Figure 1.
Workflow of seed point detection and segmentation in a 3D synthesized binary image stack.
A–E are volume rendered with the color-map's alpha values of 0.2. (A) The concave point detection (blue points) results of the binary image. (B) The concave point clustering results. All the concave points are categorized into two classes: the points on the junction of the top two touching cells are categorized into the L1 class and the other points on the junction of the bottom two touching cells are categorized into another class, L2. The light green color points are the clustering center of each class of concave points, Ĉ1 and Ĉ2. (C) The 26 cubic neighbor points (reddish purple points) of each class of CPCC points. (D) The seed points of touching cells (red points), chosen from (C) with some restricted conditions. (E) The seed points of isolated cells (the light yellow points) are the local maxima points of the Gaussian-convoluted image. (F) Results of the CC-random walker segmentation, with different cells labeled as unique random colors.
Figure 2.
Schematic diagram of concave point detection in a 2D plane.
(A) Binary image. (B) Contour image. The red point is on the contour, and the red dashed box is a mask centered at the red point. The yellow portion is where the mask intersects the background voxels of the binary image. (C) The candidate concave points (red points) meet the threshold condition. (D) The concave points (red points) meet the minimum concaveness value of its adjacent points.
Figure 3.
Seed points chosen from candidate points in a 3D synthesized binary image stack.
The stack is volume-rendered with the color-map's alpha values of 0.2. The three touching cells are named TC1, TC2 and TC3, and the light green points, Ĉ1 and Ĉ2, are the clustering centers of each class of concave points. (A) The reddish purple points are the 26 cubic neighbor points of the first CPCC point, Ĉ1. (B) The red points are the seed points chosen from the reddish purple points from (A) under some restricted conditions. (C) The reddish purple points are the 26 cubic neighbor points of the second CPCC point, Ĉ2. (D) The red points are seed points chosen from the reddish purple points of (C) under some restricted conditions. (E) The total seed points of (B) and (D). (F) The merge of all the seed points in (E) under some restricted conditions.
Figure 4.
Cell detection and segmentation on the K1 stack.
The stack is a preprocessed binary image and volume-rendered with the color-map's alpha values of 0.2. (A) The CPCC point result (light green points). The dashed circle indicates the cell-touching region. (B) The seed point (red points) of touching cells from the 26 cubic neighbor points of CPCC. (C) The seed points (light yellow points) of sparse cells. (D) Results of the CC-random walker segmentation, where different cells are labeled in unique random colors.
Figure 5.
Seed point detection and segmentation on the K2 stack.
The stack is a preprocessed binary image and is volume-rendered with the color-map's alpha values of 0.2. The black ring is a large vessel. (A) The results of the CPCC points (light green point). (B) The seed points (red points) of touching cells selected from the 26 cubic neighbor points of CPCC. (C) The seed points (light yellow points) of sparse cells obtained by extracting the local maximum of the Gaussian-convoluted image. (D) Results of the CC-random walker segmentation. Different cells are labeled in unique random colors.
Figure 6.
Comparison of different detection results achieved with the investigated methods on K1 and K2 stacks.
The top and bottom rows represent the K1 and K2 stacks. The stacks are preprocessed binary images and are volume-rendered with the color-map's alpha values of 0.2. The yellow points are the ground truth, and the red points are cell centroids achieved through different segmentation methods. The green crosses indicated that the cells that are not detected. The green arrows indicated the false detected cells.
Table 1.
Performance of cell detection results using different methods on K1–6 stacks.
Table 2.
Performance of cell detection results using different methods on C1–20 stacks.
Figure 7.
Comparison of different segmentation results achieved with the investigated methods on some two-dimensional slices.
The slices are from the 3D original and segmented results of the K1 and K2 stacks. Each cell is labeled using one gray value in the segmentation results. The green crosses indicate the under-segmented cells. The green arrows indicate the over-segmented cells. The red dashed circles indicate that most of the voxels of one cell are not segmented.
Figure 8.
Comparison of the segmentation results using three different methods.
The light green dashed circle indicates the holes in the binarization step, and the light yellow dashed circle indicates detached contours of two touching cells. (A) Seed point (blue points). The three segmentation methods are all based on the seed points. (B) The segmentation results of the k-mean algorithm, using seed points as the initial points. (C) The segmentation results of the marker-controlled watershed algorithm. (D) The segmentation results of the CC-random walker method.
Table 3.
T-test results of our method vs GFT, our method vs MSL, our method vs TWANG under confidence level = 0.05.
Figure 9.
Noise influences on the precision and recall for the K1 stack.
Salt and pepper noise is used here. The red point is the detected point, and the green dashed circle indicates a missing seed point caused by noise. (A–D) The volume-rendered (with the colormap's alpha values of 0.5) binary image stack with different levels of noise density, i.e., 0, 0.03, 0.06, and 0.09. (E–H) The seed point detection results with different levels of noise density, i.e., 0, 0.03, 0.06, and 0.09. For easy observation, the seed point is placed on the binary stack, pre-noise elimination, and the pre-noise elimination binary stack is volume-rendered with the color map's alpha values of 0.2. (I) Performance curves of the seed point detection estimation with varying noise densities.