Abstract
Image-based granulometry measures the size distribution of objects in an image of granular material. Usually, algorithms based on mathematical morphology or edge detection are used for this task. We propose an entirely new approach, using cross correlations with kernels of different shapes and sizes. We use pyramidal structure to accelerate the multi-scale searching. The local maxima of cross correlations are the primary candidates for the centers of the objects. These candidate objects are filtered using criteria based on their correlations and intersection areas with other objects. Our technique spatially localizes each object with its shape, size and rotation angle. This allows us to measure many different statistics (besides the traditional objects size distribution) e.g. the shape and spatial distribution of the objects. Experiments show that the new algorithm is greatly robust to noise and can detect even very faint and noisy objects. We use the new algorithm to extract quantitative structural characteristics of Scanning Electron Microscopy (SEM) images of porous silicon layer. The new algorithm computes the size, shape and spatial distribution of the pores. We relate these quantitative results to the fabrication process and discuss the rectangle porous silicon formation mechanism. The new algorithm is a reliable tool for the SEM image processing.
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C.P. Bean, I.S. Jacobs, Magnetic granulometry and super-paramagnetism. J. Appl. Phys. 27(12), 1448–1452 (1956)
N. Azema, M.F. Pouet, C. Berho, O. Thomas, Wastewater suspended solids study by optical methods. Colloids Surf. A 204, 131–140 (2002)
G. Matheron, Random Sets and Integral Equation (Wiley, New York, 1978)
E.R. Dougherty, J.T. Newell, J.B. Pelz, Morphological texture-based maximum-likelihood pixel classification based on local granulometric moments. Pattern Recogn. 25(10), 1181–1198 (1992)
D.S. Raimundo, P.B. Calipe, D.R. Huanca, W.J. Salcedo, Anodic porous alumina structural characteristics study based on SEM image processing and analysis. Microelectron. J. 40, 844–847 (2009)
L. Vincent, Fast Grayscale Granulometry Algorithms. In Proceedings of the International Symposium on Mathematical Morphology, Fontainebleau (1994)
Mathworks Image Processing Toolbox 6.4 demo “Granulometry of Snowflakes”, accessed on 2012. http://www.mathworks.com/products/image/demos.html?file=/products/demos/shipping/images/ipexsnow.html
N.H. Maerz, T.C. Palangio, J.A. Franklin, WipFrag image based granulometry system. In Proceedings of the FRAGBLAST, 5 Workshop on Measurement of Blast Fragmentation, Montreal, pp. 91–99 (1996)
R.C. Gonzalez, R.E. Woods, Digital Image Processing, 2nd edn. (Prentice-Hall, New Jersey, 2002)
J.P. Lewis, Fast normalized cross-correlation. Vision Interface, pp. 120–123 (1995)
S.A. Araújo, H.Y. Kim, Ciratefi: An RST-invariant template matching with extension to color images. Integr. Comput. Aided Eng. 18(1), 75–90 (2011)
H.Y. Kim, Rotation-discriminating template matching based on fourier coefficients of radial projections with robustness to scaling and partial occlusion. Pattern Recogn. 43(3), 859–872 (2010)
A. Elmoutaouakkil, L. Salvo, E. Maire, G. Peix, 2D and 3D characterization of metal foams using X-ray tomography. Adv. Eng. Mater. 4(10), 803–807 (2002)
E. Maire, N. Gimenez, V.S. Moynot, H. Sautereau, X-ray tomography and three-dimensional image analysis of epoxy-glass syntactic foams. Phil. Trans. R. Soc. A 364, 69–88 (2006)
E. Maire, P. Colombo, J. Adrien, L. Babout, L. Biasetto, Characterization of the morphology of cellular ceramics by 3D image processing of X-ray tomography. J. Eur. Ceram. Soc. 27(4), 1973–1981 (2007)
G. Takacs, V. Chandrasekhar, S. Tsai, D. Chen, R. Grzeszczuk, B. Girod, Unified real-time tracking and recognition with rotation-invariant fast features. IEEE Comp. Soc. Conf. Computer Vision and Pattern Recognition (CVPR), pp. 934–941 (2010)
H. Föll, M. Christophersen, J. Carstensen, G. Hasse, Formation and application of porous silicon. Mater. Sci. Eng. R Reports 39(4), 93–141 (2002)
D.R. Huanca, J. Ramirez-Fernandez, W.J. Salcedo, Morphological and structural effect of aluminum on macroporous silicon layer. J. Mat. Sci. Eng. 4(8), 55–59 (2010)
S.K. Ghandi, VLSI Fabrication Principles: Silicon and Gallium Arsenide (Wiley-Intercience Publication, New York, USA, 1983)
S. Wolf, Silicon Processing for the VLSI Era, vol. II (Lattice Press, California, USA, 1990)
G.L. Schnable, R.S. Keen, Aluminum metallization-advantages and limitations for integrated circuit applications. Proc. IEEE 57, 1570–1580 (1969)
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The authors thank to CNPq for the financial support.
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Kim, H.Y., Maruta, R.H., Huanca, D.R. et al. Correlation-based multi-shape granulometry with application in porous silicon nanomaterial characterization. J Porous Mater 20, 375–385 (2013). https://doi.org/10.1007/s10934-012-9607-9
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DOI: https://doi.org/10.1007/s10934-012-9607-9