Article Figures & Data
Figures
- Figure 1.
Visualization of the correlation images of six pixels. The correlation image is a two-dimensional visualization of the feature vector Ri of pixel i (e.g. R1 for pixel 1). The color (value) of each pixel shown in each correlation image is the pixel-to-pixel correlation between that pixel and the pixel marked in red. Lighter colors represent higher correlations, with the correlation scale truncated at zero. The patch is taken from the Neurofinder 02.00 training dataset and contains two cells. Pixels 1 and 2 belong to the same cell, pixels 3 and 4 belong to the same cell, and pixels 5 and 6 are background pixels. Although the pairs of pixels 1 and 2, pixels 3 and 4, and pixels 5 and 6 are not always highly correlated, their correlation images are nearly identical.
- Figure 2.
Sparse computation constructs a sparse similarity graph. Comparison of a complete similarity graph and the similarity graph constructed by sparse computation for an example patch. For the purpose of illustration, the nodes are positioned based on the two-dimensional PCA projection of the feature vectors of pixels offset by a small uniformly sampled perturbation. A, Mean intensity image of the patch with the outline of two cells marked in red and blue. B, Complete similarity graph with an edge between every pair of pixels. For the purpose of illustration, only 10,000 randomly sampled edges are shown. C, Sparse similarity graph constructed by sparse computation with a three-dimensional PCA projection and a grid resolution of κ = 25. Two clusters of pixels (marked with red and blue rectangles) are identified by Sparse Computation. These two clusters match the spatial footprints of the two cells shown in A.
- Figure 3.
Overview of the HNCcorr algorithm. The top and bottom rows, respectively, summarize the preprocessing steps and the main steps of the algorithm. A, Average intensity image of the input dataset consisting of a calcium-imaging recording. B, Average intensity image of a patch constructed for a positive seed (green) and the corresponding negative seeds (red). C, Description for computing the pairwise similarity weight between two pixels. D, HNC is the clustering model solved to segment a single cell. E, Optimal clusters for the HNC problem as a function of λ. Black pixels are selected for the cluster, denoted by S *(λ). F, Visualization of the postprocessing step. Clusters that are too small/large are discarded. The remaining cluster closest to the preferred size is selected as the footprint of a cell. G, Output for a single patch; the footprint of a cell if a cluster was selected, or “No cell” if all clusters are discarded.
- Algorithm 1:
HNCcorr - Single cell segmentation.
- Algorithm 2:
Seed selection and outer loop for HNCcorr algorithm.
- Algorithm 3:
Size-based post-processor for the HNCcorr algorithm.
- Figure 4.
Approximate percentage of active cells among annotated cells in the training datasets. To determine the activity of the cells in a movie, we used the following approximate analysis. First, we downsample the movie by averaging 10 frames. For every annotated cell, we compute the average intensity over time of the pixels in the spatial footprint. This time series is used an estimate of the signal of the cell. A cell is then considered active if the Δ f/f (Jia et al., 2011) of this time series is at least 3.5 SDs above the median of Δ f/f for a minimum of 3 potentially nonsequential time steps. Due to the approximate nature of this analysis, its interpretation should be limited to understanding the general ratio between active and inactive cells in the datasets.
- Figure 5.
Cell identification scores for the HNCcorr, CNMF, and Suite2P algorithms on the Neurofinder test datasets with active cells. For each of the listed metrics, higher scores are better. The data are taken from Neurofinder submissions Sourcery by Suite2P, CNMF_PYTHON by CNMF, 3dCNN by ssz, and submission HNCcorr by HNCcorr.
- Figure 6.
Footprints and ΔF/F signals for annotated cells in the Neurofinder training dataset 01.01 that were uniquely identified by one of the algorithms. Segmented footprints and ΔF/F signal for up to four cells are shown for each of the algorithms. Each cell also appeared in the reference annotation, but it was not identified by any of the other algorithms. The segmented spatial footprints are overlaid on the mean intensity image, scaled to show values from the first percentile up to the 99th percentile.
- Figure 7.
Footprints and ΔF/F signals for annotated cells in the Neurofinder training dataset 02.00 that were uniquely identified by one of the algorithms. Segmented footprints and ΔF/F signal for up to four cells are shown for each of the algorithms. Each cell also appeared in the reference annotation, but it was not identified by any of the other algorithms. The segmented spatial footprints are overlaid on the mean intensity image, scaled to show values from the first percentile up to the 99th percentile.
- Figure 8.
Cell identification scores on all test datasets for the three leading submissions of the Neurofinder benchmark in July 2018. For each of the listed metrics, higher scores are better. The 3dCNN entry is based on the Neurofinder submission 3dCNN by ssz. The Suite2P + Donuts (Pachitariu et al., 2013) entry is taken from the submission Sourcery by Suite2P. It uses the Donuts algorithm for datasets 00.00, 00.01, and 03.00 and the Suite2P algorithm for the remaining datasets. The HNCcorr + Conv2d entry is taken from the submission HNCcorr + conv2d by HNCcorr. It uses the Conv2d algorithm [S. Gao, (https://bit.ly/2UG7NEs)] for datasets 00.00, 00.01, and 03.00 and the HNCcorr algorithm for the remaining datasets. The results obtained with the Conv2d algorithm reported here differ slightly from the Conv2d submission on the Neurofinder benchmark since the Conv2d model was retrained by the authors of this article.
- Figure 9.
Running time results for nine training datasets of the Neurofinder benchmarks. Running times are based on a single evaluation.
- Figure 10.
F1-score for the CNMF algorithm for various values of K on nine training datasets of the Neurofinder benchmark. The parameter K specifies the number of cells to consider initially for the matrix factorization. The number n, reported in parenthesis, is the number of cells in the reference annotation of the dataset.
- Figure 11.
Cell identification scores for the CNMF algorithm for various values of K on the Neurofinder 02.01 training dataset. The parameter K specifies the number of cells to consider initially for the matrix factorization. This dataset has 178 cells in its reference annotation.
Tables
- Table 1:
Characteristics of the test datasets of the Neurofinder benchmark and their corresponding training datasets
Name Source Resolution Length Frequency Brain region Annotation method 00.00 Svoboda laboratory 512 × 512 438 s 7.00 Hz vS1 Anatomical markers 00.01 Svoboda laboratory 512 × 512 458 s 7.00 Hz vS1 Anatomical markers 01.00 Hausser laboratory 512 × 512 300 s 7.50 Hz v1 Human labeling 01.01 Hausser laboratory 512 × 512 667 s 7.50 Hz v1 Human labeling 02.00 Svoboda laboratory 512 × 512 1000 s 8.00 Hz vS1 Human labeling 02.01 Svoboda laboratory 512 × 512 1000 s 8.00 Hz vS1 Human labeling 03.00 Losonczy laboratory 498 × 467 300 s 7.50 Hz dHPC CA1 Human labeling 04.00 Harvey laboratory 512 × 512 444 s 6.75 Hz PPC Human labeling 04.01 Harvey laboratory 512 × 512 1000 s 3.00 Hz PPC Human labeling Data reproduced from Neurofinder (CodeNeuro, 2016).
- Table 2:
Dataset dependent parameter values used for the HNCcorr implementation. Parameters were selected to maximize the F1-score on the corresponding neurofinder training datasets
Dataset Patch size Radius circle Size Postprocessor Negative seeds Superpixel Lower bound Upper bound Expected size (m) 
(k) (nmin) (nmax) (navg) 00.00 31 × 31 10 pixels 5 × 5 40 pixels 150 pixels 60 pixels 00.01 31 × 31 10 pixels 5 × 5 40 pixels 150 pixels 65 pixels 01.00 41 × 41 14 pixels 5 × 5 40 pixels 380 pixels 170 pixels 01.01 41 × 41 14 pixels 5 × 5 40 pixels 380 pixels 170 pixels 02.00 31 × 31 10 pixels 1 × 1 40 pixels 200 pixels 80 pixels 02.01 31 × 31 10 pixels 1 × 1 40 pixels 200 pixels 80 pixels 03.00 41 × 41 14 pixels 5 × 5 40 pixels 300 pixels 120 pixels 04.00 31 × 31 10 pixels 3 × 3 50 pixels 190 pixels 90 pixels 04.01 41 × 41 14 pixels 3 × 3 50 pixels 370 pixels 140 pixels Data Type of test p value Figure 5 Drawn i.i.d. One-sided signed rank test HNCcorr vs. 3dCNN: p > 0.4, F1-score (uncorrected for multiple tests) HNCcorr vs. Suite2P: p > 0.2, HNCcorr vs. CNMF: p ≤ 0.05. Figure 8 Drawn i.i.d. One-sided signed rank test HNCcorr + Conv2D vs. 3dCNN: p > 0.2, F1-score (uncorrected for multiple tests) HNCcorr + Conv2D vs. Suite2P + Donuts: p > 0.1. Figure 9 Drawn i.i.d. One-sided signed rank test HNCcorr vs. Suite2P: p > 0.4, Solve time (uncorrected for multiple tests) HNCcorr vs. CNMF: p ≤ 0.10. - Table 4:
F1, Precision, and recall scores for three different clustering methods on the neurofinder 02.00 training dataset with the same seed selection and postprocessing methods as HNCcorr
Correlation similarity (sim)2 similarity Clustering model F1 Precision Recall F1 Precision Recall HNC 70.3 65.6 75.6 73.8 72.6 75.1 Spectral clustering (k-means) 46.5 41.9 52.3 49.2 49.2 49.2 Spectral clustering (threshold) 22.4 13.1 77.2 23.7 14.4 66.0 For each clustering method, results are shown with two similarities measures: correlation and (SIM)2.
Extended Data 1
The MATLAB code used to generate the results reported in this work. Instructions are provided in the readme.md file. The code requires the JSONlab toolbox, the Imagesci toolbox, and a C-compiler for MATLAB. Download Extended Data 1, ZIP file.
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