification of subtle behavioral phenotypes. Abstract This work was supported in part by CenSSIS, the Center for Subsurface Sensing and Imaging Systems, under the Engineering Research Centers Program of the National Science Foundation (Award Number EEC- 9986821) Fig 3: Configuration – independent texture map Complex Morphometric evolution Original Segmented An interesting dynamic feature: The evolution of the curvature Geometric Description of a Worm Fig 2: Relative Configuration Atlas Based Segmentation Worm Descriptor A popular approach to describe deformable shapes is through a periodic curve (Fig 1) modeled in terms of cubic B-splines and parameterized by its N control points. A worm object is represented by a periodic curve (Fig 1) modeled in terms of cubic B-splines and parameterized by its N control points. From this we can derive the median of the worm which is of particular interest to us because of the accurate estimate of the worm trajectory that it provides. Conclusion N Q Q Q X , , , 2 1 Cubic B-splines and parameterized by its N control points: Using the described segmentation and tracking principles, it is feasible the extract the evolution of individual worm curvature distribution from time-lapse wide-field microscope imagery. Alongside with the worm progression speed, it constitutes some very reliable features for classification purposes. The foundations of a very robust and powerful atlas based segmentation and tracking method for worm-like structures have been established. By design it has the capability to deal with the task of detection and tracking even when dealing with dense, highly entangled populations. Preliminary results are very encouraging and demonstrated good performance in single object tracking and even in cluttered environment. T Deformatio n Operator Progressio n Operator Deformation/Progression operators In order to design a dynamic behavior model for C-elegans worms, and based on physiological consideration the Progression and deformation Operator have been designed to allow for accurate description of the complete range of possible dynamic movements We define the generic transformation parameter: This worm description approach allows for straightforward texture mapping regardless of the actual curvature configuration and allows for ATLAS BASED segmentation 0 0 , A In the necessary implementation of the physiological constraint of the worm shapes, I can be useful to describe the worm through the local curvature of its median axis. Theoretically, the median axis of the worm can be described using an anchor Point A0 and N local curvature angles 1, θ2,…, θN] and its constant width profile [w1, w2,…, wN] Focusing on the curvature Synthetic Worm Descriptor 10 20 30 40 50 60 70 80 90 100 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 8 9 10 Dynamic modeling and Model Fitting Using a state-based formulation, we define the state of a worm at time t by its geometric configuration X(n). , ( 1) ( ()) T n n , T Segmentati on t I 1 t I 1 t I Object validation Worm Detection/ Track building Correspondence Analysis/ Worm template Optical Segmentation/ Object Detection Worm Modeling Model Design Constraints Probabilistic Tracking Prediction/ Estimation / Tracking Validation Data Detected Worms Dynamic Feature Extraction Modeling t I 1 t I 1 t I Algorithm The purpose of the measurement process is find the object model X(n), that best fits the image data. To do so we search for the transformation parameters T and [θ1, θ2,…, θN] that best fit the measurement data Z(n). The fact that the state transition relation is non linear prevents us from using KALMAN filtering approach. As a result a more strategy approach needs to be used. The idea is to compute the state posterior, p(X(n+1)|Z(t+1)), and select the next state to be the one that maximizes this (Maximum a Posteriori (MAP) estimate). p(X(n+1)|Z(n+1)), is estimated from p(X(n)|Z(n)) and Z(n) using the CONDENSATION algorithm. CONDENSATION follows the same basic iterative steps as a Kalman filter: prediction, measurement, and assimilation. Nicolas Roussel 1 , Christine A. Morton 2 , Qiang Ji 1 , Fern P. Finger 2 , Badrinath Roysam 1 1 Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180 2 Department of Biology, Rensselaer Polytechnic Institute, Troy, NY 12180 Multi-worm Segmentation Sample Benefits of the CONDENSATION approach Support for multi-modal probability distributions (Multi-object situations are better supported (less likely to lose track of objects) Robustness Computationally efficient Clutter Situation Multiworm References W. Geng, P. Cosman, C. Berry, Z. Feng, and W.R. Schafer, “Automatic Tracking, Feature Extraction and Classification of C. elegans Phenotypes,” IEEE Transactions on Biomedical Engineering. To appear in October issue of IEEE Transactions on Biomedical Engineering, 2004. J. Baek, P. Cosman, Z. Feng, J. Silver, and W. R. Schafer, “Using machine vision to analyze and classify C.elegans behavioral phenotypes quantitatively”. J. Neurosci Meth 118, pp. 9 –21, 2002. M. Isard and A. Blake, "Condensation -- conditional density propagation for visual tracking," International Journal of Computer Vision 29(1), pp. 5--28, 1998.

description

Optical Segmentation/ Object Detection. Worm Modeling. Bio-Med. Enviro-Civil. Worm template. Model Design. S2. S3. S4. S1. S5. Worm Detection/. L3. Constraints. Object validation. Segmentation. Modeling. Correspondence Analysis/. Track building. Validating TestBEDs. L2. - PowerPoint PPT Presentation

Transcript of Automated quantitative analysis of locomotory behavior Of C. elegans populations

Page 1: Automated quantitative analysis of locomotory behavior Of  C. elegans  populations

Automated quantitative analysis of locomotory behavior

Of C. elegans populations

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Fig 1: Contour modeling through B-spline

An automated image analysis system has been constructed to perform quantitative morphometry and locomotory behavior analysis of C. elegans populations from time-lapse wide-field microscope imagery. Multiple worms of varying size, age, sex, and morphology, such as would be found in typical cultures, can be analyzed simultaneously. Each worm is uniquely numbered, and its associated measurements are stored in a spreadsheet. The analysis results are also displayed in a color-coded manner for visual inspection. The system makes explicit use of flexible and detailed geometric worm models in combination with cluster analysis algorithms to achieve reliable identification, classification, and tracking, even when dealing with dense, highly entangled populations. Both short-term (frame to frame) as well as longer term (over multiple frames) movements are analyzed. When available, fluorescent marker expression can be scored in a region or organ-specific manner for each worm as long as sufficient spatial detail is available. Experimental results demonstrate robust automation of this currently tedious and subjective task. In addition to the higher throughput implied by reliable automation, it is expected that this system can also provide verifiable and objective classification of subtle behavioral phenotypes.

Abstract

This work was supported in part by CenSSIS, the Center for Subsurface Sensing and Imaging Systems, under the Engineering Research Centers Program of the National Science Foundation (Award Number EEC-9986821)

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Fig 3: Configuration – independent texture map

Complex Morphometric evolution

Original Segmented

An interesting dynamic feature: The evolution of the curvature

Geometric Description of a Worm

Fig 2: Relative Configuration

Atlas Based SegmentationWorm Descriptor

A popular approach to describe deformable shapes is through a periodic curve (Fig 1) modeled in terms of cubic B-splines and parameterized by its N control points. A worm object is represented by a periodic curve (Fig 1) modeled in terms of cubic B-splines and parameterized by its N control points. From this we can derive the median of the worm which is of particular interest to us because of the accurate estimate of the worm trajectory that it provides.

Conclusion

NQQQX ,,, 21

Cubic B-splines and parameterized by its N control points:

Using the described segmentation and tracking principles, it is feasible the extract the evolution of individual worm curvature distribution from time-lapse wide-field microscope imagery. Alongside with the worm progression speed, it constitutes some very reliable features for classification purposes.

The foundations of a very robust and powerful atlas based segmentation and tracking method for worm-like structures have been established. By design it has the capability to deal with the task of detection and tracking even when dealing with dense, highly entangled populations.Preliminary results are very encouraging and demonstrated good performance in single object tracking and even in cluttered environment. 10 20 30 40 50 60 70 80

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Deformation Operator

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Deformation/Progression operators

In order to design a dynamic behavior model for C-elegans worms, and based on physiological consideration the Progression and deformation Operator have been designed to allow for accurate description of the complete range of possible dynamic movements

We define the generic transformation parameter:

This worm description approach allows for straightforward texture mapping regardless of the actual curvature configuration and allows for ATLAS BASED segmentation

0 0,A

In the necessary implementation of the physiological constraint of the worm shapes, I can be useful to describe the worm through the local curvature of its median axis. Theoretically, the median axis of the worm can be described using an anchor Point A0 and N local curvature angles [θ1, θ2,…, θN] and its constant width profile [w1, w2,…, wN]

Focusing on the curvature

Synthetic Worm Descriptor

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Dynamic modeling and Model Fitting

Using a state-based formulation, we define the state of a worm at time t by its geometric configuration X(n).

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Track building

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Optical Segmentation/ Object Detection

Worm Modeling

Model Design

Constraints

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Validation Data Detected Worms

Dynamic Feature Extraction

Modeling

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The purpose of the measurement process is find the object model X(n), that best fits the image data. To do so we search for the transformation parameters T and [θ1, θ2,…, θN] that best fit the measurement data Z(n). The fact that the state transition relation is non linear prevents us from using KALMAN filtering approach. As a result a more strategy approach needs to be used.The idea is to compute the state posterior, p(X(n+1)|Z(t+1)), and select the next state to be the one that maximizes this (Maximum a Posteriori (MAP) estimate).p(X(n+1)|Z(n+1)), is estimated from p(X(n)|Z(n)) and Z(n) using the CONDENSATION algorithm. CONDENSATION follows the same basic iterative steps as a Kalman filter: prediction, measurement, and assimilation.

Nicolas Roussel1, Christine A. Morton2, Qiang Ji1, Fern P. Finger2, Badrinath Roysam1

1Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY 121802Department of Biology, Rensselaer Polytechnic Institute, Troy, NY 12180

Multi-worm Segmentation Sample

Benefits of the CONDENSATION approach

• Support for multi-modal probability distributions(Multi-object situations are better supported (less likely to lose track of objects)

• Robustness

• Computationally efficient

Clutter Situation

Multiworm

References

W. Geng, P. Cosman, C. Berry, Z. Feng, and W.R. Schafer, “Automatic Tracking, Feature Extraction and Classification of C. elegans Phenotypes,” IEEE Transactions on Biomedical Engineering. To appear in October issue of IEEE Transactions on Biomedical Engineering, 2004.

J. Baek, P. Cosman, Z. Feng, J. Silver, and W. R. Schafer, “Using machine vision to analyze and classify C.elegans behavioral phenotypes quantitatively”. J. Neurosci Meth 118, pp. 9 –21, 2002.

M. Isard and A. Blake, "Condensation -- conditional density propagation for visual tracking," International Journal of Computer Vision 29(1), pp. 5--28, 1998.