Volumetric Image Pattern Recognition Using Three-Way Principal Component Analysis
The aim of the paper is to develop a relaxed closed form for tensor principal component analysis (PCA) for the recognition, classification, compression and retrieval of volumetric data. The tensor PCA derives the tensor Karhunen-Loève transform which compresses volumetric data, such as organs, cells in organs and microstructures in cells, preserving both the geometric and statistical properties of objects and spatial textures in the space. Furthermore, we numerically clarify that low-pass filtering after applying the multi-dimensional discrete cosine transform (DCT) efficiently approximates the data compression procedure based on tensor PCA. These orthogonal-projection-based data compression methods for three-way data is extracts outline shapes of biomedical objects such as organs and compressed expressions for the interior structures of cells.
- 3.Mørup, M.: Applications of tensor (multiway array) factorizations and decompositions in data mining. Wiley Interdisc. Rev.: Data Mining Knowl. Discov. 1, 24–40 (2011)Google Scholar
- 9.Thompson, D.W.: On Growth and Form (The Complete Revised Edition). Dover, Minoela (1992)Google Scholar
- 10.Imiya, A., Eckhardt, U.: The Euler characteristics of discrete objects and discrete quasi-objects. CVIU 75, 307–318 (1999)Google Scholar
- 11.Sakai, T., Narita, M., Komazaki, T., Nishiguchi, H., Imiya, A.: Image hierarchy in Gaussian scale space. In: Advances in Imaging and Electron Physics, vol. 165, pp. 175–263. Academic Press (2013)Google Scholar
- 15.Oja, E.: Subspace Methods of Pattern Recognition. Research Studies Press, Baldock (1983)Google Scholar
- 17.Aubert-Broche, B., Griffin, M., Pike, G.B., Evans, A.C., Collins, D.L.: 20 new digital brain phantoms for creation of validation image data bases. IEEE TMI 25, 1410–1416 (2006)Google Scholar