An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids

• Autorzy: Atilla Sit , Julie C Mitchell , George N Phillips , Stephen J Wright
• Języki publikacji: EN

Abstrakty

EN

Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many expansion terms to describe object features along the edges and corners of the region. We overcome this problem by applying a Gram-Schmidt process to re-orthogonalize the Zernike polynomials so that they recover the orthonormality property over a specified box-shaped domain. We compare the shape retrieval performance of these new polynomial bases to that of the classical Zernike unit-ball polynomials.

Słowa kluczowe

EN

Zernike polynomials; 3D shape retrieval; reconstruction; Gram-Schmidt orthogonalization; Electron Microscopy Data Bank

• Wydawca: De Gruyter Open
• Czasopismo: Molecular Based Mathematical Biology
• Rocznik: 2013
• Tom: 1
• Strony: 75-89

Daty

otrzymano

2012-09-28

zaakceptowano

2013-03-20

online

2013-04-16

Twórcy

autor

Atilla Sit,

autor

Julie C Mitchell,

autor

George N Phillips,

autor

Stephen J Wright,

Bibliografia

• A. Björk. Solving linear least-squares problems by Gram-Schmidt orthogonalization. B.I.T., 7:1–21, 1967.
• M. Bray. Orthogonal polynomials: a set for square areas. Proc. SPIE, 5252:314-321, 2004.
• N. Canterakis. 3D Zernike moments and Zernike affine invariants for 3D image analysis and recognition. 11thScandinavian Conf. on Image Analysis, 85–93, 1999.
• G. M. Dai and V. N. Mahajan. Nonrecursive determination of orthonormal polynomials with matrix formulation.Optics Letters, 32(1):74-76, 2007.[WoS][PubMed][Crossref]
• EMDB map distribution format description, version 1.0. Document created and published by the EMDataBank.orgteam, collaboration between PDBe, RCSB-PDB, NCMI, 2010.
• S. D. Fuller. Depositing electron microscopy maps. Structure, 11(1):11–12, 2003.[Crossref][PubMed]
• J. B. Heymann, M. Chagoyen, and D. M. Belnap. Common conventions for interchange and archiving of threedimensionalelectron microscopy information in structural biology. J Struct Biol, 151(2):196–207, 2005.
• K. M. Hosny. Exact and fast computation of geometric moments for gray level images. Applied Mathematics andComputation, 189:1214–1222, 2007.[WoS]
• K. M. Hosny. A novel symmetry-based method for exact computation of 2D and 3D geometric moments. InternationalJournal of Innovative Computing, Information and Control, 8(9):6123–6140, 2012.
• K. M. Hosny and M. Hafez. An algorithm for fast computation of 3D Zernike moments for volumetric images.Mathematical Problems in Engineering, Article ID 353406, 17 pp, 2012.
• V. N. Mahajan and G. M. Dai. Orthonormal polynomials in wavefront analysis: analytical solution. J. Opt. Soc. Am.A, 24(9):2994–3016, 2007.[Crossref]
• L. Mak, S. Grandison, and R. J. Morris. An extension of spherical harmonics to region-based rotationally invariantdescriptors for molecular shape description and comparison. J Molecular Graphics and Modeling, 26(7):1035–1045,2008.
• M. Novotni and R. Klein. 3D Zernike descriptors for content based shape retrieval. Proceedings of the 8th ACMsymposium on Solid modeling and Applications, 216–225, 2003.
• M. Novotni and R. Klein. Shape retrieval using 3D Zernike descriptors. Computer-Aided Design, 36:1047–1062,2004.[Crossref]
• L. Sael, B. Li, D. La, Y. Fang, K. Ramani, R. Rustamov, and D. Kihara. Fast protein tertiary structure retrieval basedon global surface shape similarity. Proteins, 72(4):1259–1273, 2008.[Crossref][PubMed][WoS]
• M. Tagari, R. Newman, M. Chagoyen, J. M. Carazo, and K. Henrick. New electron microscopy database and deposition system. Trends Biochem Sci, 27(11):589, 2002.[PubMed][Crossref]
• V. Venkatraman, P. R. Chakravarthy and D. Kihara. Application of 3D Zernike descriptors to shape-based ligandsimilarity searching. J of Cheminformatics, 1:19, 2009.
• V. Venkatraman, L. Sael, and D. Kihara. Potential for protein surface shape analysis using spherical harmonics and3D Zernike descriptors. Cell Biochem Biophys, 54:23–32, 2009.[PubMed][Crossref][WoS]
• V. Venkatraman, Y. D. Yang, L. Sael and D. Kihara. Protein-protein docking using region-based 3D Zernike descriptors.BMC Bioinformatics, 10:407, 2009.[Crossref][PubMed]
• F. Zernike. Diffraction theory of knife-edge test and its improved form, the phase contrast method. Mon. Not. R.Astron. Soc., 94:377–384, 1934.

Identyfikatory

DOI

10.2478/mlbmb-2013-0004