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Two-Dimensional Functional Principal Component Analysis for Image Feature Extraction

Publication ,  Journal Article
Shi, H; Yang, Y; Wang, L; Ma, D; Beg, MF; Pei, J; Cao, J
Published in: Journal of Computational and Graphical Statistics
January 1, 2022

Methodologies for functional principal component analysis are well established in the one-dimensional setting. However, for two-dimensional surfaces, for example, images, conducting functional principal component analysis is complicated and challenging, because the conventional eigendecomposition approach would require the estimation of a four-dimensional covariance function, which may incur high cost in terms of time and machine memory. To circumvent such computational difficulties, we propose a novel two-dimensional functional principal component analysis for extracting functional principal components and achieving dimensionality reduction for images. Different from the conventional eigendecomposition approach, our proposed method is based on the direct estimation of the optimal two-dimensional functional principal components via tensor product B-spline, which opens up a new avenue for estimating functional principal components. We present theoretical results that prove the consistency of the proposed approach. Our method is illustrated by analyzing brain images of subjects with the Alzheimer’s Disease and the handwritten digits images. The finite sample performance of our method is further assessed with some simulation studies. Supplementary materials for this article are available online.

Duke Scholars

Published In

Journal of Computational and Graphical Statistics

DOI

EISSN

1537-2715

ISSN

1061-8600

Publication Date

January 1, 2022

Volume

31

Issue

4

Start / End Page

1127 / 1140

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 1403 Econometrics
  • 0104 Statistics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Shi, H., Yang, Y., Wang, L., Ma, D., Beg, M. F., Pei, J., & Cao, J. (2022). Two-Dimensional Functional Principal Component Analysis for Image Feature Extraction. Journal of Computational and Graphical Statistics, 31(4), 1127–1140. https://doi.org/10.1080/10618600.2022.2035738
Shi, H., Y. Yang, L. Wang, D. Ma, M. F. Beg, J. Pei, and J. Cao. “Two-Dimensional Functional Principal Component Analysis for Image Feature Extraction.” Journal of Computational and Graphical Statistics 31, no. 4 (January 1, 2022): 1127–40. https://doi.org/10.1080/10618600.2022.2035738.
Shi H, Yang Y, Wang L, Ma D, Beg MF, Pei J, et al. Two-Dimensional Functional Principal Component Analysis for Image Feature Extraction. Journal of Computational and Graphical Statistics. 2022 Jan 1;31(4):1127–40.
Shi, H., et al. “Two-Dimensional Functional Principal Component Analysis for Image Feature Extraction.” Journal of Computational and Graphical Statistics, vol. 31, no. 4, Jan. 2022, pp. 1127–40. Scopus, doi:10.1080/10618600.2022.2035738.
Shi H, Yang Y, Wang L, Ma D, Beg MF, Pei J, Cao J. Two-Dimensional Functional Principal Component Analysis for Image Feature Extraction. Journal of Computational and Graphical Statistics. 2022 Jan 1;31(4):1127–1140.

Published In

Journal of Computational and Graphical Statistics

DOI

EISSN

1537-2715

ISSN

1061-8600

Publication Date

January 1, 2022

Volume

31

Issue

4

Start / End Page

1127 / 1140

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 1403 Econometrics
  • 0104 Statistics