Segmentation of X-ray microtomography images of soil using gradient masks
Introduction
The segmentation of images to identify structural units of interest is a typical problem in geosciences and many other disciplines. One example is the analysis of pore structure in soil or other porous media based on grey scale images obtained by X-ray tomography (Wildenschild et al., 2002, Pierret et al., 2002, Kaestner et al., 2008, Vogel et al., 2010). The general problem is to find a suitable rule to attribute each pixel to either pore or solid. Ideally, the grey histogram is bimodal so that a threshold value can be easily identified. However, depending on image resolution, there are always structural features (i.e. pores) in the size range of single pixels and thus, due to what is known as ‘partial volume effect’ there is a smooth transition between pores and solid. The greater the volume fraction of structural features close to the image resolution, the more important becomes an objective and reproducible determination of segmentation thresholds because the results of subsequent analysis may be highly sensitive to this segmentation procedure.
Comparative studies support that there is rarely only one segmentation method that outperforms all others when different test images and thresholding scenarios are tested (Sahoo et al., 1988, Sezgin and Sankur, 2004). In a recent review paper concerning X-ray computed tomography images of porous materials Iassonov et al. (2009) compare various segmentation techniques, such as global thresholding, local adaptive thresholding, region growing, deformable surfaces, probabilistic fuzzy clustering and Bayesian methods, concluding that the use of local spatial information is crucial for obtaining good segmentation quality. Furthermore, they emphasise the need for reliable, consistent, computationally efficient and automated algorithms. The combination of different techniques to a hybrid method is a promising approach, when single methods fail. Therefore, we follow the approach of Pavlidis and Liow (1990) to merge region information and boundary information to an integrated technique. In their work region growing was used as a rather rough first approximation for segmentation followed by edge modification and artifact correction as post-processing steps. We suggest an approach which is especially suited for the rather simple case of two-phase classification in images with homogeneous background (i.e. without intensity drift) which allows for global thresholding. Edge detection is used as a pre-processing step to isolate those regions containing the most valuable information and to determine therewith suitable thresholds. Subsequently we apply bi-level segmentation based on region growing for the final segmentation. All presented image processing routines are coded in C/C++ and added to the QuantIm image processing library which is available at www.quantim.ufz.de.
Section snippets
Background
Fig. 1 depicts a schematic bimodal histogram of soil with 30% porosity. It is described by two Gaussian distributions representing soil matrix and pore space. The tails of the two distributions overlap to form a fuzzy region where a single threshold, Tmono, is hard to define, be it by simple histogram evaluation, entropy or class variance consideration. Vogel and Kretzschmar (1996) proposed a bi-level segmentation approach adapted to such histograms. At a lower threshold, Tmin, all voxels are
Threshold selection
The optimal choice of a threshold value between pores and solid depends on the characteristic transition in grey values when crossing the boundary between pores to solid. In case of low porosity these transition zones are too scarce to be visible in the global histogram of the image. Hence, our approach is to first select the transition zones and then to analyse the grey histogram of only those regions since the rest of the image hardly contains any further information (Gonzalez and Woods, 2002
Performance testing
Systematic testing of performance for increasing edge smoothness and signal-to-noise ratio is necessary to evaluate the robustness of our segmentation method. As an artificial test image we generated a multigaussian random field by using a Direct fourier transform method (Robin et al., 1993). Since its histogram is Gaussian, we executed a grey value transformation to gain a bimodal distribution with a predefined porosity of 5% that matches well the detectable macroporosity in the soil samples
Examples
In Fig. 6 we compare the segmentation results of three soil samples with completely different pore structures, to show the robustness of the proposed segmentation procedure.
The histograms of the original images and the masked images are compared in Fig. 7. The frequency distribution within the gradient masks differ slightly in shape while the skewness of all distributions is negative. Thus, transitions from soil matrix to partial volume pores are more frequent than transition to pure dark pore
Conclusions
A large amount of small features which are close to image resolution is a big challenge for thresholding since partial volume effects cause unimodal grey value histograms with a long tail distribution. Bi-level segmentation based on local spatial information is a suitable method which effectively excludes small fuzzy objects while boundaries of larger objects are preserved. Thereby, gradient masks assure an objective and fully automatic determination of the required thresholds. No method
Acknowledgements
We are grateful to thank Anders Kaestner for fruitful comments and suggestions that helped to improve the quality of the paper.
References (15)
- et al.
Imaging and image processing in porous media research
Advances in Water Resources
(2008) - et al.
3D reconstruction and quantification of macropores using X-ray computed tomography and image analysis
Geoderma
(2002) Unimodal thresholding
Pattern Recognition
(2001)- et al.
A survey of thresholding techniques
Computer Vision, Graphics, and Image Processing
(1988) - et al.
Topological characterization of pore space in soil sample preparation and digital image-processing
Geoderma
(1996) - et al.
Using X-ray computed tomography in hydrology: systems, resolutions, and limitations
Journal of Hydrology
(2002) - et al.
A new method for image segmentation
Computer Vision, Graphics, and Image Processing
(1989)
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