Title: An Image-Based Method for Obtaining Pore-Size Distribution of Porous Media
Journal: Environ. Sci. Technol.
Authors: Zhen Yang1, Xiao-Feng Peng1, Duu-Jong Lee2 and Ming-Yuan Chen2 
Corresponding author: Xiao-Feng Peng

Institute: 
1. Laboratory of Phasechange and Interfacial Transport Phenomena, Department of Thermal Engineering, Tsinghua Universiy, Beijing 100084, China
2. Chemical Engineering Department, National Taiwan University, Taipei, 106 Taiwan, China

The original and creativity of paper: A new method for obtaining pore-size distribution (PSD) was discovered. 

Summary: 
The purpose of this paper is to develop a new method for obtaining pore-size distribution (PSD). A MATLAB program was composed to make the method applicable for image analysis. Image tests on wastewater biofouling layer samples showed the validity and feasibility of the method for analyzing intrinsic porous structures. The structural information obtained by this method can facilitate the understanding of transport phenomena, e.g., water flow and species diffusion inside porous structures.

Image conversion methods

1. CLSM images which contain 3-D structure of the test fouling layer (255 grayscale format, 512 × 512 pixels in resolution, 47 images in total scanned at uniform intervals in the layer thickness direction) were converted into bileveled images using Otsu’s method. In the bileveled images, white pixels (one in a pixel value) represent pore area, while black pixel value (zero in pixel value) are solid mass.
2. The bileveled images having the same sequential number in each series were combined into a single image. The value of a pixel is set to zero if its value in the four serial (β-D-glucopyranose, proteins, nucleic acids, and α-polysaccharides) is always zero; otherwise, the value pixel is set to one. According to this method, in which pixels having a value of one are truly pore areas.
3. The composite image series were used to construct the 3-D fouling layer structure, as shown in Figure 1. After that, this 3-D structural information was used for PSD measurement.

Fig. 1 Restructed 3-D fouling layer. 
PSD measurement
1. Determine the critical radius Rc,i for each unity-valued pixel (pixel in pore region). The critical radius is defined as the maximum radius of a sphere (for 3-D structures) or a circle (for 2-D structures) that has its center at the considered pixel and covers only the unity-valued pixels.
2. For each pixel having the largest Rc,0, its surrounding pixels within the distance of Rc,0 are identified and designated as the volume/area of the largest pores.
3. For each pixel having the second largest Rc,1, its surrounding pixels within the distance of Rc,1 are identified and denoted as the volume/area of the second largest pores if they have not been designated previously or not included in the region designated by the previous radius.
4. Repeat step 3 for pixels having the third largest Rc,2, and then for the forth largest Rc,3...until Rc,i reaches one pixel length.

In this case, MATLAB program was composed to realize the function proposed in the above four steps.

PSD analyses and results
1. Figure 2 (b) show the pore patterns which was obtained by applying the proposed method.

Fig. 2 Cross-sectional image at 19 ?m deep): (a) Bileveled image (pore in white), (b) color-scaled pore size (solid in black).
Moreover, more details can be extracted by observing PSD and pore number distribution, as shown in Fig. 3 (a) and (b), respectively. 

Fig. 3 PSD analysis of the two examples (A, pore area, D, pore diameter): (a) PSD, (b) Pore number distributions.
Interestingly, this method can effectively solve the confusion on how to define a pore, and give an explicit definition on local pore structure. Therefore, it can reduce misinterpret pore structure when dealing with complicated geometries.
In summary, the proposed method could be applied to analyze 3-D pore structures for intrinsic porous media of which images of structures can be acquired using microscopes and in other photographic ways. This discovery helpful for further understanding of structural influence on transport on transport processes inside porous structures.
Application & further study: This methodology can be applied to extract information from fouled membrane image. 

By Monruedee Moonkhum
Email: moon@gist.ac.kr