Automated segmentation of overlapped nuclei using concave point detection and segment grouping
Introduction
Analyzing the morphology of nuclei is important to study nuclei polarization and arrangement on a micro-patterned substrate [1], [2]. And it is an essential step to learn the contribution of the nucleus to the mechanical properties of cells [3]. However, the assessment of nuclei is a huge task for manual measurement. Manual segmentation is subjective and time consuming for large number of nuclei analysis. Thus, automatic nuclei segmentation is needed.
Many algorithms have been proposed to split overlapped cells or nuclei automatically [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. Watershed method is one of the most popular methods to segment overlapped nuclei [4], [5], [6]. Method in [5] is based on watershed. Method in [6] and the first method in [4] are based on marker-controlled watershed. Watershed is not good at dealing with highly overlapped nuclei and is easy to cause over segmentation problem. Marker-controlled watershed reduces over segmentation, but the detection of markers is still not accurate in high overlapped nuclei. The second method proposed in [4] is pixel classification-based supervised segmentation. Another pixel classification-based nuclei segmentation method using Bayesian classification is proposed in [8]. One common defect of pixel classification-based method is its high computational complexity. Curvature detection is another method that is widely used in nuclei segmentation [9], [10], [11], [12], [13], [14], [15]. Different methods to detect concave points were employed. The accuracy of nuclei segmentation is highly dependent on the accuracy of concave point detection. These concave point detection methods are easily affected by noisy nucleus boundary. Unobvious concave point cannot be detected. There is either over segmentation or under segmentation problems in these methods. In [16], nucleus contours are approximated to line segments using a variation of Ramer-Douglas-Peucker algorithm [17]. Sharp turns and inflexion points are detected by evaluating angular change of the line segments. Then contours segmented by sharp turns and inflexion points are set into groups to fit to an ellipse if they satisfy certain criteria. As curvature changes slowly at unobvious concave point, its line segment approximation may miss the unobvious concave point and combine curves in two nuclei as one line segment. In addition, because some nuclei contour segments are short and noisy, it is difficult to find an accurate geometric center by this algorithm. Thus, the group of contours is affected.
To overcome the limitations mentioned above, a novel method is proposed in this paper. Concave points are detected and contour segments are set into groups to fit to ellipses. The contribution of our method can be summarized in three aspects:
- (1)
Level set method is proposed to extract contours and evaluate whether a nucleus is blurry. The three-phase level set method proposed in [18] is employed in the detection of nucleus contour for the first time. It’s able to obtain a closed and smooth contour without any loss of corner or small turn information in contour. The detection result is used to judge whether the nucleus is well focused during image acquisition, which is helpful to set parameters automatically in concave point detection.
- (2)
A novel concave point detection algorithm is proposed. Instead of calculating angles or convexity on edge pixels, a candidate point detection method is proposed. Features are extracted on these candidate points. The robustness of concave point detection is improved. In addition, a candidate point is considered to be a concave point if it fulfills either obvious concave point extraction algorithm or unobvious concave point algorithm. Two different algorithms are proposed which focus on these two kinds of concave point respectively.
- (3)
A simple but efficient method to set contour segments into groups is proposed. The three criteria proposed in initial grouping and group verification are able to ensure that contour segments in the same group belong to one nucleus.
This paper is organized as follows. In Section 2, a three-phase level set method [18] is employed to detect the contour of nucleus. Concave points are detected and contour are split into segments by the concave points. In Section 3, the contour segments are assigned into groups. Each group of contour segments is fitted to an ellipse. Experimental results and conclusion are presented in Sections 4 and 5 respectively.
Section snippets
Contour extraction and concave point detection
It’s a challenge to smooth nucleus contours without smoothing the turns of contours. Nucleus edge may be blurry and the slope of some turns may change slowly. It’s easy to lose useful information during the process of smoothing. Three-phase level set is employed to extract nucleus contour as an initial segmentation. An image is segmented into three regions: nucleus, transition area and background.
Then a group of candidate points are detected. Concave points are further selected from candidate
Segment grouping and ellipses processing
Contours C are split into contour segments by concave points. Ci is the contour segment between concave points Pi and . Ci is connected with and . Before ellipses fitting, two cases are discussed according to the number of concave points:
Case 1: Nc ≤ 3. If the nucleus is an isolate one. If or contour are split into two or three segments. Any two segments are connected by concave point. Thus, grouping is not needed and the contour or contour segments are
Experimental results and discussion
To verify the proposed method, two datasets from Biomechanics and Biomaterial Laboratory, Beijing Institute of Technology are tested. Two kinds of polyacrylamide substrates are prepared according to [34]. In curved surface substrate, the camera focus on one sight and there are lots of fuzzy nuclei. The fuzzy nuclei are important to study the mechanics of cell mechanosensing [35] but always hard to be detected by normal methods. The mean size of nuclei ellipses is 9.9 × 7.4 pixels in curve
Conclusion
A new algorithm to split overlapped nuclei is proposed in this paper. Three-phase level set method is implemented for nucleus contour detection for the first time, which enables the extraction of a smooth nucleus contour. Meanwhile, its result is used to evaluate whether the nucleus is blurry. This is helpful in obtaining corner point detection parameters automatically and exactly. Harris classic corner point detector is employed to detect corners in nuclei image. The detection method makes
Acknowledgements
We would like to express our gratitude to Dr. Dilip K. Prasad from Nanyang Technological University, Singapore for providing his code of the algorithm in [16]. We also want to thank Biomechanics and Biomaterial Laboratory, Beijing Institute of Technology for providing nucleus images.
Wanjun Zhang received B.E. degree from Zhengzhou University, China in 2012. She is currently a Ph.D. candidate at Beijing Institute of Technology, China. Her research interest is medical image processing.
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Wanjun Zhang received B.E. degree from Zhengzhou University, China in 2012. She is currently a Ph.D. candidate at Beijing Institute of Technology, China. Her research interest is medical image processing.
Huiqi Li received Ph.D. degree from Nanyang Technological University, Singapore in 2003. She is currently a professor at Beijing Institute of Technology. Her research interests are image processing and computer-aided diagnosis.