Fig 1.
Comparison of positive (A) and negative (B) phase contrast images of the MCF 10A cells.
In the positive phase contrast image, cells with larger height show reversed image contrast, while in the negative phase contrast image, all cells have consistent image contrast.
Fig 2.
Cell image segmentation result obtained with different methods.
(A) In the thresholding method, the segmentation result is sensitive to the selection of the threshold value. The detected contours shrink with increasing threshold value. (B) Cell image segmentation with the region based active contour method. (C) Comparison of the contours obtained with the region based active contour method and the thresholding method with different threshold values. It is apparent that both methods underestimate cell actual boundary.
Fig 3.
Contour expansion method for cell boundary detection.
(A) It is assumed that cells have illustrated height profile with one peak located above cell nucleus. In negative phase contrast images, the light intensity of cells is proportional to cell height. Therefore, the light intensity distribution over cell surface is similar to height profile of cells with one peak located above each cell body. (B) Mesh plot of the light inteisity for a selected cell marked with yellow arrows in Fig 2A and 2B. The light intensity decreases towards the cell boundary, which is consistent with the illustration shown in (A). (C) Quiver plot of the gradient of light intensity for the selected cell. Over cell surface, the gradient of light intensity pointing outwards. (D) The procedure of the contour expansion method for cell boundary detection: (a) The raw negative phase contrast image of the selected cell. (b) The thresholding method was used to get a preliminary mask for the selected cell. (c) The boundary of the mask was extracted and taken as the initial contour. (d) With contour expansion method, the initial contour is driven by the field of gradient of light intensity to gradually converge to the cell boundary. (e) The contour is finally converged at the boundary of the cell, where the contour achieves the minimum energy. The comparison of the contour detected with the thresholding method and the proposed method is shown in (B). It is clear that the proposed method provides an improved estimation of the cell boundary.
Fig 4.
(A) Variation of the mean light intensity and (B) its time derivative along detected contours during contour expansion. The mean light intensity gradient decreases with time and mostly reaches its steady state value after about 40 times iteration. The time derivative of the mean light intensity was used as the termination condition for the iteration.
Fig 5.
Segmentation of the clustered cells using the watershed method.
(A) Raw negative phase contrast image. (B) Preliminarily detected mask map with the thresholding method (threshold = 45). (C) Negate of the distance transform. The inset shows the mesh plot of an area marked by a green arrow. (D) Watershed transform for the detection and segmentation of the clustered cells. The yellow masks are detected isolated cells and the green masks are detected clustered cells. The inset is the enlarged area marked by a green arrow, where four cells are aggregated. The watershed method detected eight cells in the area.
Fig 6.
Peak detection for cell localization.
(A) Multiple peaks could be detected in a single cell with the raw image due to the existence of bright spots in the image. (B) The image smoothness is implemented prior to the peak detection. With the smoothed image, only one peak is detected.
Fig 7.
Segmentation of the clustered cells through peak detection.
(A) Raw phase contrast image with detected peaks for the clustered cells. (B) Mask area preliminarily detected with the thresholding method. (C) Segmentation of the mask area based on the distance between the pixels and the detected peaks inside the mask area. Each pixel is associated with the peak which has the shortest distance with it. In the figure, the subareas for individual cells are plotted as different colours. (D) Boundaries of the subareas were extracted as the initial contours for contour expansion operation. (E) After contour expansion, the final contours for each cell were obtained with improved estimation of cell boundaries.
Fig 8.
Contour expansion operation with different gains.
(A) When the gains α and β are large, the internal energy dominates the evolution of contours and the contours tends to shrink to minimize the total energy. (B) With decreased gains, the final detected boundaries expanded and were closer to the cell boundaries. (C) When α and β further decreases to 0.01, optimized estimations of cell boundaries with more details are obtained. (D) Mesh plot of the selected area showing cells and converged contours with different combination ofα and β. The combination α = β = 1 gives poor estimation of cell boundaries compared with the other two combinations.
Fig 9.
The contour expansion operation is robust to the selected threshold value.
The contour expansion was performed with the initial contours obtained with threshold value of 45 (A) and 65 (B). The final converged contours are close to each other, as shown in (C), which implies that the contour expansion operation is robust with respect to the selection of threshold value. (D) The enlarged image for the selected area in (C).
Fig 10.
Comparison of boundary detection obtained with different methods for isolated cells.
(A) The boundaries detected with the thresholding method, region based active contour method, and the contour expansion method for all isolated cells in the field of view. (B) Comparison of the areas enclosed by the contours detected with different methods. The proposed method detects much larger areas than the other two methods.
Fig 11.
Demonstration of cell localization, boundary detection, and segmentation of the clustered cells.
(A) For the negative phase contrast image, peaks of light intensity are detected for all cells, as indicated by red circles. (B) Preliminary masks are obtained with the thresholding method. Masks in green are areas with multiple peaks indicating clustered cells. Masks in yellow are areas with single cell. (C) The boundaries of the preliminarily detected masks are extracted to serve as initial contours for individual cells. (D) Contour expansion method is applied to detect cell boundaries for all cells in the-field-of-view. Except one oversegmentation (marked by a yellow arrow) and one falsely detected cell from a debris (marked by a blue arrow), all the other cells are successfully segmented.
Fig 12.
Cell image segmentation result for phase contrast images from four different experiments.
(A) Raw negative phase contrast images. (B) Segmentation result with false segmented cells pointed by arrows.
Table 1.
Summary of the false segmentation rates obtained with the proposed method.