过冷水滴飞溅图像的分析
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摘要
飞机防结冰技术近几十年得以迅猛发展。研究表明飞机表面材料和过冷水滴,与机翼表面结冰之间存在一定联系。通过飞机冰风洞实验,模拟了过冷水滴结冰环境,研究了不同材料的干湿性能在飞机防结冰上的效果。实验表明干性材料,过冷水滴撞击后不易残留在机翼表面,减小形成冰层的机率,而湿性材料则与之相反。以前,人们用肉眼直接从过冷水滴飞溅图像中,根据水滴飞溅的不同形状,判断材料的干湿性能。由于这种判断方法效率不高,以及人为判断的不一致性,从而引入数字图像处理方法处理实验图像,来判断材料的干湿性能。
本文在实验中采集了大量的过冷水滴飞溅图像,研究了过冷水滴在撞击飞机表面过程中水滴飞溅的现象,定义了一个多维特征空间用于描述图像中飞溅水滴的特征。这个特征空间由图像的平均亮度,均熵,熵的方差,霍夫变换以及相关统计值组成。通过200张试样图像的分析,得出水滴飞溅图像的类别。结合k均值聚类算法将图像分为干表面图像,湿表面图像,干湿混合表面图像三个类别。
整个飞机冰风洞实验,共测试了9个标准试件。根据图像分类的结果判断试件材料的干湿性,8个试件能正确地分为干或湿状态,1个试件发生误判。研究结果表明自动分析图像较好地解决了由于手工分析所造成的耗时及准确性问题,试件分类的正确率达到89%。
The research on super-cooled large droplets (SLD) has been developing dramatically in recent years. It proves that super-cooled large droplets impingement onto airfoil and aircraft materials have a great effect on aircraft icing. In the research facility of icing wind tunnel at Cranfield University, it aims to classify images into wet/dry surface with the intention of sample identification. The droplets ran quicker onto dry samples so that it could protect airfoil from icing. In the past, droplet splashing images were arranged manually to identify the surface condition, which simulated the aerofoil in SLD icing environment. However, due to the inefficiency of physical analysis and inconsistent perspectives on the same droplet splashing image, digital image processing techniques are used to technically improve image classification in accordance with droplet splashing models.
A great number of droplets splashing images are captured through aircraft icing experiments. This thesis defines a multi-dimensional feature space as average brightness, average entropy, standard deviation of entropy and Hough line, with a ratio of entropy and Hough lines to characterize the images as criteria of classification. Based on manual analysis of 200 training images, classification group has been defined as four. After the organization by k-means algorithm, images can be categorized into dry surface, wet surface, and ambiguous images.
Among 9 samples, eight samples succeed to be identified into wet/dry behavior. Meanwhile, one sample is to false classification since the raw images are insufficient to represent the entire droplets splash impact events. However, there are three samples left to be validated by humans. The droplet splash images can be processed quickly and correctly, due to time consumption by human classification.
本文在实验中采集了大量的过冷水滴飞溅图像,研究了过冷水滴在撞击飞机表面过程中水滴飞溅的现象,定义了一个多维特征空间用于描述图像中飞溅水滴的特征。这个特征空间由图像的平均亮度,均熵,熵的方差,霍夫变换以及相关统计值组成。通过200张试样图像的分析,得出水滴飞溅图像的类别。结合k均值聚类算法将图像分为干表面图像,湿表面图像,干湿混合表面图像三个类别。
整个飞机冰风洞实验,共测试了9个标准试件。根据图像分类的结果判断试件材料的干湿性,8个试件能正确地分为干或湿状态,1个试件发生误判。研究结果表明自动分析图像较好地解决了由于手工分析所造成的耗时及准确性问题,试件分类的正确率达到89%。
The research on super-cooled large droplets (SLD) has been developing dramatically in recent years. It proves that super-cooled large droplets impingement onto airfoil and aircraft materials have a great effect on aircraft icing. In the research facility of icing wind tunnel at Cranfield University, it aims to classify images into wet/dry surface with the intention of sample identification. The droplets ran quicker onto dry samples so that it could protect airfoil from icing. In the past, droplet splashing images were arranged manually to identify the surface condition, which simulated the aerofoil in SLD icing environment. However, due to the inefficiency of physical analysis and inconsistent perspectives on the same droplet splashing image, digital image processing techniques are used to technically improve image classification in accordance with droplet splashing models.
A great number of droplets splashing images are captured through aircraft icing experiments. This thesis defines a multi-dimensional feature space as average brightness, average entropy, standard deviation of entropy and Hough line, with a ratio of entropy and Hough lines to characterize the images as criteria of classification. Based on manual analysis of 200 training images, classification group has been defined as four. After the organization by k-means algorithm, images can be categorized into dry surface, wet surface, and ambiguous images.
Among 9 samples, eight samples succeed to be identified into wet/dry behavior. Meanwhile, one sample is to false classification since the raw images are insufficient to represent the entire droplets splash impact events. However, there are three samples left to be validated by humans. The droplet splash images can be processed quickly and correctly, due to time consumption by human classification.
引文
[1] Hardy, J. K. “Protection of aircraft against ice”. RAE Report SME, 1946, 3380.
[2] Messinger, B. L. “Equilibrium temperature on an unheated icing surface as a function of airspeed”. J. Aeronautical Sci., 1953, 20, 29-41.
[3] Langmuir, I. & Blodgett, K. B. “A mathematical investigation of water droplet trajectories”. Army Air Forces Technical Report, 1946, 5418.
[4] Sand, W.R., Politovich, M.K. and Veal, D.L. “Effects of icing on performance of a research aircraft.” J. Aircraft, 1984, 21, 708-715
[5] Cooper, W.A., Politovich, M. K. and Veal, D. L. “Icing Conditions encountered by a research aircraft.” J. Climate Appl. Meteror., 1984 23, 1427-1440.
[6] Federal Aviation Administration, Federal Aviation Regulations, Part 25 “Airworthiness Standards, Transport Category Airplanes.” U.S. Govt. Printing Office, Washington, D.C., 1974, revised 1982, 158pp.
[7] Marwitz, J., Politovich, M., Bernstein, B., Ralph, F., Neiman, P., Ashenden, R., and Bresch, J. “Meteorological Conditions Associated with the ATR-72 Aircraft Accident near Roselawn, Indiana on 31 October 1994”, Bull. Amer. Meteor. Soc., 1996 Vol. 78, pp. 41-52.
[8] Politovich, M. K. “Aircraft Icing Caused by Large Supercooled Droplets”, J. Appl. Meteor., 1989, Vol. 28, pp. 856-864.
[9] Gent, R.W., Dart, N.P. and Cansdale, J.T. “Aircraft Icing”. Phil. Trans. R. Soc. Lond. 2000, 358, 2873-2911
[10] NASA Icing Branch , “SLD Technology Roadmap”. http://icebox.grc.nasa.gov/tasks/index.html (accessed in 05/03/2007)
[11] R. W. Gent, J. M. Ford, R. J. Moser, D. R. Miller. “SLD Research in the UK” FAA In-Flight Icing Ground De-icing International Conference and Exhibition, Chicago, Illinois June 16-20, 2003.
[12] Gent, R.W. Dart, N.P. “Prediction of ice accretion formed from large supercooled water droplets”. DERA reportDERA/MSS5/CR9800014/1.0 April 1998.
[13] Dart,.N.P, et al “Results from large droplet ice accretion tests in the ACT Artington Icing Wind Tunnel.” DERA report DERA/MSS5/CR980015/1.0 April 1998.
[14] Gent, R.W, Hammond, Dr D.W., and Burkitt, G.P. “Results from Large Droplet Ice Accretion Tests in the ACT Luton Icing Wind Tunnel.” DERA report DERA/MSS/MSTR2/CR000627/1.0, Oct 2000.
[15] Ford, J.M, Gent, R.W, Moser, R.J. “Results from Super-cooled large Droplet Splash tests in the ACT Luton Icing Wind Tunnel.” QinetiQ customer report. QINETIQ/FST/CR024146, September 2002.
[16] Gent, R.W. “TRAJICE2- A Combined Water Droplet Trajectory and Ice Accretion Prediction Program for Aerofoils.” Royal Aircraft Establishment Technical Report TR90054, November 1990. Cited in: R. W. Gent, J. M. Ford, R. J. Moser, D. R. Miller. “SLD Research in the UK” FAA In-Flight Icing Ground De-icing International Conference and Exhibition, Chicago, Illinois June 16-20, 2003.
[17] Press, A.J, Dart, N.P, “ICECREMO user guide – version 3.” ICECREMO/SPEC/DERA/ND990506/3, April 2000. Cited in: R. W. Gent, J. M. Ford, R. J. Moser, D. R. Miller. “SLD Research in the UK” FAA In-Flight Icing Ground De-icing International Conference and Exhibition, Chicago, Illinois June 16-20, 2003.
[18] Quero, M. Q. BIODOC: “Droplet Impact and Heat Transfer”. (unpublished PHD thesis), Cranfield University, Cranfield, 2004.
[19] “Aircraft Icing Handbook” USA Civil Aviation Authority 2000, p. 1-20.
[20] “Icing” Cited in: “Aviation Weather Tutorial”. http://virtualskies.arc.nasa.gov/weather/tutorial/tutorial4.html(accessed 27/03/2007).
[21] Thoroddsen, S. T. “The Eject Sheet Generated by the Impact of a Drop”. Journal of Fluid Mechanics. 2002, vol. 451, pp. 371-381.
[22] S.C. Tan, M. Papadakis, “GENERAL EFFECTS OF LARGE DROPLET DYNAMICS ON ICE ACCRETION MODELING” presented at the 41st Aerospace Sciences Meeting and Exhibit 6-9 January 2003, Reno, AIAA Paper 2003-392.
[23] Purvis, R. and Smith, F. T., “Large Droplet Impact on Water Layers” AIAA paper 2004-0414, presented at the 42nd Aerospace Sciences Meeting and Exhibition, Reno Nevada, January 2004.
[24] Luxford G, Hammond D, & Ivey P, “ Role of Droplet Distortion & Break-up in Large Droplet Aircraft Icing”, presented at the AIAA 42nd Aerospace Sciences Meeting and Exhibition, Jan 2004, Reno, AIAA Paper 2004-0411
[25] Luxford G, Hammond D, & Ivey P, “Modelling, Imaging and Measurement of Distortion, drag and Break-up of Aircraft-icing Droplets”, presented at the AIAA 43rd Aerospace Sciences Meeting and Exhibition, Jan 2005, Reno, AIAA Paper 2005-0071
[26] Hammond D W, Quero M, Ivey P, Miller D, Purvis R , McGregor, O & Tan J, “Analysis and Experimental Aspects of the Impact of Supercooled Water Drops into Thin Water Films”, presented at the AIAA 43rd Aerospace Sciences Meeting and Exhibition, Jan 2005, Reno, AIAA Paper 2005-0077
[27] Quero M, Hammond D W, Purvis R , Smith F T, “Analysis of Supercooled Water Droplet Impact on a Thin Water Layer and Ice Growth”, presented at the AIAA 44rd Aerospace Sciences Meeting and Exhibition, Jan 2006, Reno, AIAA Paper 2006-466.
[28] Rothmayer, A. P., and Krakos, J. A., “Residual Drop Impacts and Thin Film Dynamics” AIAA paper 2004-0057, presented at the 42nd Aerospace Sciences Meeting and Exhibition, Reno Nevada, January 2004.
[29] Miller, D.R., Lynch, C.J. and Tate, P.A. “Overview of High Speed Close-Up Imaging in an Icing Environment”. AIAA paper 2004–0407, presented at 42nd Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 5–8, 2004
[30] Gent, R.W, Dart, N.P. “Progress in the prediction of ice accretion formed from super-cooled large water droplets.” DERA report DERA/MSS/MSTR2/CR990420/1.0 September 1999.
[31] Myers T. G & Hammond D. W, “Ice and water film growth from incoming supercooled droplets”, Int. J of Heat & Mass Transfer 42, pp 2233-2242, 1999.
[32] Ford, J.M. “Evaluation of modifications made to the ACT Icing Wind Tunnel in order to generate Super-cooled large droplets.” QinetiQ customer report QINETIQ/FST/CR024119, July 2002.
[33] Gent, R.W, Ford, J.M, Moser, R.J, Miller D.R “Results from SLD Mass loss Tests in the ACT Luton Icing Wind Tunnel.” 41st AIAA Aerospace Sciences Meeting and Exhibit. January 2003.
[34] Hastings, E. C. Jr & Weinstein, L. M. “Preliminary Indications of Water Film Distribution on an Aerofoil in a Water Spray”, NASA technical memo number 85796, 1984.
[35] Feo A., Rogles, F. Urdiales, M. “The Measurement of Water Film Thicknesses on Aerofoils in Heavy Rain Conditions using Conductance Sensors” AGARD, Effects of Adverse Weather on Aerodynamics 14 p (SEE N92-21679 12-03); INTERNATIONAL ORGANIZATION; 1991.
[36] Feo, A., “Icing Scaling with Surface Film Thickness Similarity for High LWC Conditions”, Madrid INTA (Instituto Nacional de Tecnia Aeroespacial) Report AE/PRO/4420/184/INTA/00 13pp.
[37] Lavergne, G., Platet, B. “Droplet Impingement on a Cold and Wet Wall.” ONERA/CERT/DMAE/MH, September 2000. Cited in: Gent, R.W, Ford, J.M, Moser, R.J, Miller D.R “Results from SLD Mass loss Tests in the ACT Luton Icing Wind Tunnel.” 41st AIAA Aerospace Sciences Meeting and Exhibit. January 2003.
[38] Tan, Chiong-Siew, “A Tentative Mass Loss Model for Simulating Water Drop Splash”, AIAA paper 2004-0410, presented at the 42nd Aerospace Sciences Meeting and Exhibition, Reno Nevada, January 2004.
[39] Hammond, D. W., Luxford, G. and Ivey, P., “The Cranfield University Icing Tunnel” AIAA paper 2003-0901, presented at the 41th Aerospace Sciences Meeting and Exhibition, Reno Nevada, January 2003.
[40] Hammond, D.W. “Investigation into Super cooled Large Droplet Splashing”. Commissioned by the CAA (contract 623), March, 2005. ( to be published)
[41] McGregor, O. G. and Dalton, R. P. “Development of an Ultrasonic Probe to Measure Water Film Thickness”, QinetiQ report QinetiQ/04/01010, 2004, pp 28. Cited in: Hammond, D.W. “Investigation into Super cooled Large Droplet Splashing”. Commissioned by the USA CAA (contract 623), March, 2005.
[42] Mark S. Nixon, Alberto S. Aguado. "Feature Extraction and Image Processing" Newnes, (First Edition) 2002.
[43] Cranfield University Applied Mathematics and Computing Group. “Digital Image Processing (2)”. Lecture Notes, 2006.
[44] “Open Source Computer Vision Library Reference Manual”. Intel Corporation, Version 001, December 8, 2000
[45] “OpenCV Manual”. http://public.cranfield.ac.uk/soe/c5354/teaching/dip/opencv/manual/(accessed 17/02/2007).
[46] N. Kiryati ,Y. Eldar and A.M. Bruckstein , "A Probabilistic Hough Transform ",Pattern Recognition 1991, vol.24, pp. 303-316.
[47] Webb, A. "Statistical Pattern Recognition" Butterworth Heinemann, Second Edition 2002.
[2] Messinger, B. L. “Equilibrium temperature on an unheated icing surface as a function of airspeed”. J. Aeronautical Sci., 1953, 20, 29-41.
[3] Langmuir, I. & Blodgett, K. B. “A mathematical investigation of water droplet trajectories”. Army Air Forces Technical Report, 1946, 5418.
[4] Sand, W.R., Politovich, M.K. and Veal, D.L. “Effects of icing on performance of a research aircraft.” J. Aircraft, 1984, 21, 708-715
[5] Cooper, W.A., Politovich, M. K. and Veal, D. L. “Icing Conditions encountered by a research aircraft.” J. Climate Appl. Meteror., 1984 23, 1427-1440.
[6] Federal Aviation Administration, Federal Aviation Regulations, Part 25 “Airworthiness Standards, Transport Category Airplanes.” U.S. Govt. Printing Office, Washington, D.C., 1974, revised 1982, 158pp.
[7] Marwitz, J., Politovich, M., Bernstein, B., Ralph, F., Neiman, P., Ashenden, R., and Bresch, J. “Meteorological Conditions Associated with the ATR-72 Aircraft Accident near Roselawn, Indiana on 31 October 1994”, Bull. Amer. Meteor. Soc., 1996 Vol. 78, pp. 41-52.
[8] Politovich, M. K. “Aircraft Icing Caused by Large Supercooled Droplets”, J. Appl. Meteor., 1989, Vol. 28, pp. 856-864.
[9] Gent, R.W., Dart, N.P. and Cansdale, J.T. “Aircraft Icing”. Phil. Trans. R. Soc. Lond. 2000, 358, 2873-2911
[10] NASA Icing Branch , “SLD Technology Roadmap”. http://icebox.grc.nasa.gov/tasks/index.html (accessed in 05/03/2007)
[11] R. W. Gent, J. M. Ford, R. J. Moser, D. R. Miller. “SLD Research in the UK” FAA In-Flight Icing Ground De-icing International Conference and Exhibition, Chicago, Illinois June 16-20, 2003.
[12] Gent, R.W. Dart, N.P. “Prediction of ice accretion formed from large supercooled water droplets”. DERA reportDERA/MSS5/CR9800014/1.0 April 1998.
[13] Dart,.N.P, et al “Results from large droplet ice accretion tests in the ACT Artington Icing Wind Tunnel.” DERA report DERA/MSS5/CR980015/1.0 April 1998.
[14] Gent, R.W, Hammond, Dr D.W., and Burkitt, G.P. “Results from Large Droplet Ice Accretion Tests in the ACT Luton Icing Wind Tunnel.” DERA report DERA/MSS/MSTR2/CR000627/1.0, Oct 2000.
[15] Ford, J.M, Gent, R.W, Moser, R.J. “Results from Super-cooled large Droplet Splash tests in the ACT Luton Icing Wind Tunnel.” QinetiQ customer report. QINETIQ/FST/CR024146, September 2002.
[16] Gent, R.W. “TRAJICE2- A Combined Water Droplet Trajectory and Ice Accretion Prediction Program for Aerofoils.” Royal Aircraft Establishment Technical Report TR90054, November 1990. Cited in: R. W. Gent, J. M. Ford, R. J. Moser, D. R. Miller. “SLD Research in the UK” FAA In-Flight Icing Ground De-icing International Conference and Exhibition, Chicago, Illinois June 16-20, 2003.
[17] Press, A.J, Dart, N.P, “ICECREMO user guide – version 3.” ICECREMO/SPEC/DERA/ND990506/3, April 2000. Cited in: R. W. Gent, J. M. Ford, R. J. Moser, D. R. Miller. “SLD Research in the UK” FAA In-Flight Icing Ground De-icing International Conference and Exhibition, Chicago, Illinois June 16-20, 2003.
[18] Quero, M. Q. BIODOC: “Droplet Impact and Heat Transfer”. (unpublished PHD thesis), Cranfield University, Cranfield, 2004.
[19] “Aircraft Icing Handbook” USA Civil Aviation Authority 2000, p. 1-20.
[20] “Icing” Cited in: “Aviation Weather Tutorial”. http://virtualskies.arc.nasa.gov/weather/tutorial/tutorial4.html(accessed 27/03/2007).
[21] Thoroddsen, S. T. “The Eject Sheet Generated by the Impact of a Drop”. Journal of Fluid Mechanics. 2002, vol. 451, pp. 371-381.
[22] S.C. Tan, M. Papadakis, “GENERAL EFFECTS OF LARGE DROPLET DYNAMICS ON ICE ACCRETION MODELING” presented at the 41st Aerospace Sciences Meeting and Exhibit 6-9 January 2003, Reno, AIAA Paper 2003-392.
[23] Purvis, R. and Smith, F. T., “Large Droplet Impact on Water Layers” AIAA paper 2004-0414, presented at the 42nd Aerospace Sciences Meeting and Exhibition, Reno Nevada, January 2004.
[24] Luxford G, Hammond D, & Ivey P, “ Role of Droplet Distortion & Break-up in Large Droplet Aircraft Icing”, presented at the AIAA 42nd Aerospace Sciences Meeting and Exhibition, Jan 2004, Reno, AIAA Paper 2004-0411
[25] Luxford G, Hammond D, & Ivey P, “Modelling, Imaging and Measurement of Distortion, drag and Break-up of Aircraft-icing Droplets”, presented at the AIAA 43rd Aerospace Sciences Meeting and Exhibition, Jan 2005, Reno, AIAA Paper 2005-0071
[26] Hammond D W, Quero M, Ivey P, Miller D, Purvis R , McGregor, O & Tan J, “Analysis and Experimental Aspects of the Impact of Supercooled Water Drops into Thin Water Films”, presented at the AIAA 43rd Aerospace Sciences Meeting and Exhibition, Jan 2005, Reno, AIAA Paper 2005-0077
[27] Quero M, Hammond D W, Purvis R , Smith F T, “Analysis of Supercooled Water Droplet Impact on a Thin Water Layer and Ice Growth”, presented at the AIAA 44rd Aerospace Sciences Meeting and Exhibition, Jan 2006, Reno, AIAA Paper 2006-466.
[28] Rothmayer, A. P., and Krakos, J. A., “Residual Drop Impacts and Thin Film Dynamics” AIAA paper 2004-0057, presented at the 42nd Aerospace Sciences Meeting and Exhibition, Reno Nevada, January 2004.
[29] Miller, D.R., Lynch, C.J. and Tate, P.A. “Overview of High Speed Close-Up Imaging in an Icing Environment”. AIAA paper 2004–0407, presented at 42nd Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 5–8, 2004
[30] Gent, R.W, Dart, N.P. “Progress in the prediction of ice accretion formed from super-cooled large water droplets.” DERA report DERA/MSS/MSTR2/CR990420/1.0 September 1999.
[31] Myers T. G & Hammond D. W, “Ice and water film growth from incoming supercooled droplets”, Int. J of Heat & Mass Transfer 42, pp 2233-2242, 1999.
[32] Ford, J.M. “Evaluation of modifications made to the ACT Icing Wind Tunnel in order to generate Super-cooled large droplets.” QinetiQ customer report QINETIQ/FST/CR024119, July 2002.
[33] Gent, R.W, Ford, J.M, Moser, R.J, Miller D.R “Results from SLD Mass loss Tests in the ACT Luton Icing Wind Tunnel.” 41st AIAA Aerospace Sciences Meeting and Exhibit. January 2003.
[34] Hastings, E. C. Jr & Weinstein, L. M. “Preliminary Indications of Water Film Distribution on an Aerofoil in a Water Spray”, NASA technical memo number 85796, 1984.
[35] Feo A., Rogles, F. Urdiales, M. “The Measurement of Water Film Thicknesses on Aerofoils in Heavy Rain Conditions using Conductance Sensors” AGARD, Effects of Adverse Weather on Aerodynamics 14 p (SEE N92-21679 12-03); INTERNATIONAL ORGANIZATION; 1991.
[36] Feo, A., “Icing Scaling with Surface Film Thickness Similarity for High LWC Conditions”, Madrid INTA (Instituto Nacional de Tecnia Aeroespacial) Report AE/PRO/4420/184/INTA/00 13pp.
[37] Lavergne, G., Platet, B. “Droplet Impingement on a Cold and Wet Wall.” ONERA/CERT/DMAE/MH, September 2000. Cited in: Gent, R.W, Ford, J.M, Moser, R.J, Miller D.R “Results from SLD Mass loss Tests in the ACT Luton Icing Wind Tunnel.” 41st AIAA Aerospace Sciences Meeting and Exhibit. January 2003.
[38] Tan, Chiong-Siew, “A Tentative Mass Loss Model for Simulating Water Drop Splash”, AIAA paper 2004-0410, presented at the 42nd Aerospace Sciences Meeting and Exhibition, Reno Nevada, January 2004.
[39] Hammond, D. W., Luxford, G. and Ivey, P., “The Cranfield University Icing Tunnel” AIAA paper 2003-0901, presented at the 41th Aerospace Sciences Meeting and Exhibition, Reno Nevada, January 2003.
[40] Hammond, D.W. “Investigation into Super cooled Large Droplet Splashing”. Commissioned by the CAA (contract 623), March, 2005. ( to be published)
[41] McGregor, O. G. and Dalton, R. P. “Development of an Ultrasonic Probe to Measure Water Film Thickness”, QinetiQ report QinetiQ/04/01010, 2004, pp 28. Cited in: Hammond, D.W. “Investigation into Super cooled Large Droplet Splashing”. Commissioned by the USA CAA (contract 623), March, 2005.
[42] Mark S. Nixon, Alberto S. Aguado. "Feature Extraction and Image Processing" Newnes, (First Edition) 2002.
[43] Cranfield University Applied Mathematics and Computing Group. “Digital Image Processing (2)”. Lecture Notes, 2006.
[44] “Open Source Computer Vision Library Reference Manual”. Intel Corporation, Version 001, December 8, 2000
[45] “OpenCV Manual”. http://public.cranfield.ac.uk/soe/c5354/teaching/dip/opencv/manual/(accessed 17/02/2007).
[46] N. Kiryati ,Y. Eldar and A.M. Bruckstein , "A Probabilistic Hough Transform ",Pattern Recognition 1991, vol.24, pp. 303-316.
[47] Webb, A. "Statistical Pattern Recognition" Butterworth Heinemann, Second Edition 2002.