Pattern clustering based on noise modeling in wavelet space

We describe an effective approach to object or feature detection in point patterns via noise modeling. This is based on use of a redundant or non-pyramidal wavelet transform. Noise modeling is based on a Poisson process. We illustrate this new method with a range of examples. We use the close relationship between image (pixelated) and point representations to achieve the result of a clustering method with constant-time computational cost.

[1]  Mats Bengtsson,et al.  Using the potts glass for solving the clustering problem , 1995, Int. J. Neural Syst..

[2]  Keinosuke Fukunaga,et al.  A Graph-Theoretic Approach to Nonparametric Cluster Analysis , 1976, IEEE Transactions on Computers.

[3]  A. Raftery,et al.  Nearest-Neighbor Clutter Removal for Estimating Features in Spatial Point Processes , 1998 .

[4]  Fionn Murtagh,et al.  Image restoration with noise suppression using a multiresolution support. , 1995 .

[5]  C. Fraley,et al.  Nonparametric Maximum Likelihood Estimation of Features in Spatial Point Processes Using Voronoï Tessellation , 1997 .

[6]  A. Raftery,et al.  Detecting features in spatial point processes with clutter via model-based clustering , 1998 .

[7]  Jean-Luc Starck,et al.  1 - Restauration des images multi-échelles par l'algorithme à trous , 1994 .

[8]  Adrian E. Raftery,et al.  Fitting straight lines to point patterns , 1984, Pattern Recognit..

[9]  M. J. R. Healy,et al.  New Trends in Data Analysis and Applications , 1984 .

[10]  Michiel P. van Oeffelen,et al.  An algorithm for pattern description on the level of relative proximity , 1983, Pattern Recognit..

[11]  Vito Di Gesù,et al.  Detection of diffuse clusters in noise background , 1986, Pattern Recognit. Lett..

[12]  J. Morlet,et al.  Wave propagation and sampling theory—Part I: Complex signal and scattering in multilayered media , 1982 .

[13]  Michael Spann,et al.  A new approach to clustering , 1990, Pattern Recognit..

[14]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

[15]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[16]  Azriel Rosenfeld,et al.  Cluster detection in background noise , 1989, Pattern Recognit..

[17]  Anil K. Jain,et al.  Single-link characteristics of a mode-seeking clustering algorithm , 1979, Pattern Recognit..

[18]  P. M. Narendra,et al.  Image Segmentation with Directed Trees , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  M. Shensa.  The Discrete Wavelet Transform , 1991 .

[20]  F. James Rohlf,et al.  Function-Point Cluster Analysis , 1973 .

[21]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[22]  Charles T. Zahn,et al.  Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters , 1971, IEEE Transactions on Computers.

[23]  Jun S. Huang,et al.  A heuristic method for separating clusters from noisy background , 1990, Pattern Recognit..

[24]  A. Raftery,et al.  Model-based Gaussian and non-Gaussian clustering , 1993 .

[25]  Craig Gotsman,et al.  A cluster detection algorithm based on percolation theory , 1991, Pattern Recognit. Lett..

[26]  C. Fraley,et al.  Nonparametric Maximum Likelihood Estimation of Features in Spatial Point Processes Using Voronoï Tessellation , 1997 .

[27]  V. Di Gesù,et al.  Some statistical properties of the minimum spanning forest , 1983, Pattern Recognit..

[28]  Hans-Peter Kriegel,et al.  A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise , 1996, KDD.

[29]  Gérard Govaert,et al.  Gaussian parsimonious clustering models , 1995, Pattern Recognit..

[30]  G. MallatS..  A Theory for Multiresolution Signal Decomposition , 1989 .

[31]  J. M. Gelb,et al.  Cosmological N‐Body Simulations , 1991 .

[32]  Richard C. Dubes,et al.  Remarks on some statistical properties of the minimum spanning forest , 1986, Pattern Recognit..

[33]  Azriel Rosenfeld,et al.  Model-based cluster analysis , 1993, Pattern Recognit..

[34]  Mark J. Shensa,et al.  The discrete wavelet transform: wedding the a trous and Mallat algorithms , 1992, IEEE Trans. Signal Process..

[35]  Fionn Murtagh,et al.  A Survey of Algorithms for Contiguity-Constrained Clustering and Related Problems , 1985, Comput. J..

[36]  D. Wishart.  Clustan : user manual , 1978 .

[37]  E. Slezak,et al.  Identification of structures from galaxy counts: use of the wavelet transform , 1990 .

[38]  Yiu-Fai Wong,et al.  A new clustering algorithm applicable to multispectral and polarimetric SAR images , 1993, IEEE Trans. Geosci. Remote. Sens..

[39]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[40]  A. Bijaoui,et al.  Objective Detection of Voids and High-Density Structures in the First CfA Redshift Survey Slice , 1993 .

[41]  Richard C. Dubes,et al.  A Variation on a Nonparametric Clustering Method , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[42]  Vincent Kanade,et al.  Clustering Algorithms , 2021, Wireless RF Energy Transfer in the Massive IoT Era.

[43]  Riichiro Mizoguchi,et al.  A Nonparametric Algorithm for Detecting Clusters Using Hierarchical Structure , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[44]  Fionn Murtagh,et al.  Image restoration with noise suppression using the wavelet transform , 1994 .

[45]  Fionn Murtagh,et al.  Multiresolution Support Applied to Image Filtering and Restoration , 1995, CVGIP Graph. Model. Image Process..