Figure 1.
Histogram equalized 2D sample images from our image dataset.
Sample images with (time point, z-slice) pairs at (A) (5,13), (B) (9,14), (c) (10,11), (D)(25,14), (E) (36,15), and (F) (83,18). Each image has dimension: 241×241 pixels and has voxel resolutions: x =
y = 0.385 and
z = 3 microns.
Figure 2.
Flow diagram of proposed method.
Detailed block diagrams of our proposed methods. Two dimensional (2D) version of the original 3D (A) Input image, (B) Pre-processed image, (C) Locally enhanced image (LEI) image; 2D version of the volume rendered images as (D) result of rough centroid extraction, (E) refined result after local shape analysis of LEI profiles, and (F) final result of centroid extraction after combining fragmented nuclei.
Figure 3.
An Example of processing results for candidate regions and enhanced image.
Two dimensional (2D) version of the original 3D (A) Input image, (B) Preprocessed image, (C) Candidate masks, (D) Candidate regions, and (E) Locally enhanced image (LEI).
Figure 4.
Procedure for extraction of candidate nuclei centroids (Stage-1).
Block diagram shows how we obtain candidate centroids systematically from locally enhanced image. (A) Locally enhanced image (LEI), (B) Candidate centroids. Spherical color regions indicate centers of local maxima regions.
Figure 5.
Procedure for refining the results of initial centroid detection (Stage-2).
Block diagram shows the procedure for refining the results of Stage-1 detection. (A) Rough centroids, (B)Locally enhanced image (LEI), and (C) Stage-2 centroids after removing some false centroids in Stage-1.
Figure 6.
Procedure for combining fragmented nuclei (Stage-3).
Schematic diagram shows the iterative grouping of fragmented nuclei if exist. (A) Stage-2 detection results, (B) Final nuclei centroids.
Figure 7.
Results for centroid extraction at various stages of our method.
(A, D) Stage-1 results of centroid extraction after local maxima searching for a sample image at t70, (B, E) Refined results of Stage-1 centroids after profile shape analysis using locally enhanced image (Stage-2), and (C, F) Refined results of Stage-2 centroids after combining fragmented nuclei (Stage-3). Top and bottom rows show the results for Variant-1 and Variant-2, respectively.
Table 1.
Results for nuclei extraction at various stages of centroid extraction.
Figure 8.
Results for centroid extraction by proposed method (Variant-2) for lower time–point images.
(A–E) Preprocessed and manually thresholed 3D images (volume rendered) for time points t10, t12, t14, t40, and t45, respectively. (F–J) Corresponding results of centroid extraction. All individual centroids are represented by spherical regions using different colors.
Figure 9.
Results for centroid extraction by proposed method (Variant-2) for higher time–point images.
(A–E) Preprocessed and manually thresholed 3D images (volume rendered) for time points t57, t70, t77, t85, and t97, respectively. (F–J) Corresponding results of centroid extraction. All individual centroids are represented by spherical regions using different colors.
Figure 10.
Visual comparison of estimated centroids with corresponding ground–truth centroids.
Volume rendered view of the estimated and ground-truth centroids for images at time point (A, D) t12, (B, E) tp14, and (C, F) t85, respectively. Top row shows the results by our method, while bottom row shows the same by the method, proposed by Bao et al. Yellow and Green spheres show the estimated centroids by our and Bao’s methods, while pink spheres show ground–truth (GT) centroids. Blue color in the figures shows the overlapped regions between the estimated and GT centroids.
Figure 11.
Results of number of estimated nuclei by our method.
Blue and red graphs show the plots of the estimated nuclei for (A) Variant-1 and (B) Variant-2 of our method and Bao’s method, respectively. The green graph shows manually identified GT centroids. These plots involve 100 3D images, captured at 100 discrete time points in the early developmental period of mouse–embryo.
Figure 12.
Comparison of Sensitivity, Precision, and RMSE metrics for estimated nuclei (Variant-1).
Performance of nuclei detection over 100 time points (i.e., 100 3D images) in terms of (A) Sensitivity, (B) Precision, and (C) Root Mean Square Error (RMSE). Blue and red graphs show the performance curves for our proposed and Bao’s method, respectively.
Figure 13.
Comparison of Sensitivity, Precision, and RMSE metrics for estimated nuclei (Variant-2).
Performance of nuclei detection over 100 time points (i.e., 100 3D images) in terms of (A) Sensitivity, (B) Precision, and (C) Root Mean Square Error (RMSE). Blue and red graphs show the performance curves for our proposed and Bao’s method, respectively.
Table 2.
Overall detection performances of proposed method.
Figure 14.
Results for average sensitivity, precision, and RMSE.
(A – C) Average sensitivity, (D – F) Average precision, and (G – I) Average RMSE for image series (t1– t66), (B) (t67– t100), and (C) (t1– t100), respectively. Series (t1– t66) and (t67– t100) indicate fixed and variable number of nuclei, while series (t1– t100) indicates the whole dataset. Blue, red, and green bars show the average performances with standard error bars for the proposed method with (i) Variant-1, (ii) Variant-2, and the previous method, respectively.