Chord-length Function Research Articles

Improving FIB-SEM Reconstructions by Using Epoxy Resin Embedding

Segmentation of FIB-SEM data remains a major challenge to achieving accurate reconstructions. Epoxy embedding is used in this article to eliminate background data from SEM images in order to aid in segmentation and generate 3D reconstructions of conventional high surface area CLs from FIB-SEM images. Two CL samples with the same composition but different hours of operation, namely, beginning of life (BOL), i.e. post conditioning, and end of life (EOL), i.e., post failure, were used. The samples were imaged with and without epoxy embedding to characterize the difference in the structure of the sample due to sample preparation. Further, the use of two CL samples allowed the quantification of the differences in the structure of the CL due to degradation and ensure validity of the sample preparation across multiple CL samples. Image analysis showed that a simple thresholding algorithm, such as Otsu, was sufficient to accurately segment the images for the sample with epoxy embedding due to the lack of background features. Statistical descriptors, such as porosity, two-point correlation function, chord length function, specific interface area and pore size distribution, and effective diffusion coefficient are used to quantify the differences in the reconstructed structures of the CLs with different sample preparation. Results showed that the CL reconstructions of the epoxy embedded samples had a higher porosity, larger pore sizes and lower specific interface area due to the more accurate segmentation and removal of background features.

Improving FIB-SEM Reconstructions By Using Epoxy Resin Embedding

Focus ion beam-scanning electron microscopy (FIB-SEM) is a viable technique to visualize and reconstruct the morphology of polymer electrolyte membrane fuel cell (PEMFC) porous media, such as catalyst layers (CLs) (1,2) and micro-porous layers (MPLs) (3,4), with a high resolution of few nanometers. FIB-SEM provides morphological information about the solid and pore phase from which several statistical descriptors and effective transport properties (2) can be extracted to characterize the random heterogeneous structure. A major challenge in the analysis of the FIB-SEM images is the binarization of the grey scale images into the solid and pore phases (5). This problem arises because the SEM detects the solid particles inside the pores which are not in the plane of the image. This adds to the complexity of the segmentation by introducing an additional dependency to not only distinguish between the pore and solid phase but also, distinguish between solid phase in the plane of the image and solid phase in the background. In order to tackle this problem, advanced segmentation algorithms have been developed (5,6). However, these algorithms lack consistency across datasets and often require manual intervention which limits their robustness. Binarization can be improved by enhancing the sample preparation for the image acquisition. This has been done by penetrating the pores with filling material by embedding the sample in an epoxy based resin (7,8) or silicon based resin (9), platinum vapor deposition (10) and atomic layer deposition (ALD) of zinc oxide (11). ALD and platinum vapor deposition result in partial filling of the pores but provide a higher contrast from the carbon rich backbone. However, due to the partial filling manual corrections and additional image filtering operations are required post segmentation of the images. Epoxy and silicon based resin embedding results in complete filling of the pores but provides a very low contrast for the images. Ghosh et al. (8) recently showed that images obtained using the backscattered electrons (BSE) provide a better contrast than the secondary electron (SE) images (8,9) for a PEMFC CL embedded with an epoxy based resin. However, Ghosh et al. (8) only examined and compared 2D images of the CL. Comparison of a full 3D reconstruction of the PEMFC CL using FIB-SEM with and without epoxy embedding has yet to be performed. In the present article, 3D reconstructions of a conventional high surface area CL are performed using FIB-SEM images of the same sample treated with and without epoxy embedding to analyze the differences in image analysis and structure for both the modes of sample preparation. Figure 1 below shows the raw images obtained using SE mode for the sample without epoxy embedding and BSE mode for the sample with epoxy embedding. Multiple stacks of images are processed from both the datasets to ensure global validity of the results. Image processing operations are performed to further enhance the raw images before segmentation. Image analysis reveals that a simple thresholding algorithm, such as Otsu, is sufficient to accurately segment the images for the sample with epoxy embedding due to the lack of background features. Comparison of the reconstructions for the two modes suggests an increase in porosity and chord length function (12) for the sample imaged using epoxy embedding due to a more accurate segmentation. Transport simulations are being carried out to compute the effective transport properties.

Stochastic Reconstruction and Transport Simulation of PEFC Catalyst Layers

Understanding mass transport in polymer electrolyte fuel cells (PEFCs) is critical to improve reactant and water transport in catalyst layers. Numerical simulation techniques can be used to gain a detailed understanding of transport within the catalyst layer structure. The accuracy of these simulations is dependent on the accuracy of the physical domain and the mathematical models. While detailed mathematical models of mass, charge and energy transport have been presented in literature, there has been limited work in understanding the catalyst layer structure. Reconstructions of PEFC catalyst layers are therefore crucial to understand its microstructure and to obtain transport properties via simulation. Imaging techniques such as X-ray tomography (micro-CT) or scanning electron microscopy (SEM), even though informative, cannot easily be used to understand how different porous media parameters (e.g., pore sizes, connectivity) control its transport properties (e.g., effective diffusivity) as the structure is not mathematically characterized. The method of stochastic reconstruction on the other hand, uses geometry based statistical descriptors in order to create reconstructions. The statistical descriptors are related to the geometric properties of the porous media, e.g., the two point correlation function is related to the interface area and the chord length function is related to pore size. The method of stochastic reconstruction is cost and time efficient, can account for the stochastic nature of porous media, and provides a way to characterize the porous media by its statistical descriptors. Most of the fuel cell literature is composed of imaging based reconstructions [1,2]. A few catalyst layer stochastic reconstructions use either simple statistical descriptors, such as two-point correlation functions, or heuristic approach, e.g., creating the structure based on a sphere packing algorithm [3,4]. Due to the limited stochastic information and idealized building blocks, these reconstructions might not truly represent the complex microstructure of PEFC porous media, which consists of non-spherical fractal carbon particles [5]. The use of multiple correlation functions together with simulated annealing [6] could provide an improved method to reconstruct the complex PEFC porous media, and to analyze the relation between porous media structure and transport properties. In this work, a modified simulated annealing method based on one proposed by Yeong and Torquato [6] is used to reconstruct a three-dimensional and multi-phase microstructure representative of a catalyst layer (CL). A two dimensional version of the program was used to reconstruct a PEFC CL earlier [7]. The new improved method uses a multigrid hierarchical annealing technique to significantly reduce the reconstruction time and ascertains long range connectivity. The multigrid method performs reconstructions in sequential refinement stages and has been found to result in reconstruction time reduction by 2-3 orders of magnitude. The new method uses a biased pixel swapping method compared to conventional random swapping for faster and more accurate reconstruction. The biased pixel swapping has reduced the reconstruction time by almost an order of magnitude, while also improving the accuracy of the reconstructions by an order of magnitude. Multiple statistical descriptors are used in combination to generate a structure, which provides a better representation of the PEFC CL structure. An algorithm for automatically generating a computational mesh and a mathematical model of the transport process in the catalyst layer has also been developed. Mass and electron transport are simulated on the reconstructions using the open source package OpenFCST [8]. The effective transport properties of the reconstructions are close to the reference structure value, e.g., the ratio of difusibility values of the reconstructions to diffusibility values of reference was found to be in the range of 0.9-0.96. The new method allows us to reconstruct detailed high-resolution structures with high accuracy in practical amount of time, e.g., a reconstruction of size 300x300x300 can now be reconstructed in 24-30 hours instead of several weeks. The effect of different stochastic descriptors on the transport properties will also be studied in future. Overall, the current work provides a novel methodology to characterize and reconstruct PEFC porous media from statistical descriptors in a time and cost effective manner.[1] K. Lange et al. Electrochim. Acta. 2012, 85, 322-331 [2] W. Epting et al. Adv. Funct. Mater. 2012, 22, 555-560 [3] P. Mukherjee et al. J. Electrochem. Soc. 2006, 153, A840-A849 [4] K. Lange et al. J. Electrochem. Soc. 2010, 157, B1434-B1442 [5] D. Banham et al. J. Power Sources. 2011, 196, 5438–5445[6] C. Yeong et al. Physical Review E. 1998, 57, 495-506 [7] L. Pant et al. Phys. Rev. E. 2014, 90, 023306[8] Open Fuel Cell Simulation Toolbox (openFCST). Available at www.openfcst.org Figure 1

Chord-Length Shape Features for Human Activity Recognition

Despite their high stability and compactness, chord-length shape features have received relatively little attention in the human action recognition literature. In this paper, we present a new approach for human activity recognition, based on chord-length shape features. The most interesting contribution of this paper is twofold. We first show how a compact, computationally efficient shape descriptor; the chord-length shape features are constructed using 1-D chord-length functions. Second, we unfold how to use fuzzy membership functions to partition action snippets into a number of temporal states. On two benchmark action datasets (KTH and WEIZMANN), the approach yields promising results that compare favorably with those previously reported in the literature, while maintaining real-time performance.

A Fourier Shape Descriptor Based on Multi-Level Chord Length Function

A novel Fourier shape descriptor based on multi-level chord length function(MCLFD)is proposed for shape retrieval in this paper.It is derived from equal-arc-length partitions of the shape contour.Compared with the existing Fourier shape descriptors,MCLFD is not only simple to compute but also can reflect the shape's global features and fine details.The MPEG-7 contour shape database and the plant leaf shape database which is taken from nature,are used to test the retrieval performance of MCLFD.The experimental results show that the MCLFD has a very higher retrieval performance than the existing Fourier shape descriptors.The experimental results of adding noises also demonstrate that MCLFD is very robustness.

A more accurate reconstruction system matrix for quantitative proton computed tomography

An accurate system matrix is required for quantitative proton CT (pCT) image reconstruction with iterative projection algorithms. The system matrix is composed of chord lengths of individual proton path intersections with reconstruction pixels. In previous work, reconstructions were performed assuming constant intersection chord lengths, which led to systematic errors of the reconstructed proton stopping powers. The purpose of the present work was to introduce a computationally efficient variable intersection chord length in order to improve the accuracy of the system matrix. An analytical expression that takes into account the discrete stepping nature of the pCT most likely path (MLP) reconstruction procedure was created to describe an angle-dependent effective mean chord length function. A pCT dataset was simulated with GEANT4 using a parallel beam of 200 MeV protons intersecting a computerized head phantom consisting of tissue-equivalent materials with known relative stopping power. The phantom stopping powers were reconstructed with the constant chord length, exact chord length, and effective mean chord length approaches, in combination with the algebraic reconstruction technique. Relative stopping power errors were calculated for each anatomical phantom region and compared for the various methods. It was found that the error of approximately 10% in the mean reconstructed stopping power value for a given anatomical region, resulting from a system matrix with a constant chord length, could be reduced to less than 0.5% with either the effective mean chord length or exact chord length approaches. Reconstructions with the effective mean chord length were found to be approximately 20% faster than reconstructions with an exact chord length. The effective mean chord length method provides the possibility for more accurate, computationally efficient quantitative pCT reconstructions.

High orders of the Weyl expansion for quantum billiards: resurgence of periodic orbits, and the Stokes phenomenon

A formalism is developed for calculating high coefficients c r of the Weyl (high energy) expansion for the trace of the resolvent of the Laplace operator in a domain B with smooth boundary ∂ B The c r are used to test the following conjectures. ( a ) The sequence of c r diverges factorially, controlled by the shortest accessible real or complex periodic geodesic. ( b ) If this is a 2-bounce orbit, it corresponds to the saddle of the chord length function whose contour is first crossed when climbing from the diagonal of the Möbius strip which is the space of chords of B . ( c ) This orbit gives an exponential contribution to the remainder when the Weyl series, truncated at its least term, is subtracted from the resolvent; the exponential switches on smoothly (according to an error function) where it is smallest, that is across the negative energy axis (Stokes line). These conjectures are motivated by recent results in asymptotics. They survive tests for the circle billiard, and for a family of curves with 2 and 3 bulges, where the dominant orbit is not always the shortest and is sometimes complex. For some systems which are not smooth billiards (e. g. a particle on a ring, or in a billiard where ∂ B is a polygon), the Weyl series terminates and so no geodesics are accessible; for a particle on a compact surface of constant negative curvature, only the complex geodesics are accessible from the Weyl series.