A differential structure approach to membrane segmentation in electron tomography

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Abstract

Electron tomography allows three-dimensional visualization of cellular landscapes in molecular detail. Segmentation is a paramount stage for the interpretation of the reconstructed tomograms. Although several computational approaches have been proposed, none has prevailed as a generic method and thus segmentation through manual annotation is still a common choice. In this work we introduce a segmentation method targeted at membranes, which define the natural limits of compartments within biological specimens. Our method is based on local differential structure and on a Gaussian-like membrane model. First, it isolates information through scale-space and finds potential membrane-like points at a local scale. Then, the structural information is integrated at a global scale to yield the definite segmentation. We show and validate the performance of the algorithm on a number of tomograms under different experimental conditions.

Introduction

Electron tomography (ET) has consolidated its position as the leading technique for visualizing the molecular organization of the cell environment (Lucic et al., 2005, Frank, 2006, Barcena and Koster, 2009, Ben-Harush et al., 2010). The computational stages to derive three-dimensional reconstructions (or tomograms) from the acquired images are well established (Lucic et al., 2005). Nevertheless, their interpretation is not straightforward due to different factors such as the limited tilt range conditions, the low signal-to-noise ratio (SNR, which is particularly poor in cryoET) and the inherent biological complexity. Significant efforts are thus spent to facilitate the interpretation by several stages of post-processing of the tomograms (Volkmann, 2010), which, in the particular case of pleomorphic structures, are primarily noise reduction and segmentation.

Noise reduction intends to improve the SNR and, though there are several alternative methods (e.g. vander Heide et al., 2007, Fernandez, 2009), anisotropic nonlinear diffusion has become the standard tool in the field (Frangakis and Hegerl, 2001, Fernandez and Li, 2003, Fernandez and Li, 2005). The SNR of the tomogram and the denoising method have an influence on the performance of the subsequent segmentation process (Volkmann, 2010). In addition, segmentation is also affected by the artefacts due to the limited tilt range in ET (the ‘missing wedge’ in Fourier space), which produce a significant loss of resolution of the tomogram along the beam direction, thereby making the spatial features in that direction look elongated and blurred.

Segmentation aims to decompose the tomogram into its structural components by identifying the sets of voxels that constitute them. Though tedious and subjective, manual segmentation is the simplest and the most common approach, which consists in that the user assigns the structural features using visualization tools (e.g. He et al., 2008). Several automatic or semi-automatic approaches have been proposed in the field (Sandberg, 2007, Volkmann, 2010). There exist methods based on simple density thresholds (Sandberg, 2007) or more sophisticated optimal thresholding (Cyrklaff et al., 2005), the Watershed transform extended to 3D (Volkmann, 2002), eigenvector analysis of an affinity matrix (Frangakis and Hegerl, 2002), active contours (Bartesaghi et al., 2005), oriented filters (Sandberg and Brega, 2007) and fuzzy logic (Garduno et al., 2008). Also, template matching with simple 3D geometric templates has been proposed for tomograms with relatively good SNR and contrast (Lebbink et al., 2007). Recent reviews discuss about the characteristics, advantages and drawbacks of the different segmentation techniques presented so far in the field (Sandberg, 2007, Volkmann, 2010). Out of all computational methods, the Watershed transform is perhaps the only one that has achieved a fairly good level of dissemination (Volkmann, 2010) and even has been used as a basis to develop further methods or tools (Salvi et al., 2008, Fernandez-Busnadiego et al., 2010). Despite the wealth of methods available and their potential, none has stood out as a general applicable method yet, and manual segmentation still remains the prevalent method. Most popular ET software packages incorporate intuitive graphical tools to assist the user to segment and annotate tomograms, and progressively they are incorporating some of the most known computational techniques (namely, thresholding and the Watershed transform) in order to make segmentation a semi-automatic process.

Detection of membranes plays an important role in segmentation as they encompass compartments within biological specimens, define the limits of the intracellular organelles and the cells themselves, etc.. Several segmentation approaches presented in the field are well suited to membrane detection. The oriented filters (Sandberg and Brega, 2007) showed promising results, but it worked in 2D on a slice-by-slice basis and the 3D models were then created by stacking the membrane contours. Template matching with cuboid-shaped templates (Lebbink et al., 2007) managed to segment fairly well membranes with high contrast. However, this is not the case in cryoET. Furthermore, it was computationally intensive and high performance computing (Fernandez, 2008) was necessary. These two methods have not proved to be robust to deal with high membrane curvature either. The Watershed transform has shown good performance in segmenting membranous structures, such as the Golgi apparatus in good contrast tomograms (Volkmann, 2002). Nevertheless, such performance has not been exhibited under high noise, low contrast conditions, as reported recently (Moussavi et al., 2010). The latter work combined template matching with an elliptical model for the cell membrane and succeeded in extracting the cell boundaries. Nevertheless, it is so specific that it could not be applied for a general case involving any type of membrane-bound organelle. Some other work combined the Watershed transform with an energy-based approach (Nguyen and Ji, 2008), but user intervention was still required and there were a number of parameters difficult to tune.

In this work we present an algorithm for membrane segmentation that relies on local differential structure. The method produces an output map that represents how well every point in the tomogram fit a membrane model. From this map, the definite segmentation is obtained. We evaluate the performance of the algorithm on a number of tomograms under different SNR and contrast conditions.

Section snippets

Membrane model

At a local level, a membrane can be considered as a plane-like structure with certain thickness (Fernandez and Li, 2003, Fernandez and Li, 2005). The density along the normal direction progressively decreases as a function of the distance to the centre of the membrane. This density variation across the membrane can be modelled by a Gaussian function (Fig. 1(a) and (b)) and can be expressed as:I(r)=D02πσ0e-r22σ02where r runs along the direction normal to the membrane, D0 is a constant to set the

Algorithm for membrane detection

The algorithm comprises a number of stages that can be grouped into two main blocks. Fig. 2 shows a flow diagram of the algorithm. The first three stages are intended to isolate information at a suitable scale and find potential membrane-like features according to local detectors. The two last stages are, however, aimed to analyze and integrate the structural information at a global scale. In the following, the different stages are described in detail. The procedure assumes that high grey-scale

Validation

Validation of segmentation algorithms is a difficult topic, as already discussed in the field (Sandberg, 2007, Sandberg and Brega, 2007, Garduno et al., 2008). Most of the segmentation works demonstrate the performance of the methods according to illustrative visual results. Garduno et al. (2008) first addressed the topic and proposed objective criteria to compare the automatic method versus the “ground truth” given by manual segmentation. Other works have proposed and adapted metrics based on

Results

The segmentation algorithm was tested with several tomograms taken under different experimental conditions, including cryo-tomography and the use of contrast agents. The tomograms were preprocessed to rescale the density to a common range of [0, 1], with high values representing electron dense objects. They were also cropped to focus on an area of interest. No other preprocessing was applied to the tomograms (e.g. denoising). The optimal results were obtained using the same basic parameter

Discussion and conclusion

An algorithm to segment membranes in tomograms has been presented. It relies on a simple local membrane model and the local differential structure to determine points whose neighbourhood resembles plane-like features. Those points are then further analyzed to determine which of them do actually constitute the membranes. The performance of algorithm has been analyzed on a number of tomograms that may be considered representatives of standard experimental conditions in electron tomography. In

Acknowledgments

The authors wish to thank Dr. O. Medalia and Dr. W. Baumeister for the D. discoideum dataset, Dr. G.A. Perkins for the mitochondrion dataset, and Dr. E.P.W. Ward, Dr. T.J.V. Yates and Dr. P.A. Midgley for the mesoporous silica dataset. This work has been partially supported by the Spanish Ministry of Science (MCI-TIN2008-01117), the Spanish National Research Council (CSIC-PIE200920I075) and J. Andalucia (P10-TIC-6002). A.M.S. is a fellow of the Spanish FPI programme.

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