3D Clumped Cell Segmentation Using Curvature Based Seeded Watershed

Abstract

Image segmentation is an important process that separates objects from the background and also from each other. Applied to cells, the results can be used for cell counting which is very important in medical diagnosis and treatment, and biological research that is often used by scientists and medical practitioners. Segmenting 3D confocal microscopy images containing cells of different shapes and sizes is still challenging as the nuclei are closely packed. The watershed transform provides an efficient tool in segmenting such nuclei provided a reasonable set of markers can be found in the image. In the presence of low-contrast variation or excessive noise in the given image, the watershed transform leads to over-segmentation (a single object is overly split into multiple objects). The traditional watershed uses the local minima of the input image and will characteristically find multiple minima in one object unless they are specified (marker-controlled watershed). An alternative to using the local minima is by a supervised technique called seeded watershed, which supplies single seeds to replace the minima for the objects. Consequently, the accuracy of a seeded watershed algorithm relies on the accuracy of the predefined seeds. In this paper, we present a segmentation approach based on the geometric morphological properties of the 'landscape' using curvatures. The curvatures are computed as the eigenvalues of the Shape matrix, producing accurate seeds that also inherit the original shape of their respective cells. We compare with some popular approaches and show the advantage of the proposed method.

Keywords: Gaussian curvature; Weingarten map; catchment basin; manifold; mean curvature; shape operator; topographic distance; watershed; watershed transform.

Figure 1

In panel (a), a parametric curve in ℝ is shown with the normals at sampled points. The region where the normals are converging has negative curvature, while the opposite is true for where the normals diverge. In panel (b), a parametric surface is depicted, with the two principal directions s(= X_u) and t(= X_υ) at the point P. A portion of the tangent plane to the surface at the point P is also shown in transparent grid, as determined by s and t, and the corresponding normal $\mathbf{N}=\frac{\mathbf{s}\times \mathbf{t}}{|\mathbf{s}\times \mathbf{t}|}$ is the indicated up arrow. The principal directions correspond with the maximum and minimum curvature directions on the surface. All of these images are better visualized in color.

Figure 2

Panel (a) shows a 2D image, while panel (b) shows the same image as an embedded surface. In panel (c), the detected seeds are shown. Panel (d) shows the labels for the two seeds in (c).

Figure 3

3D rendering of two objects in (a). The located seeds, $Ct=k_1^{+}{k}_2^{+}{k}_3^{+}$, are visualized in 3D in panel (b). The final segmentation is shown in panel (c).

Figure 4

A superposition of the bounding contours on the original image.

Figure 5

Flow of the processing steps in the proposed method.

Figure 6

Illustration of the key steps in the proposed segmentation method. Panel (a) is a slice of the original volume to be segmented; (b) is the resulting foreground from the chan-vese method; In panel (c) the obtained seeds are shown; while the resulting segmentation is shown in (d).

Figure 7

Qualitative performance of the 4 methods on a selected volume of simulated HL-60 cell line. Panel (a) shows the original volume. The nuclei are randomly color-coded to distinguish one from another as generated by each method: (b) CellSegm, (c) MINS, (d) ground truth segmentation, (e) SMMF, (f) Proposed.

Figure 8

3D Qualitative comparison of the 4 methods on a sample real data. The top and bottom rows show the 3D volume and a selected 2D slice respectively. Panel (a) shows the original data. The remaining panels are the segmentation results generated by: (b) CellSegm, (c) MINS, (d) SMMF, (e) Proposed method. While the quality indexes suggest good performance on the simulated dataset, the performance on heavily clamped nuclei is low for the CellSegm and SMMF methods. The results from MINS is unable to match the shape of individual cells compared to the proposed method. The first row shows the 3D rendered volume, while the bottom row shows a fixed slice of the volume.

Figure 9

Panel (a) shows a 3D view of a WILD TYPE laval brain nuclei. In panel (b), the 3D segmentation is rendered in ImageJ. In panels (c) and (d) enlarged portions are shown from the original and reconstructed images. Panel (e) shows the quantitative characteristics of the nuclei in the volume.

Figure 10

Panel (a) is a depiction of a MUTANT TYPE larval brain nuclei in 3D volume in ZEN. In panel (b), the 3D segmentation is visualized in ImageJ. In panels (c) and (d) enlarged regions are shown from the original and reconstructed images. Panel (e) similarly shows the quantitative description of the cells.

Figure 11

Panel (a) is a depiction of another MUTANT TYPE 2 larval brain nuclei in 3D volume in ZEN. In panel (b) the 3D reconstruction is shown. The noisy background (GFP) is separated from the true signals using the ACWE [3]. In panels (c) and (d) enlarged regions are shown from the original and reconstructed images. The clustering of the nuclei in panel (e) is based on the segmentation in panel (a).