Shape classification using smooth principal components

We suggest and assess a novel approach to shape classification using smooth functional principal components. This gives a rotation, location and scale invariant classifier. Our experiments show that this approach can outperform a number of competitors including conventional Eigenshape methods and time series methods. The degree of smoothing associated with the best classification performance is determined automatically using cross-validation.

[1]  Gareth M. James,et al.  Functional linear discriminant analysis for irregularly sampled curves , 2001 .

[2]  H. Cardot Nonparametric estimation of smoothed principal components analysis of sampled noisy functions , 2000 .

[3]  B. K. Alsberg Representation of spectra by continuous functions , 1993 .

[4]  Vincent Fontaine,et al.  AUTOMATIC CLASSIFICATION OF ENVIRONMENTAL NOISE EVENTS BY HIDDEN MARKOV MODELS , 1998 .

[5]  Hiroshi Murase,et al.  Moving object recognition in eigenspace representation: gait analysis and lip reading , 1996, Pattern Recognit. Lett..

[6]  C. Radhakrishna Rao,et al.  Prediction of Future Observations in Growth Curve Models , 1987 .

[7]  Fabrice Druaux,et al.  Particles shape analysis and classification using the wavelet transform , 2000, Pattern Recognit. Lett..

[8]  J. J. Rajan,et al.  Model Order Selection For The Singular Value Decomposition And The Discrete Karhunen-Loeve Transform Using A Bayesian Approach , 1997 .

[9]  K A Do,et al.  Discriminant Analysis of Event‐Related Potential Curves Using Smoothed Principal Components , 1999, Biometrics.

[10]  Joel A. Rosiene,et al.  A fast wavelet-based Karhunen-Loeve transform , 1998, Pattern Recognit..

[11]  Kie B. Eom Shape recognition using spectral features , 1998, Pattern Recognit. Lett..

[12]  Ben Pinkowski Multiscale fourier descriptors for classifying semivowels in spectrograms , 1993, Pattern Recognit..

[13]  B. Silverman,et al.  Functional Data Analysis , 1997 .

[14]  C. Hurvich,et al.  High Breakdown Methods of Time Series Analysis , 1993 .

[15]  R. Tibshirani,et al.  Penalized Discriminant Analysis , 1995 .

[16]  Sven Loncaric,et al.  A survey of shape analysis techniques , 1998, Pattern Recognit..

[17]  Stéphane Mallat,et al.  Silhouette recognition using high-resolution pursuit , 1999, Pattern Recognit..

[18]  E. A. Sylvestre,et al.  Principal modes of variation for processes with continuous sample curves , 1986 .

[19]  Amanda J. Goode,et al.  Semi-parametric classification of noisy curves , 2003, Pattern Recognit..

[20]  Peter Hall,et al.  A Functional Data—Analytic Approach to Signal Discrimination , 2001, Technometrics.

[21]  Thioulouse Jean,et al.  FUNCTIONAL DATA ANALYSIS OF CURVE ASYMMETRY WITH APPLICATION TO THE COLOR PATTERN OF HYDROPSYCHE CONTUBERNALIS HEAD CAPSULE , 1997 .

[22]  M. Priestley,et al.  A Study of Autoregressive and Window Spectral Estimation , 1981 .

[23]  R. Glendinning Testing for a jump in the periodogram , 1997 .

[24]  W. W. Daniel Applied Nonparametric Statistics , 1979 .

[25]  K. J. Utikal,et al.  Inference for Density Families Using Functional Principal Component Analysis , 2001 .

[26]  Chein-I Chang,et al.  Unsupervised hyperspectral image analysis with projection pursuit , 2000, IEEE Trans. Geosci. Remote. Sens..

[27]  Rainer von Sachs,et al.  Estimating the Spectrum of a Stochastic Process in the Presence of a Contaminating Signal , 1993, IEEE Trans. Signal Process..

[28]  Richard H. Glendinning,et al.  Robust shape classification , 1999, Signal Process..

[29]  Peter J. Diggle,et al.  Spectral Analysis of Replicated Biomedical Time Series , 1997 .

[30]  Alois Kneip,et al.  Nonparametric-estimation of Common Regressors for Similar Curve Data , 1994 .

[31]  Anil K. Jain,et al.  Deformable template models: A review , 1998, Signal Process..

[32]  B. Silverman,et al.  Smoothed functional principal components analysis by choice of norm , 1996 .

[33]  Trevor Hastie,et al.  Statistical Measures for the Computer-Aided Diagnosis of Mammographic Masses , 1999 .

[34]  Takio Kurita,et al.  Invariant distance measures for planar shapes based on complex autoregressive model , 1994, Pattern Recognit..

[35]  Matti Pietikäinen,et al.  An Experimental Comparison of Autoregressive and Fourier-Based Descriptors in 2D Shape Classification , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[36]  M. Narasimha Murty,et al.  A genetic approach for selection of (near-) optimal subsets of principal components for discrimination , 1995, Pattern Recognit. Lett..