Elsevier

Pattern Recognition

Volume 33, Issue 8, August 2000, Pages 1383-1393
Pattern Recognition

Model-based segmentation of nuclei

https://doi.org/10.1016/S0031-3203(99)00119-3Get rights and content

Abstract

A new approach for the segmentation of nuclei observed with an epi-fluorescence microscope is presented. The proposed technique is model based and uses local feature activities in the form of step-edge segments, roof-edge segments, and concave corners to construct a set of initial hypotheses. These local feature activities are extracted using either local or global operators and corresponding hypotheses are expressed as hyperquadrics. A neighborhood function is defined over these features to initiate the grouping process. The search space is expressed as an assignment matrix with an appropriate cost function to ensure local and neighborhood consistency. Each possible configuration of nucleus defines a path and the path with least overall error is selected for final segmentation. The system is interactive to allow rapid localization of large numbers of nuclei. The operator then eliminates a small number of false alarms and errors in the segmentation process.

Introduction

Automatic delineation of cell nuclei is an important step in mapping functional activities into structural components in cell biology. This paper examines delineation of individual nucleus that are observed with an epi-fluorescence microscope. The nuclei that we are dealing with are in mammary cells. These cells cover the capillaries that carry milk in the breast tissues. The nuclei of interest reside in a thin layer that surround a particular type of capillary in the tissue. The intent is to build the necessary computational tools for large-scale population studies and hypothesis testing. These nuclei may be clumped together, thus, making quick delineation infeasible. At present stage, we are working on 2D crossing-section images of the tissue which are obtained by focusing the optical system at specific locations along the z-axis. Thus, we can assume that the nuclei abut but do not overlap each other. An example is shown in Fig. 1(a). Previous efforts in this area have been focused on thresholding, local geometries, and morphological operators for known cell size [1], [2]. Others have focused on an optimal cut path that minimizes a cost function in the absence of shape, size, or other information [3], [4], [5], [6], [7].

In this paper, we propose a new approach that utilizes both step-edge and roof-edge boundaries to partition a clump of nuclei in a way that is globally consistent. In this context, images are binarized and boundaries – corresponding to step edges – are recovered. Next, concave corners are extracted from polygonal approximation of the initial boundary segments. These corners provide possible cues to where two adjacent nuclei may come together. Thresholding separates big clumps consisting of several nuclei squeezed together. The boundaries between every two adjacent nuclei inside one clump are not detected by thresholding since they have higher intensities, as shown in Fig. 1(b) and (c). Thus, crease segments are detected [8], [9], [10], [11] which provide additional boundary conditions for the grouping process, as shown in Fig. 1(d). These crease segments correspond to trough edges and are treated as common boundaries between adjacent nuclei. False creases may be extracted in the process. However, since our algorithm need not use all the segments provided, false crease segments can be discarded in the grouping stage in favor of the global optimization. A unique feature of our system is in hyperquadric representation of each hypothesis and the use of this representation for global consistency. The main advantage of such a parameterized representation – as opposed to polygonal representation – is better stability in shape description from partial information. In this fashion, each step-edge boundary segment belongs to one and only one nucleus while each roof-edge boundary segment is shared by two and only two nuclei. These initial hypotheses and their localized inter-relationship provides the basis for search in the grouping step. This is expressed in terms of an adequate cost function and minimized through dynamic programming. The final result of this computational step is then shown to a user for verification and elimination of false alarms.

In the next section, we will briefly review each step of the representation process and parameterization of each hypothesis in terms of hyperquadric. This will be followed by the details of the grouping protocol, results on real data, and concluding remarks.

Section snippets

Representation

The initial step of the computational process is to collect sufficient cues from local feature activities so that a set of hypotheses – not all of them correct – can be constructed for consistent grouping. These initial steps include thresholding, detection of concave points from boundary segments, extraction of crease segments from images, and hyperquadric representation of each possible hypothesis.

Grouping for nuclei

Let each clump be represented by nb boundary segments bi,i=1,…,nb and nc crease segments ci,i=1,…,nc. We assume that there are at most nb nuclei in the clump because each nucleus should have at least one boundary segment detected to indicate its existence. The nucleus Φi correspondent to the index of bi is defined as a set of boundary and crease segments belonging to the ith nucleus. Note that Φi does not necessarily include bi and may be empty. All the segments in a certain Φi is fitted by the

Conclusion

We have presented a new approach for segmentation of nuclei based on partial geometric information. Two key issues are hyperquadric fitting and assignment matrix. Hyperquadric representation can model a broad range of shapes from partial boundary information. The assignment matrix, on the other hand, converts the segmentation problem into a constrained optimization problem. Our approach aims for global consistency, and as a result, it is less error prone and generates a few false alarm for

Acknowledgements

Authors thank Dr. Mary Helen Barcellos-Hoff and Mr. Sylvain Costes for motivating the problems, valuable discussion, and providing the data used in this experiment. This work is supported by the Director, Office of Energy Research, Office of Computation and Technology Research, Mathematical, Information, and Computational Sciences Division, and Office of Biological and Environmental Research of the U. S. Department of Energy under contract No. DE-AC03-76SF00098 with the University of

About the Author—GE CONG received the BS degree in electrical engineering from Wuhan University, Wuhan, China in 1992 and the Ph.D degree in computer science from Institute of Automation, Chinese Academy of Sciences in 1997. He is currently a staff scientist in Lawrence Berkeley National Laboratory. His research interests include computer vision, pattern recognition and bioinformatics.

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About the Author—GE CONG received the BS degree in electrical engineering from Wuhan University, Wuhan, China in 1992 and the Ph.D degree in computer science from Institute of Automation, Chinese Academy of Sciences in 1997. He is currently a staff scientist in Lawrence Berkeley National Laboratory. His research interests include computer vision, pattern recognition and bioinformatics.

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