A Model Based Neuron Detection Approach Using Sparse Location
Priors
Electronic Imaging, Burlingame, CA 30th January 2017
Soumendu Majee1
Dong Hye Ye1
Gregery T. Buzzard2
Charles A. Bouman1
1 Department of ECE Purdue University; 2Department of Mathematics Purdue University;
Introduction
§ There has been a recent push towards mapping the brain
§ Need high temporal(time) and spatial resolution functional imaging of brain for long duration
§ Calcium imaging with fast fluorescent indicators like GCaMP6 can do: • Temporal resolution: milliseconds • Spatial resolution: microns
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Motivation for Neuron Detection
§ Calcium imaging is done via fluorescence microscopy • Speed limited by sequential laser scan
§ How to make it faster? • Find neuron locations and focus
measurements on those locations only
3 * Levene, Michael J., et al. "In vivo multiphoton microscopy of deep brain tissue." Journal of neurophysiology 91.4 (2004): 1908-1912.
Mouse brain being imaged by multi-photon fluorescence Microscopy *
Challenges for Detecting Neurons in GCaMP6 Images
§ Large volume size
§ Highly noisy volume
§ Neuron morphology can vary
§ Large illumination variation across the image
§ Cylindrical blood vessels look similar to neurons
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Neuron affected by GCaMP over-expression Background
noise
Normal Neuron
Blood Vessel
Our Solution
§ Our approach: MBND (Model Based Neuron Detection using sparse location priors)
§ Formulate as an image reconstruction problem
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Training Data
Neuron Shape Models
Forward Model
Background Model
Dendite Model
Prior Model
Test Data
Compute
MAP Estimate
Location Images
Get Neuron Centers
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Y = A(k )X (k )
k=1
η
∑ + Bθ +WI +WG
Image Nx1
Impulsive noise Nx1
Convolution operator
with Neuron shapes as kernel
NxN
Background offset coefficients Mx1
Truncated iDCT
matrix NxM
Gaussian noise Nx1
Location image Nx1
X (1)
X (2)
A(1)
A(2)
A(1)X (1)
A(2)X (2)
A(1)X (1) + A(2)X (2)
Forward Model
η : number of shape modelsWe use η = 2
Formulating the MAP Cost Function
§ Neurons and dendrites sparsely distributed in image • , , are sparse • Use sparsity as a prior for MAP estimate
§ Joint MAP estimate of , , , :
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X (1)* ,X (2)* ,WI*,θ * = argmin
X (1) ,X (2 ) ,WI ,θ
12σWG
2 Y − A(k )X (k )
k=1
2
∑ −WI − Bθ2
2
+ 1σ k
X (k )1
k=1
2
∑ + 1σWI
WI 1
⎛
⎝⎜
⎞
⎠⎟
X (1) X (2) WI
X (1) X (2) θ WI
Shape models
Location images
Dendrites: Impulsive
noise
Low-Frequency
Background Offset
Sparsity Prior
Minimizing the MAP Cost Function
§ Cost function is convex
§ Use ICD (Iterative Co-ordinate Descent) to minimize cost function
– Globally convergent for ICD
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Cost function value vs iteration number
Estimating Neuron Center Locations
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Compute
MAP estimate
Optimization Block
X (1)
Y
X (2)
Calculate Local
Maxima
Calculate Local
Maxima
Location of Neuron centers
Test Image
Shape models
Parameters
Z
BBT
Σ
!Z
Background offset
Training volume
Training Neuron Shape Models: Overview
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Z
BBT
Σ
!Z
Background offset
Training volume
Training patches (normal neuron)
Training patches (over-expressed neuron)
Extract NormalNeuronPatches
Estimate shape model:
Eigenimage for the highest
eigenvalue
Estimate shape model:
Eigenimage for the highest
eigenvalue
Extract Over-
expressed Neuron Patches
Manually determine centers of neurons
79 normal neuron patches and 5 over-expressed neuron patches extracted from training volume
Training Neuron Shape Models: Overview
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Trained Shape Models
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Eigen-images for normal neuron patches
Eigen-images for over-expressed neuron patches
Eigen-values for normal neuron patches
Eigen-values for over-expressed neuron patches Choose eigen-image of highest eigenvalue as shape model
Choose eigen-image of highest eigenvalue as shape model
Baseline for Comparison
§ As baseline we compare with a widely used method CellSegm • CellSegm is a toolbox for automated cell detection and
segmentation for fluorescence microscopy • Method overview:
– Iterative thresholding – Hole filling – Classification based on size of region above threshold
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Experiments
§ Select testing volume : • Subset of the full volume: cannot get ground truth for full
volume • Size(x,y,z): 101×104×21 • # Neurons present : 23
§ For both CellSegm and MBND tune parameters to get the best F-score on the test volume
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F-score= 2×precision× recallprecision+recall
precision=#detectedneuronsthataretrue#detectedneurons recall=#detectedneuronsthataretrue#trueneurons
Comparison with Baseline: Slice 8
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MBND: Precision = 0.95 Recall = 0.87 F-score = 0.91 Baseline: Precision = 0.18 Recall = 0.10 F-score=0.13
Slice 08
Test image Annotated Ground Truth
Baseline MBND Legend: True Positive False positive False negative
16 Slice 18
Test image
Baseline
MBND: Precision = 0.95 Recall = 0.87 F-score = 0.91 Baseline: Precision = 0.18 Recall = 0.10 F-score=0.13
MBND Legend: True Positive False positive False negative
Comparison with Baseline: Slice 18 Annotated Ground Truth
Comparison with Baseline Method
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Precision Recall plot comparison between our proposed method and CellSegm
• Run MBND on test data • Vary neuron
regularizer • Fix other parameters • Get a series of
precision-recall values
• Run CellSegm on test data • Vary threshold • Fix other parameters • Get a series of
precision-recall values
σ 1
Conclusion
§ Proposed a novel model based neuron detection method
– Robust to illumination variation and image noise – More accurate than CellSegm – Demonstrated results on real datasets
§ Our method can be extended to use multiple eigen-images in shape model using group sparsity
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Acknowledgements
§ We acknowledgement support from: • The National Science Foundation (Grant # 1318894).
§ We also thank: • Prof. Meng Cui and Dr. Lingjie Kong, Purdue University
for providing the GCaMP6 labeled Calcium imaging data used for evaluating our neuron detection algorithm
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Thank you!
