A Model Based Neuron Detection Approach Using Sparse Location Priors

Transcription

1 A Model Based Neuron Detection Approach Using Sparse Location Priors Electronic Imaging, Burlingame, CA 30 th January 2017 Soumendu Majee 1 Dong Hye Ye 1 Gregery T. Buzzard 2 Charles A. Bouman 1 1 Department of ECE Purdue University; 2 Department of Mathematics Purdue University;

2 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 2

3 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 Mouse brain being imaged by multi-photon fluorescence Microscopy * * Levene, Michael J., et al. "In vivo multiphoton microscopy of deep brain tissue." Journal of neurophysiology 91.4 (2004):

4 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 Normal Neuron Blood Vessel Neuron affected by GCaMP overexpression Background noise 4

5 Our Solution Our approach: MBND (Model Based Neuron Detection using sparse location priors) Formulate as an image reconstruction problem Training Data Neuron Shape Models Test Data Background Model Dendite Model Forward Model Compute MAP Estimate Location Images Get Neuron Centers Prior Model 5

6 Forward Model Image Nx1 Convolution operator with Neuron shapes as kernel NxN Location image Nx1 Truncated idct matrix NxM Background offset coefficients Mx1 Impulsive noise Nx1 Gaussian noise Nx1 η k=1 Y = A (k ) X (k ) + Bθ + W I + W G X (1) A (1) A (1) X (1) A (1) X (1) + A (2) X (2) η : number of shape models We use η = 2 X (2) A (2) X (2) A (2) 6

7 Formulating the MAP Cost Function Neurons and dendrites sparsely distributed in image,, are sparse X (1) X (2) W I Use sparsity as a prior for MAP estimate Joint MAP estimate of,,, : X (1) X (2) θ W I 2 1 X (1)*, X (2)*,W * I,θ * = argmin X (1),X (2 ),W I,θ 2 2σ Y A(k ) X (k ) W I Bθ WG k= X (k ) + 1 W σ 1 I 1 k=1 k σ WI Shape models Location images Dendrites: Impulsive noise Low- Frequency Background Offset Sparsity Prior 7

8 Minimizing the MAP Cost Function Cost function is convex Use ICD (Iterative Coordinate Descent) to minimize cost function Globally convergent for ICD Cost function value vs iteration number 8

9 Estimating Neuron Center Locations X (1) Test Image Y Optimization Block Compute MAP estimate Calculate Local Maxima Calculate Local Maxima Location of Neuron centers Shape models Parameters X (2) 9

10 Training Neuron Shape Models: Overview Training volume Z!Z Σ BB T Background offset 10

11 Training Neuron Shape Models: Overview Training volume BB T Z Σ!Z Manually determine centers of neurons Extract Normal Neuron Patches Extract Overexpressed Neuron Patches Training patches (normal neuron) Training patches (over-expressed neuron) Estimate shape model: Eigenimage for the highest eigenvalue Estimate shape model: Eigenimage for the highest eigenvalue 79 normal neuron patches and 5 over-expressed neuron patches extracted from training volume Background offset 11

12 Trained Shape Models Eigen-images for normal neuron patches Eigen-values for normal neuron patches Choose eigen-image of highest eigenvalue as shape model Eigen-values for over-expressed neuron patches Eigen-images for over-expressed neuron patches Choose eigen-image of highest eigenvalue as shape model 12

13 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 13

14 Experiments Select testing volume : Subset of the full volume: cannot get ground truth for full volume Size(x,y,z): # Neurons present : 23 For both CellSegm and MBND tune parameters to get the best F-score on the test volume # detected neurons that are true precision= # detected neurons recall= # detected neurons that are true # true neurons F-score = 2 precision recall precision+recall 14

15 Comparison with Baseline: Slice 8 Test image Annotated Ground Truth MBND: Precision = 0.95 Recall = 0.87 F-score = 0.91 Baseline: Precision = 0.18 Recall = 0.10 F-score=0.13 Baseline MBND Legend: True Positive False positive False negative Slice 08 15

16 Comparison with Baseline: Slice 18 Test image Annotated Ground Truth MBND: Precision = 0.95 Recall = 0.87 F-score = 0.91 Baseline: Precision = 0.18 Recall = 0.10 F-score=0.13 Baseline MBND Legend: True Positive False positive False negative Slice 18 16

17 Comparison with Baseline Method Precision Recall plot comparison between our proposed method and CellSegm Run MBND on test data Vary neuron regularizer σ 1 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 17

18 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 18

19 Acknowledgements We acknowledgement support from: The National Science Foundation (Grant # ). 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 19

20 Thank you! 20