Multidimensional Median Filters for Finding Bumps in Chemical Sensor Datasets

Jeffrey C. Miecznikowski, Kimberly F. Sellers, William F. Eddy

Department of Biostatistics, Roswell Park Cancer Institute, SUNY University at Buffalo, Buffalo, USA.
Department of Mathematics and Statistics, Georgetown University, Washington DC, USA.
Department of Statistics, Carnegie Mellon University, Pittsburgh, USA.

DOI: 10.4236/jst.2012.21005                

Abstract

Feature detection in chemical sensors images falls under the general topic of mathematical morphology, where the goal is to detect “image objects” e.g. peaks or spots in an image. Here, we propose a novel method for object detection that can be generalized for a k-dimensional object obtained from an analogous higher-dimensional technology source. Our method is based on the smoothing decomposition, Data = Smooth + Rough, where the “rough” (i.e. residual) object from a k-dimensional cross-shaped smoother provides information for object detection. We demonstrate properties of this procedure with chemical sensor applications from various biological fields, including genetic and proteomic data analysis.

Keywords

Bump Hunting; Image Analysis; Spatial Smoothing; Feature Detection; Mathematical Morphology

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. Agard, R. Steinberg, and R. Stroud, “Quantitative Analysis of Electrophoretograms: A Mathematical Approach to Super-Resolution,” Analytical Biochemistry, Vol. 111, No. 2, 1981, pp. 257-268. doi:10.1016/0003-2697(81)90562-5
[2]	E. Bertin and S. Arnouts, “Sextractor: Software for Source Extraction,” Astronomy and Astrophysics, Vol. 14, No. 4, 1996.
[3]	T. Lindeberg, “Feature Detection with Automatic Scale Selection,” International Journal of Computer Vision, Vol. 30, No. 2, 1998, pp. 79-116. doi:10.1023/A:1008045108935
[4]	K. Coombes, H. Fritsche Jr., C. Clarke, J. Chen, K. Baggerly, J. Morris, L. Xiao, M. Hung, and H. Kuerer, “Quality Control and Peak Finding for Proteomics Data Collected from Nipple Aspirate Fluid by Surface-Enhanced Laser Desorption and Ionization,” Clinical Chemistry, Vol. 49, No. 10, 2003, pp. 1615-1623. doi:10.1373/49.10.1615
[5]	P. Cutler, G. Heald, I. R. White, and J. Ruan, “A Novel Approach to Spot Detection for Two-Dimensional Gel Electrohporesis Images Using Pixel Value Collection,” Proteomics, Vol. 3, No. 4, 2003, pp. 392-401. doi:10.1002/pmic.200390054
[6]	D. S. Lalush, “Effects of Spot and Background Defects on Quantitative Data from Spotted Microarrays,” Proceedings of the 25th Annual International Conference of the IEEE, Vol. 4, 2003, pp. 3563-3566.
[7]	K. Coombes, S. Tsavachidis, J. Morris, K. Baggerly, M. Hung and H. Kuerer, “Improved Peak Detection and Quantification of Mass Spectrometry Data Acquired from Surface-Enhanced Laser Desorption and Ionization by Denoising Spectra with the Undecimated Discrete Wavelet Transform,” Proteomics, Vol. 5, No. 16, 2005, pp. 4107-4117. doi:10.1002/pmic.200401261
[8]	A. Jain and D. Zongker, “Feature Selection: Evaluation, Application, and Small Sample Performance,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 2, 1997, pp. 153-158. doi:10.1109/34.574797
[9]	B. Guo, R. Damper, S. Gunn and J. Nelson, “A Fast Separability-Based Feature-Selection Method for High- Dimensional Remotely Sensed Image Classification,” Pattern Recognition, Vol. 41, No. 5, 2008, pp. 1653-1662. doi:10.1016/j.patcog.2007.11.007
[10]	J. Serra, “Image Analysis and Mathematical Morphology 1982,” Academic Press, New York, 1986, pp. 370-382.
[11]	P. Maragos, “Tutorial on Advances in Morphological Image Processing and Analysis,” Optical Engineering, Vol. 26, No. 7, 1987, pp. 623-632.
[12]	P. Maragos and R. Schafer, “Morphological Filters Part I: Their Set-Theoretic Analysis and Relations to Linear Shift-Invariant Filters,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 35, No. 8, 1987, pp. 1153-1169.
[13]	P. Maragos and R. Schafer, “Morphological Filters Part II: Their Relations to Median, Order-Statistic, and Stack Filters,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 35, No. 8, 1987, pp. 1170-1184. doi:10.1109/TASSP.1987.1165254
[14]	P. Maragos, R. Schafer and M. Butt, “Mathematical Morphology and Its Applications to Image and Signal Processing,” Springer, New York, 1996. doi:10.1007/978-1-4613-0469-2
[15]	P. Soille, “Morphological Image Analysis: Principles and Applications,” Springer-Verlag, New York, 2003.
[16]	D. Gavrila, J. Giebel, M. Perception, D. Res and G. Ulm, “Shape-Based Pedestrian Detection and Tracking,” IEEE Intelligent Vehicle Symposium, Vol. 1, 2002, pp. 8-14.
[17]	L. Tarassenko, P. Hayton, N. Cerneaz and M. Brady, “Novelty Detection for the Identification of Masses in Mammograms,” Fourth International Conference on Artificial Neural Networks, Cambridge, 26-28 June 1995, pp. 442-447.
[18]	E. Saber and A. Murat Tekalp, “Frontalview Facedetection and Facial Feature Extraction Using Color, Shape and Symmetry Based Cost Functions,” Pattern Recognition Letters, Vol. 19, No. 8, 1998, pp. 669-680. doi:10.1016/S0167-8655(98)00044-0
[19]	Y. Wang, C. Chua and Y. Ho, “Facial Feature Detection and Face Recognition from 2D and 3D Images,” Pattern Recognition Letters, Vol. 23, No. 10, 2002, pp. 1191- 1202. doi:10.1016/S0167-8655(02)00066-1
[20]	E. Lehmann and G. Casella, “Theory of Point Estimation,” Springer, New York, 1998.
[21]	T. Apostol and I. Makai, “Mathematical Analysis,” Addison-Wesley, Reading, 1974.
[22]	L. Wasserman, “All of Statistics: A Concise Course in Statistical Inference,” Springer, New York, 2004.
[23]	G. Casella and R. L. Berger, “Statistical Inference,” Dux- bury Press, Belmont, 1990.
[24]	J. Miecznikowski, K. Sellers and W. Eddy, “Multidemensional Median Filters for Finding Bumps,” Technical Re- port 907, SUNY University at Buffalo, Buffalo, 2009.
[25]	M. Karas, U. Bahr, A. Ingendoh, E. Nordhoff, B. Stahl, K. Strupat and F. Hillenkamp, “Principles and Applications of Matrix-Assisted UV-Laser Desorption/Ionization Mass Spectrometry,” Analytica Chimica Acta, Vol. 241, No. 2, 1990, pp. 175-185. doi:10.1016/S0003-2670(00)83645-4
[26]	K. Sellers, J. Miecznikowski, S. Viswanathan, J. Minden and W. Eddy, “Lights, Camera, Action: Quantitative Ana- lysis of Systematic Variation in Two-Dimensional Difference Gel Electrophoresis,” Electrophoresis, Vol. 28, No. 18, 2007, pp. 3324-3332. doi:10.1002/elps.200600793
[27]	J. Miecznikowski, S. Damodaran, K. Sellers, D. Coling, R. Salvi and R. Rabin, “A Comparison of Imputation Procedures and Statistical Tests for the Analysis of Two- Dimensional Electrophoresis Data,” Proteome Science, Vol. 9, No. 14, 2011, p. 66.
[28]	J. Mergliano and J. Minden, “Caspase-Independent Cell Engulfment Mirrors Cell Death Pattern in Drosophila Embryos,” Development, Vol. 130, No. 23, 2003, pp. 5779- 5789. doi:10.1242/dev.00824
[29]	L. Gong, M. Puri, M. Unlu, M. Young, K. Robertson, S. Viswanathan, A. Krishnaswamy, S. Dowd and J. Minden, “Drosophila Ventral Furrow Morphogenesis: A Proteomic Analysis,” Development, Vol. 131, No. 3, 2004, pp. 643-656. doi:10.1242/dev.00955
[30]	J. Miecznikowski, D. Wang, S. Liu, L. Sucheston and D. Gold, “Comparative Survival Analysis of Breast Cancer Microarray Studies Identifies Important Prognostic Genetic Pathways,” BMC Cancer, Vol. 10, No. 1, 2010, p. 573. doi:10.1186/1471-2407-10-573
[31]	M. Schena, D. Shalon, R. Davis and P. Brown, “Quantitative Monitoring of Gene Expression Patterns with a Complementary DNA Microarray,” Science, Vol. 270, No. 5235, 1995, pp. 467-470. doi:10.1126/science.270.5235.467
[32]	R. Gentleman, “Bioinformatics and Computational Biology Solutions Using R and Bioconductor,” Springer, New York, 2005. doi:10.1007/0-387-29362-0
[33]	C. Schr?der, A. Jacob, S. Tonack, T. Radon, M. Sill, M. Zucknick, S. Rüffer, E. Costello, J. Neoptolemos, T. Crnogorac-Jurcevic, et al., “Dual-Color Proteomic Profiling of Complex Samples with a Microarray of 810 Cancer-Re- lated Antibodies,” Molecular & Cellular Proteomics, Vol. 9, No. 6, 2010, pp. 1271-1280. doi:10.1074/mcp.M900419-MCP200
[34]	M. Eisen, P. Spellman, P. Brown and D. Botstein, “Cluster Analysis and Display of Genomewide Expression Patterns,” Proceedings of the National Academy of Sciences, Vol. 95, No. 25, 1998, pp. 14863-14868. doi:10.1073/pnas.95.25.14863
[35]	A. Alizadeh, M. Eisen, R. Davis, C. Ma, I. Lossos, A. Rosenwald, J. Boldrick, H. Sabet, T. Tran, X. Yu, et al., “Distinct Types of Diffuse Large b-Cell Lymphoma Identified by Gene Expression Profiling,” Nature, Vol. 403, No. 6769, 2000, pp. 503-511. doi:10.1038/35000501
[36]	J. Khan, J. Wei, M. Ringnér, L. Saal, M. Ladanyi, F. Westermann, F. Berthold, M. Schwab, C. Antonescu, C. Peterson, et al., “Classification and Diagnostic Prediction of Cancers Using Gene Expression Profiling and Artificial Neural Networks,” Nature Medicine, Vol. 7, No. 6, 2001, pp. 673-679. doi:10.1038/89044
[37]	G. Fink, P. Spellman, G. Sherlock, M. Zhang, V. Iyer, K. Anders, M. Eisen, P. Brown, D. Botstein and B. Futcher, “Comprehensive Identification of Cell Cycle-Regulated Genes of the Yeast Saccharomyces Cerevisiae by Microarray Hybridization,” Molecular Biology of the Cell, Vol. 9, No. 12, 1998, pp. 3273-3297.
[38]	B. Silverman, “Density Estimation for Statistics and Data Analysis,” Chapman & Hall/CRC, 1986.
[39]	J. Tukey, “Exploratory Data Analysis,” Addison-Wesley, New York, 1977.
[40]	M. Minnotte and D. Scott, “The Mode Tree: A Tool for Visualization of Nonparametric Density Features,” Journal of Computational and Graphical Statistics, Vol. 2, No. 1, 1993, pp. 51-68. doi:10.2307/1390955
[41]	J. Miecznikowski, D. Wang and A. Hutson, “Bootstrap Mise Estimators to Obtain Bandwidth for Kernel Density Estimation,” Communications in Statistics Simulation and Computation, Vol. 39, No. 7, 2010, pp. 1455-1469. doi:10.1080/03610918.2010.500108
[42]	Y. Kang, T. Techanukul, A. Mantalaris and J. Nagy, “Comparison of Three Commercially Available DIGE Analysis Software Packages: Minimal User Intervention in Gel-Based Proteomics,” Journal of Proteome Research, Vol. 8, No. 2, 2009, pp. 1077-1084. doi:10.1021/pr800588f
[43]	Y. Chao, H. Zengyou and Y. Weichuan, “Comparison of Public Peak Detection Algorithms for Maldi Mass Spectrometry Data Analysis,” BMC Bioinformatics, Vol. 10, No. 4, 2009.