Application of the rolling ball algorithm to measure phase volume fraction from backscattered electron images
Introduction
In metallurgy it is a common practice to use metallography to characterize microstructures and interpret details on composition and thermo-mechanical processing of metals and alloys. In the past few decades, scanning electron microscopy (SEM) has become a powerful and versatile technique for microstructural characterization. The backscattering electron (BSE) operation mode is, in particular, commonly used to investigate microstructural features in which differences in atomic number, i.e. chemical composition, are expected [1]. Thus, BSE images can be suitable to characterize metallic phases resulting from long-range diffusional transformation, in which solute partition typically takes place.
Phase fractions can be quantified by using the manual point counting method, as described in the ASTM E562 standard [2]. Grid points are distributed throughout the investigated image and an operator visually discriminates which points lie within each phase and on the phase boundaries. The percentage of points assigned to a particular phase gives its volume fraction. However, identifying the exact location of phase boundaries by eye can be subjective and prone to operator bias. Moreover, according to the aforementioned standard, depending on the user expertise the quantification procedure takes from 15 to 30 min per image, revealing the inefficiency of the method. Therefore, digital image processing techniques based on semi or fully automated approaches are now preferred.
Measuring phase volume fraction in a greyscale image using digital processing techniques usually involves thresholding image segmentation [3]. In the bi-level thresholding, the constituent phases are separated by their pixel grey intensity above and below a particular threshold grey value and then converted to binary (black and white) images. Although the measurement time per image can be significantly reduced, here, similar to the manual point counting method [2], visually identifying the correct location of phase boundaries in order to set a threshold can be challenging. To circumvent this, automatic thresholding methods have been proposed. In addition to the widely used Otsu method [4] several other automatic thresholding approaches have been considered, such as entropy method [5], moment preserving method [6], minimum error method [7] and histogram shape-based methods [[8], [9], [10]]. For a bi-level thresholding problem, they all define a single threshold value for the entire image. However, using global thresholding based algorithms can result in incorrect segmentation when the contrast between objects and background is poor, i.e. the grey histogram distribution is close to unimodal, or the background grey intensity is non-uniform. This is often the case in BSE images. Background intensity in the matrix phase is usually not uniform over an image and varies between images due to differences in contrast caused by distinct crystallographic grain orientations, and non-homogeneous alloying element distribution.
Local adaptive thresholding is an alternative to deal with such situations. Here, threshold values are locally defined based on two main approaches: partitioning an image into overlapping sub-images, or by statistically examining the grey intensities in the neighborhood of each pixel [3]. In the first approach, the optimal threshold for each sub-image is calculated by investigating its histogram. For unimodal distributions, the threshold is defined by interpolating the local thresholds found for neighboring sub-images. A final step consists in finding a threshold value for every pixel in the image [11]. In the second approach, local thresholds are determined based on local image characteristics, such as the mean value of the local intensity distribution and standard deviation [12,13], the mean of the maximum and minimum grey values [14] or the local grey intensity gradient magnitude [15]. Although local thresholding methods may yield considerably good segmentation, they are computationally much more expensive than global thresholding techniques. Furthermore, these algorithms require the specification of some parameters, e.g. a window size with sufficient foreground and background pixels, for the threshold to be computed. Even though some algorithms have suggested values for the input parameters, better results are typically achieved after adjusting these values according to the characteristics of the investigated image.
To decrease the number of user input parameters as well as computational time, an attractive alternative is to correct the image background before applying a global thresholding. The so-called “rolling ball algorithm”, introduced over three decades ago to correct the background of biomedical images [16,17], has become a commonly used technique in the field of medical image processing, including fluorescence [[18], [19], [20], [21]], epifluorescence [22] and computed tomography [23,24] imaging. The concept of the algorithm consists of visualizing a 2-dimensional (2-D) greyscale image as a 3-dimensional (3-D) profile, with the pixel grey values of the image being the surface height. Then a sphere is rolled at this surface such that a background surface is created. By subtracting (or adding) this background surface from the original image the grey intensity variation of the image background is removed [[16], [17]]. The rolling ball algorithm has meanwhile been applied for background correction in a wide range of fields, such as in signal filtering [25], terrain conductivity measurement [26], mapping of trees [27], X-ray spectra background fitting [28], painting surface measurement [29], analysis of marine topography [30], particle angularity quantification [31], etc. For materials characterization, however, only Shvedchenko and Suvorova [32] have recently used the rolling ball algorithm to correct background of scanning transmission electron microscopy (STEM) images in order to measure nanoparticle sizes. To the best of the authors' knowledge applying the rolling ball algorithm for background correction in SEM imaging, in particular BSE images, has not been attempted so far.
Hence, the purpose of the present work is two-fold. First, the rolling ball algorithm is applied to correct uneven BSE image's background. Here, an approach to select the ball size is established. Second, a systematic procedure is proposed to define an appropriate threshold value, aided by electron backscattered diffraction (EBSD) mapping. This methodology is used to quantify α phase volume fractions in a two-phase β-metastable Ti-5553 alloy, due to its current industrial relevance and the lack of systematic procedures to measure the α phase fraction in titanium alloys via automated image analysis.
Section snippets
Material and equipment
The material used in this study is a Ti-5553 alloy with chemical composition in wt% as follows: 5.39 Al, 5.01 V, 5.03 Mo, 2.80 Cr, 0.32 Fe, 0.03 Si, 0.01 Zr, 0.15 O, 0.002 H, 0.01 C and Ti balance. The alloy was received in the as-forged condition and cut into 60 × 10 × 3 mm3 sheet specimens for heat treatment tests. Heat treatments were performed in a Gleeble 3500 thermo-mechanical simulator (Dynamic System Inc., Poestenkill, NY) under ~0.002 Pa vacuum atmosphere and consisted of subjecting
Image pre-processing
To set the same threshold grey value to different BSE images of a sample and to BSE images of different samples isothermally treated for different times at the same temperature, it is important that the lower and upper grey intensity limits in the images are the same. Thus, to ensure that the grey intensity range is always identical, histogram normalization is performed. It consists of applying a linear stretching operation such that the original grey intensity range f, spanning from x1 (lower
Discussion
The method proposed in this study has shown to be a tool to accurately perform image segmentation and compute phase volume fraction requiring comparatively little user input, which increases the reproducibility of the results. In contrast, local adaptive thresholding approaches require in general several user input parameters. In the proposed method, as little as one EBSD map is needed for automated phase quantification and, depending on the image resolution and foreground feature size, image
Conclusion
In this work a systematic method has been proposed for automated measurement of phase volume fractions from SEM/BSE images. MATLAB is the environment used here as its interpreted language together with its built-in functions make data processing and image analysis fast and convenient. In order to correct uneven background, frequently seen on BSE imaging, the rolling ball algorithm is implemented. Here, the algorithm executes morphological closing operations using a spherical structuring element
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC), Canada, Grant number: RGPIN-2015-04259. Further, they would like to thank Prof. Chad Sinclair for constructive discussions and valuable insights given.
Data availability
The MATLAB code required to reproduce these findings is available to download from https://github.com/marianamendesr/rollingball. The raw/processed images required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
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