12.3.1.6.1 Moment Computation, Computation of Moments

Zernike, F.,
Diffraction theory of the cut procedure and its improved form, the phase contrast method,
Physica(1), 1934, pp. 689-704. German title: Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode For a detailed description:
HTML Version. BibRef 3400

Bhatia, A.B., and Wolf, E.,
On the circle polynomials of Zernike and related orthogonal sets,
CambridgePhil(50), 1954, pp. 40-48. BibRef 5400

Medalia, A.I.,
Dynamic Shape Factors of Particles,
Powder TechnologyNo. 4, 1970/71, pp. 117-138. BibRef 7000

Hsia, T.C.,
A Note on Invariant moments in Image Processing,
SMC(11), 1981, pp. 831-834. BibRef 8100

Zakaria, M.F., Vroomen, L.J., Zsombor-Murray, P.J.A., and van Kessel, J.M.H.M.,
Fast Algorithm for the Computation of Moment Invariants,
PR(20), No. 6, 1987, pp. 639-643.
WWW Version. BibRef 8700

Teh, C.H., and Chin, R.T.,
On Image Analysis by the Methods of Moments,
PAMI(10), No. 4, July 1988, pp. 496-513.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 8807
And: CVPR88(556-561).
IEEE Abstract. IEEE Top Reference. A discussion of various moment techniques for descriptions. BibRef

Teh, C.H., and Chin, R.T.,
On Digital Approximation of Moment Invariants,
CVGIP(33), No. 3, March 1986, pp. 318-326.
WWW Version. BibRef 8603

Sluzek, A.[Andrzej],
Using Moment Invariants to Recognize and Locate Partially Occluded 2D Objects,
PRL(7), 1988, pp. 253-257. BibRef 8800

Sluzek, A.[Andrzej],
Identification of Planar Objects in 3-D Space from Perspective Projections,
PRL(7), 1988, pp. 59-63. BibRef 8800

Sluzek, A.[Andrzej],
Identification And Inspection Of 2-D Objects Using New Moment-Based Shape Descriptors,
PRL(16), No. 7, July 1995, pp. 687-697. BibRef 9507

Sluzek, A.[Andrzej],
On moment-based local operators for detecting image patterns,
IVC(23), No. 3, 1 March 2005, pp. 287-298.
WWW Version. 0501
BibRef

Islam, M.S.[M. Saiful], Sluzek, A.[Andrzej],
Relative scale method to locate an object in cluttered environment,
IVC(26), No. 2, 1 February 2008, pp. 259-274.
WWW Version. 0711
BibRef
Earlier:
3D Object Localization Using Local Shape Features,
ICARCV06(1-6).
IEEE DOI Link 0612
Relative scale; Object localization; Multidimensional hashing BibRef

Sluzek, A.[Andrzej],
Building Local Features from Pattern-Based Approximations of Patches: Discussion on Moments and Hough Transform,
JIVP(2009), No. 2009, pp. xx-yy.
WWW Version. 0903
BibRef

Budrikis, Z.L.[Zigmantas L.], Hatamian, M.[Mehdi],
Moment generator,
US_Patent4,745,567, May 17, 1988
WWW Version. BibRef 8805

Chen, K.P.[Ke-Ping],
Efficient Parallel Algorithms for the Computation of Two-Dimensional Image Moments,
PR(23), No. 1-2, 1990, pp. 109-119.
WWW Version. BibRef 9000

Sanniti di Baja, G.[Gabriella],
O(N) Computation of Projections and Moments from the Labeled Skeleton,
CVGIP(49), No. 3, March 1990, pp. 369-378.
WWW Version. BibRef 9003

Salzman, D.B.,
A Method of General Moments for Orienting 2D Projections of Unknown 3D Objects,
CVGIP(50), No. 2, May 1990, pp. 129-156.
WWW Version. BibRef 9005

Pan, Y.,
A Note on Efficient Parallel Algorithms for the Computation of Two-Dimensional Image Moments,
PR(24), No. 9, 1991, pp. 917.
WWW Version. BibRef 9100

Pawlak, M.,
On The Reconstruction Aspects of Moment Descriptors,
IT(38), 1992, pp. 1698-1708. BibRef 9200
Earlier:
On The Reconstruction Aspects of Moment Descriptions,
IEEE_Symposium. Info. TheorySan Diego, January 1990. BibRef

Khotanzad, A., Lu, J.H.,
Classification of Invariant Image Representations Using a Neural Network,
ASSP(38), No. 6, June 1990, pp. 1028-1038. BibRef 9006
Object Recognition Using a Neural Network and Invariant Zernike Features,
CVPR89(200-205).
IEEE Abstract. IEEE Top Reference. BibRef

Khotanzad, A., Hong, Y.H.,
Invariant Image Recognition by Zernike Moments,
PAMI(12), No. 5, May 1990, pp. 489-497.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9005
Earlier:
Rotation Invariant Pattern Recognition Using Zernike Moments,
ICPR88(I: 326-328).
IEEE DOI Link
IEEE Top Reference. BibRef

Khotanzad, A., Hong, Y.H.,
Rotation Invariant Image Recognition Using Features Selected via a Systematic Method,
PR(23), No. 10, 1990, pp. 1089-1101.
WWW Version. BibRef 9000

Pawlak, M.[Miroslaw], Liao, S.X.[Simon X.],
On Digital Approximation of Moment Descriptors,
MGV(3), No. 1/2, 1994, pp. 61-68. See also On the Accuracy of Zernike Moments for Image Analysis. BibRef 9400

Xin, Y., Pawlak, M.[Miroslaw], Liao, S.X.[Simon X.],
Accurate Computation of Zernike Moments in Polar Coordinates,
IP(16), No. 2, February 2007, pp. 581-587.
IEEE DOI Link 0702
BibRef

Dai, M., Baylou, P., and Najim, M.,
An Efficient Algorithm for Computation of Shape Moments from Run-Length Codes or Chain Codes,
PR(25), No. 10, October 1992, pp. 1119-1128.
WWW Version. Moments from the boundary. BibRef 9210

Jiang, X.Y., and Bunke, H.,
Simple and Fast Computation of Moments,
PR(24), No. 8, 1991, pp. 801-806.
WWW Version. BibRef 9100

Leu, J.G.[Jia-Guu],
Computing A Shape's Moments from Its Boundary,
PR(24), No. 10, 1991, pp. 949-957.
WWW Version. Efficiently computing shape moments from the boundary elements. BibRef 9100

Li, B.C.[Bing-Cheng], Shen, J.[Jun],
Pascal Triangle Transform Approach to the Calculation of 3D Moments,
GMIP(54), No. 4, July 1992, pp. 301-307. BibRef 9207

Mukundan, R.,
Estimation of Quaternion Parameters from Two Dimensional Image Moments,
GMIP(54), No. 4, July 1992, pp. 345-350. BibRef 9207

Singer, M.H.,
A General Approach to Moment Calculation for Polygons and Line Segments,
PR(26), No. 7, July 1993, pp. 1019-1028.
WWW Version. BibRef 9307

Philips, W.,
A New Fast Algorithm for Moment Computation,
PR(26), No. 11, November 1993, pp. 1619-1621.
WWW Version. BibRef 9311

Fu, C.W., Yen, J.C., Chang, S.,
Calculation Of Moment Invariants Via Hadamard Transform,
PR(26), No. 2, February 1993, pp. 287-294.
WWW Version. BibRef 9302

Li, B.,
The Moment Calculation of Polyhedra,
PR(26), No. 8, August 1993, pp. 1229-1233.
WWW Version. BibRef 9308

Li, B.C.,
A New Computation of Geometric Moments,
PR(26), No. 1, January 1993, pp. 109-113.
WWW Version. BibRef 9301

Li, B.C., Shen, J.,
Fast Computation of Moment Invariants,
PR(24), No. 8, 1991, pp. 807-813.
WWW Version. BibRef 9100

Li, B.C., Shen, J.,
2-Dimensional Local Moment, Surface Fitting and Their Fast Computation,
PR(27), No. 6, June 1994, pp. 785-790.
WWW Version. BibRef 9406

Sardana, H.K., Daemi, M.F., Ibrahim, M.K.,
Global Description of Edge Patterns Using Moments,
PR(27), No. 1, January 1994, pp. 109-118.
WWW Version. BibRef 9401

Lin, W.G., Wang, S.S.,
A Note on the Calculation of Moments,
PRL(15), No. 11, November 1994, pp. 1065-1070. BibRef 9411

Mukundan, R., Ramakrishnan, K.R.,
Computation of Legendre and Zernike Moments,
PR(28), No. 9, September 1995, pp. 1433-1442.
WWW Version. BibRef 9509

Heywood, M.I., Noakes, P.D.,
Fractional Central Moment Method for Movement-Invariant Object Classification,
VISP(142), No. 4, August 1995, pp. 213-219. BibRef 9508

Li, B.C.[Bing-Cheng],
High-order moment computation of gray-level images,
IP(4), No. 4, April 1995, pp. 502-505.
IEEE DOI Link 0402
BibRef

Taubin, G., and Cooper, D.B.,
Object Recognition Based on Moment (or Algebraic) Invariants,
GICV92(Chapter 19). BibRef 9200

Taubin, G., and Cooper, D.B.,
Recognition and Positioning of Piecewise Algebraic Objects,
DARPA90(508-514). BibRef 9000

Taubin, G.[Gabriel], Cooper, D.B.[David B.],
Recognition and Positioning of Rigid Objects Using Algebraic Moment Invariants,
SPIE(1570), 1991, pp. 175-186. BibRef 9100

Taubin, G.,
Recognition and Positioning of Rigid Objects Using Algebraic and Moment Invariants,
Ph.D.May 1991, BibRef 9105 Brown BibRef

Taubin, G., Bolle, R.M., and Cooper, D.B.,
Representing and Comparing Shapes Using Shape Polynomials,
CVPR89(510-516).
IEEE Abstract. IEEE Top Reference. Shape is a probability measure (how likely a point here is going to be in the object) and compactness measure. Matches thus can be made to contours, sets of points, etc. BibRef 8900

Subrahmonia, J.[Jayashree], Cooper, D.B., Keren, D.[Daniel],
Practical Reliable Bayesian Recognition of 2D and 3D Objects Using Implicit Polynomials and Algebraic Invariants,
PAMI(18), No. 5, May 1996, pp. 505-519.
IEEE Abstract. IEEE Top Reference.
WWW Version. 9606
BibRef
Earlier: BrownLEMS-107, 1992. Bayes Nets. Mahalanobis Distance. High degree polynomial surfaces for descriptions. BibRef

Subrahmonia, J., Keren, D., Cooper, D.B.,
Recognizing mice, vegetables and hand printed characters based on implicit polynomials, invariants and Bayesian methods,
ICCV93(320-324).
IEEE DOI Link 0403
BibRef

Keren, D., Subrahmonia, J., Cooper, D.B.,
Robust object recognition based on implicit algebraic curves and surfaces,
CVPR92(791-794).
IEEE Abstract. IEEE Top Reference. 0403
BibRef

Keren, D., Subrahmonia, J., Taubin, G., Cooper, D.B.,
Bounded and Unbounded Implicit Polynomial Curves and Surfaces, Mahalanobis Distances, and Geometric Invariants, for Robust Object Recognition,
DARPA92(769-777). BibRef 9200

Yang, L.R.[Lu-Ren], Albregtsen, F.[Fritz],
Fast and Exact Computation of Cartesian Geometric Moments Using Discrete Greens Theorem,
PR(29), No. 7, July 1996, pp. 1061-1073.
WWW Version. 9607
BibRef

Yang, L.R.[Lu-Ren], Albregtsen, F.[Fritz], Taxt, T.[Torfinn],
Fast computation of 3-D geometric moments using a discrete Gauss' theorem,
CAIP95(649-654).
Springer DOI Link 9509
BibRef

Chung, K.L.,
Computing Horizontal/Vertical Convex Shapes Moments on Reconfigurable Meshes,
PR(29), No. 10, October 1996, pp. 1713-1717.
WWW Version. Hough Transform. BibRef 9610

Wong, W.H., Siu, W.C., and Lam, K.M.,
Generation of Moment Invariants and Their Uses for Character Recognition,
PRL(16), 1995, pp. 115-123. BibRef 9500

Shen, T.W., Lun, D.P.K., Siu, W.C.,
On the Efficient Computation of 2-D Image Moments Using the Discrete Radon-Transform,
PR(31), No. 2, February 1998, pp. 115-120.
WWW Version. 9802
BibRef

Hupkens, T.M., and de Clippeleir, J.,
Noise and Intensity Invariant Moments,
PRL(16), 1995, pp. 371-376. BibRef 9500

Mertzios, B.G., Tsirikolias, K.,
Statistical Shape Discrimination and Clustering Using an Efficient Set of Moments,
PRL(14), 1993, pp. 517-522. BibRef 9300

Strachan, N.J.C., Nesvadba, P., Allen, A.R.,
A Method for Working out the Moments of a Polygon,
PRL(11), 1990, pp. 351-354. BibRef 9000

Liu, W., Chen, S.S., Cavin, R.,
A Bit-Serial VLSI Architecture for Generating Moments in Real Time,
SMC(23), 1993, pp. 539-546. BibRef 9300

Yang, L., Albregtsen, F., Taxt, T.,
Fast Computation of 3-Dimensional Geometric Moments Using a Discrete Divergence Theorem and a Generalization to Higher Dimensions,
GMIP(59), No. 2, March 1997, pp. 97-108. 9704
BibRef

Shen, D.G.[Ding-Gang], Ip, H.H.S.,
Generalized Affine Invariant Image Normalization,
PAMI(19), No. 5, May 1997, pp. 431-440.
IEEE Abstract. IEEE Top Reference.
WWW Version. 9705
Generalized Complex moments. Makes strong claims regarding normalization. See also Affine invariant detection of perceptually parallel 3D planar curves. BibRef

Ip, H.H.S.[Horace H.S.], Shen, D.G.[Ding-Gang], Cheung, K.K.T.[Kent K.T.],
Affine Invariant Retrieval of Binary Patterns Using Generalized Complex Moments,
Visual97(xx). BibRef 9700

Sand, F.[Francis], Dougherty, E.R.[Edward R.],
Robustness of granulometric moments,
PR(32), No. 9, September 1999, pp. 1657-1665.
WWW Version. BibRef 9909

Kim, W.Y., Kim, Y.S.,
Robust Rotation Angle Estimator,
PAMI(21), No. 8, August 1999, pp. 768-773.
IEEE Abstract. IEEE Top Reference.
WWW Version. Rotation angle for rotation symmetric patterns. BibRef 9908

Klette, R.[Reinhard], Zunic, J.[Jovisa],
Digital Approximation of Moments of Convex Regions,
GMIP(61), No. 5, September 1999, pp. 274-298. BibRef 9909

Shu, H.Z.[Hua-Zhong], Luo, L.M.[Li-Min], Bao, X.D.[Xu-Dong], Yu, W.X.[Wen-Xue], Han, G.[Guoniu],
An Efficient Method for Computation of Legendre Moments,
GM(62), No. 4, July 2000, pp. 237-262. 0006
BibRef

Zhou, J.D., Shu, H.Z., Luo, L.M., Yu, W.X.,
Two new algorithms for efficient computation of Legendre moments,
PR(35), No. 5, May 2002, pp. 1143-1152.
WWW Version. 0202
BibRef

Shu, H.Z., Luo, L.M., Yu, W.X., Zhou, J.D.,
Fast computation of Legendre moments of polyhedra,
PR(34), No. 5, May 2001, pp. 1119-1126.
WWW Version. 0102
BibRef

Shu, H.Z., Luo, L.M., Yu, W.X., Fu, Y.,
A new fast method for computing Legendre moments,
PR(33), No. 2, February 2000, pp. 341-348.
WWW Version. 0001
BibRef

Balslev, I.[Ivar], Døring, K.[Kasper], Eriksen, R.D.[René Dencker],
Weighted central moments in pattern recognition,
PRL(21), No. 5, May 2000, pp. 381-384. 0005
BibRef

Demi, M., Paterni, M., Benassi, A.,
The First Absolute Central Moment in Low-Level Image Processing,
CVIU(80), No. 1, October 2000, pp. 57-87.
WWW Version. 0010
BibRef

Demi, M.,
On the gray-level central and absolute central moments and the mass center of the gray-level variability in low-level image processing,
CVIU(97), No. 2, February 2005, pp. 180-208.
WWW Version. 0412
BibRef

Mukundan, R., Ramakrishnan, K.R.,
Moment Functions in Image Analysis: Threoy and Applications,
World Scientific1998, ISBN 981-02-3524-0. BibRef 9800

Sossa-Azuela, J.H., Yáñez-Márquez, C., Díaz de León S., J.L.,
Computing geometric moments using morphological erosions,
PR(34), No. 2, February 2001, pp. 271-276.
WWW Version. 0011
BibRef

di Gesù, V., Palenichka, R.M.,
A fast recursive algorithm to compute local axial moments,
SP(81), No. 1, February 2001, pp. 265-273. 0102
BibRef

Palenichka, R.M., Zaremba, M.B., Valenti, C.,
A fast recursive algorithm for the computation of axial moments,
CIAP01(95-100).
IEEE Top Reference. 0210
BibRef

Palenichka, R.M.[Roman M.], Zaremba, M.B.[Marek B.],
A fast algorithm for the computation of axial moments and its application to the orthogonal fitting of curves,
PR(36), No. 7, July 2003, pp. 1519-1528.
WWW Version. 0304
BibRef

Wu, C.H.[Chin-Hsiung], Horng, S.J.[Shi-Jinn], Lee, P.Z.[Pei-Zong],
A new computation of shape moments via quadtree decomposition,
PR(34), No. 7, July 2001, pp. 1319-1330.
WWW Version. 0105
BibRef

Wu, C.H.[Chin-Hsiung], Horng, S.J.[Shi-Jinn],
Run-Length Chain Coding and Scalable Computation of a Shape's Moments Using Reconfigurable Optical Buses,
SMC-B(34), No. 2, April 2004, pp. 845-855.
IEEE Abstract. IEEE Top Reference. 0404
BibRef

Wu, C.H.[Chin-Hsiung], Horng, S.J.[Shi-Jinn], Wen, C.F.[Ching-Feng], Wang, Y.R.[Yuh-Rau],
Fast and scalable computations of 2D image moments,
IVC(26), No. 6, 1 June 2008, pp. 799-811.
WWW Version. 0804
Image moments; Moment invariants; Suffix sums; Scalable algorithm; Pattern recognition; Reconfigurable optical buses BibRef

Jacobs, M.[Mathews], Blu, T.[Thierry], Unser, M.[Michael],
An Exact Method for Computing the Area Moments of Wavelet and Spline Curves,
PAMI(23), No. 6, June 2001, pp. 633-642.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0106
BibRef
Earlier:
Exact Computation of Area Moments for Spline and Wavelet Curves,
ICPR00(Vol III: 127-130).
IEEE DOI Link
HTML Version. 0009
Computation of moments of the region bounded by a curve represented by a scaling function or wavelet basis. It is a scaler product -- filter on the coefficients. BibRef

Sheynin, S.A.[Stanislav A.], Tuzikov, A.V.[Alexander V.],
Explicit formulae for polyhedra moments,
PRL(22), No. 10, August 2001, pp. 1103-1109.
HTML Version. 0108
BibRef

Tuzikov, A.V., Sheynin, S.A., Vasiliev, P.V.,
Computation of volume and surface body moments,
PR(36), No. 11, November 2003, pp. 2521-2529.
WWW Version. 0309
BibRef

Sheynin, S.A., Tuzikov, A.V.,
Formulae for Polytope Volume and Surface Moments,
ICIP01(III: 720-723).
IEEE Abstract. IEEE Top Reference. 0108
BibRef

Sheynin, S.A.[Stanislav A.], Tuzikov, A.V.[Alexander V.],
Moment computation for objects with spline curve boundary,
PAMI(25), No. 10, October 2003, pp. 1317-1322.
IEEE Abstract. IEEE Top Reference. 0310
BibRef
Earlier:
Area and Moment Computation for Objects with a Closed Spline Boundary,
CAIP03(33-40).
WWW Version. 0311
Computation from the spline curve. BibRef

Belkasim, S.O., Kamel, M.S.[Mohamed S.],
Fast computation of 2-D image moments using biaxial transform,
PR(34), No. 9, September 2001, pp. 1867-1877.
WWW Version. 0108
BibRef

Belkasim, S.O., Hassan, E., Obeidi, T.,
Explicit invariance of Cartesian Zernike moments,
PRL(28), No. 15, 1 November 2007, pp. 1969-1980.
WWW Version. 0711
Image analysis; Invariance; Moment invariants; Pattern recognition; Feature extraction; Cartesian Zernike moments BibRef

Sivakumar, K.[Krishnamoorthy], Balagurunathan, Y.[Yoganand], Dougherty, E.R.[Edward R.],
Asymptotic joint normality of the granulometric moments,
PRL(22), No. 14, December 2001, pp. 1537-1543.
HTML Version. 0110
BibRef

Chung, K.L.[Kuo-Liang], Yan, W.M.[Wen-Ming], Liao, Z.H.[Zhi-Hor],
Fast Computation of Moments on Compressed Grey Images using Block Representation,
RealTimeImg(8), No. 2, April 2002, pp. 137-144.
WWW Version. 0208
BibRef

Gu, J., Shu, H.Z., Toumoulin, C., Luo, L.M.,
A novel algorithm for fast computation of Zernike moments,
PR(35), No. 12, December 2002, pp. 2905-2911.
WWW Version. 0209
BibRef

Yang, G.Y., Shu, H.Z., Toumoulin, C., Han, G.N., Luo, L.M.,
Efficient Legendre moment computation for grey level images,
PR(39), No. 1, January 2006, pp. 74-80.
WWW Version. 0512
BibRef

Martinez, J., Thomas, F.,
Efficient computation of local geometric moments,
IP(11), No. 9, September 2002, pp. 1102-1111.
IEEE DOI Link 0210
BibRef

Chong, C.W.[Chee-Way], Raveendran, P., Mukundan, R.,
A comparative analysis of algorithms for fast computation of Zernike moments,
PR(36), No. 3, March 2003, pp. 731-742.
WWW Version. 0301
BibRef

Chong, C.W.[Chee-Way], Raveendran, P., Mukundan, R.,
Translation invariants of Zernike moments,
PR(36), No. 8, August 2003, pp. 1765-1773.
WWW Version. 0304
BibRef

Suhling, M., Arigovindan, M., Hunziker, P., Unser, M.,
Multiresolution Moment Filters: Theory and Applications,
IP(13), No. 4, April 2004, pp. 484-495.
IEEE DOI Link 0404
BibRef
Earlier:
Multiresolution moment filters,
ICIP02(I: 393-396).
IEEE Abstract. IEEE Top Reference. 0210
BibRef

Liu, J.[Jin], Zhang, T.X.[Tian-Xu],
Fast algorithm for generation of moment invariants,
PR(37), No. 8, August 2004, pp. 1745-1756.
WWW Version. 0407
See also Matching and normalization of affine deformed image from regular moments. BibRef

Heikkilä, J.[Janne],
Pattern matching with affine moment descriptors,
PR(37), No. 9, September 2004, pp. 1825-1834.
WWW Version. 0407
BibRef

Suk, T.[Tomás], Flusser, J.[Jan],
Projective Moment Invariants,
PAMI(26), No. 10, October 2004, pp. 1364-1367.
IEEE Abstract. IEEE Top Reference. 0409
We show that projective moment invariants exist in a form of infinite series containing moments with positive as well as negative indices. See also Pattern Recognition by Affine Moment Invariants. BibRef

Suk, T.[Tomás], Flusser, J.[Jan],
Vertex-Based Features for Recognition of Projectively Deformed Polygons,
PR(29), No. 3, March 1996, pp. 361-367.
WWW Version. BibRef 9603
Earlier:
The projective invariants for polygons,
CAIP95(729-734).
Springer DOI Link 9509
Not really segments. See also Point-based projective invariants. BibRef

Flusser, J.[Jan], Suk, T.[Tomás],
Rotation Moment Invariants for Recognition of Symmetric Objects,
IP(15), No. 12, December 2006, pp. 3784-3790.
IEEE DOI Link 0611
BibRef
Earlier:
Construction of Complete and Independent Systems of Rotation Moment Invariants,
CAIP03(41-48).
WWW Version. 0311
BibRef

Suk, T., Flusser, J.,
Graph method for generating affine moment invariants,
ICPR04(II: 192-195).
IEEE DOI Link 0409
BibRef

Mukundan, R.,
Some Computational Aspects of Discrete Orthonormal Moments,
IP(13), No. 8, August 2004, pp. 1055-1059.
IEEE DOI Link 0409
BibRef

Pan, H.[Hong], Xia, L.Z.[Liang-Zheng],
Exact and fast algorithm for two-dimensional image wavelet moments via the projection transform,
PR(38), No. 3, March 2005, pp. 395-402.
WWW Version. 0412
BibRef

Wang, G.B.[Guo-Bao], Wang, S.G.[Shi-Gang],
Parallel recursive computation of the inverse Legendre moment transforms for signal and image reconstruction,
SPLetters(11), No. 12, December 2004, pp. 929-932.
IEEE Abstract. IEEE Top Reference. 0412
BibRef

Wang, G.B.[Guo-Bao], Wang, S.G.[Shi-Gang],
Recursive computation of Tchebichef moment and its inverse transform,
PR(39), No. 1, January 2006, pp. 47-56.
WWW Version. 0512
BibRef

Kotoulas, L., Andreadis, I.,
Efficient hardware architectures for computation of image moments,
RealTimeImg(10), No. 6, December 2004, pp. 371-378.
WWW Version. 0501
BibRef

Kotoulas, L., Andreadis, I.,
Real-Time Computation of Zernike Moments,
CirSysVideo(15), No. 6, June 2005, pp. 801-809.
IEEE Abstract. IEEE Top Reference. 0506
BibRef

Kotoulas, L., Andreadis, I.,
Fast Computation of Chebyshev Moments,
CirSysVideo(16), No. 7, July 2006, pp. 884-888.
IEEE DOI Link 0608
BibRef

Kotoulas, L., Andreadis, I.,
Accurate Calculation of Image Moments,
IP(16), No. 8, August 2007, pp. 2028-2037.
IEEE DOI Link 0709
BibRef

Kotoulas, L., Andreadis, I.,
Fast Moment Generating Architectures,
CirSysVideo(18), No. 4, April 2008, pp. 533-537.
IEEE DOI Link 0804
BibRef

Kotoulas, L., Andreadis, I.,
An Efficient Technique for the Computation of ART,
CirSysVideo(18), No. 5, May 2008, pp. 682-686.
IEEE DOI Link 0711
BibRef

Chung, K.L.[Kuo-Liang], Chen, P.C.[Ping-Chin],
An efficient algorithm for computing moments on a block representation of a grey-scale image,
PR(38), No. 12, December 2005, pp. 2578-2586.
WWW Version. 0510
BibRef

Yap, P.T.[Pew-Thian], Paramesran, R.,
An Efficient Method for the Computation of Legendre Moments,
PAMI(27), No. 12, December 2005, pp. 1996-2002.
IEEE DOI Link 0512
BibRef

Wee, C.Y.[Chong-Yaw], Paramesran, R.[Raveendran],
Efficient computation of radial moment functions using symmetrical property,
PR(39), No. 11, November 2006, pp. 2036-2046.
WWW Version. 0608
Radial moments; Zernike; Pseudo-Zernike; Computational complexity; Radial polynomials; Symmetrical property; Memory storage reduction; Inverse transform BibRef

Wee, C.Y.[Chong-Yaw], Paramesran, R.[Raveendran], Mukundan, R.,
Fast computation of geometric moments using a symmetric kernel,
PR(41), No. 7, July 2008, pp. 2369-2380.
WWW Version. 0804
Geometric moments with symmetric kernel (SGM); Fast computation; Symmetrical property; Numerical instability; Invariant properties; Zernike moments; Efficient representation; Computation BibRef

Wee, C.Y.[Chong-Yaw], Paramesran, R.[Raveendran],
On the computational aspects of Zernike moments,
IVC(25), No. 6, 1 June 2007, pp. 967-980.
WWW Version. 0704
Zernike moments; Approximation error; Geometrical error; Numerical error; Square-to-circular mapping; Exact Zernike moments BibRef

Wee, C.Y.[Chong-Yaw], Paramesran, R.[Raveendran], Takeda, F.[Fumiaki],
Sorting of rice grains using Zernike moments,
RealTimeIP(4), No. 4, November 2009, pp. xx-yy.
Springer DOI Link 0911
BibRef

Wee, C.Y.[Chong-Yaw], Paramesran, R.[Raveendran],
Derivation of blur-invariant features using orthogonal Legendre moments,
IET-CV(1), No. 2, June 2007, pp. 66-77.
WWW Version. 0905
BibRef

Yap, P.T.[Pew-Thian], Paramesran, R.[Raveendran],
Eigenmoments,
PR(40), No. 4, April 2007, pp. 1234-1244.
WWW Version. 0701
Moments; Orthogonalization; Image representation; Invariants; Noise robust features; Rayleigh quotient; Generalized eigenvalue problem BibRef

Aubreton, O., Voon, L.Y.[Lew Yan], Lamalle, B., Cathebras, G.,
A new method for implementing moment functions in a CMOS retina,
MVA(16), No. 6, 2006, pp. 384-392.
Springer DOI Link 0603
BibRef
And: A1, A2, A4, A3:
Hardware Computation of Moment Functions in a Silicon Retina using Binary Patterns,
ICIP06(3293-3296). 0610

IEEE DOI Link BibRef

Singh, C.[Chandan],
Improved quality of reconstructed images using floating point arithmetic for moment calculation,
PR(39), No. 11, November 2006, pp. 2047-2064.
WWW Version. 0608
Geometric moments; Zernike moments; Pattern recognition; Feature extraction; Image reconstruction BibRef

Hwang, S.K.[Sun-Kyoo], Kim, W.Y.[Whoi-Yul],
A novel approach to the fast computation of Zernike moments,
PR(39), No. 11, November 2006, pp. 2065-2076.
WWW Version. 0608
Zernike moments; Fast method; Symmetry/anti-symmetry; Discrete Zernike moments BibRef

Papakostas, G.A., Boutalis, Y.S., Papaodysseus, C.N., Fragoulis, D.K.,
Numerical error analysis in Zernike moments computation,
IVC(24), No. 9, September 2006, pp. 960-969.
WWW Version. 0608
Zernike moments; Recursive computation; Finite precision error; Numerical stability; Image vision; Feature extraction BibRef

Papakostas, G.A., Boutalis, Y.S., Karras, D.A., Mertzios, B.G.,
Fast numerically stable computation of orthogonal Fourier-Mellin moments,
IET-CV(1), No. 1, March 2007, pp. 11-16.
WWW Version. 0905
BibRef

Papakostas, G.A., Karakasis, E.G., Koulouriotis, D.E.,
Efficient and accurate computation of geometric moments on gray-scale images,
PR(41), No. 6, June 2008, pp. 1895-1904.
WWW Version. 0802
Geometric moments; Image block representation; Feature extraction BibRef

Papakostas, G.A., Karakasis, E.G., Koulouriotis, D.E.,
Novel moment invariants for improved classification performance in computer vision applications,
PR(43), No. 1, January 2010, pp. 58-68,.
Elsevier DOI Link
WWW Version. 0909
Moment invariants; Image block representation; Slice moments; Feature extraction; Computer vision; Pattern recognition BibRef

Chung, K.L.[Kuo-Liang], Liu, Y.W.[Yau-Wen], Yan, W.M.[Wen-Ming],
A hybrid gray image representation using spatial- and DCT-based approach with application to moment computation,
JVCIR(17), No. 6, December 2006, pp. 1209-1226.
WWW Version. 0711
DCT; Gray image representation; Linear interpolation; Moment computation; PSNR; Spatial data structures BibRef

Fu, B.[Bo], Zhou, J.Z.[Jian-Zhong], Li, Y.H.[Yu-Hong], Zhang, G.J.[Guo-Jun], Wang, C.[Cheng],
Image analysis by modified Legendre moments,
PR(40), No. 2, February 2007, pp. 691-704.
WWW Version. 0611
Modified Legendre moments; Legendre moments; Feature representation capability; Translation invariance BibRef

Martinez, J.[Judit], Porta, J.M.[Josep M.], Thomas, F.[Federico],
A Matrix-Based Approach to the Image Moment Problem,
JMIV(26), No. 1-2, November 2006, pp. 105-113.
Springer DOI Link 0701
BibRef

Zhu, H.Q.[Hong-Qing], Shu, H.Z.[Hua-Zhong], Xia, T.[Ting], Luo, L.M.[Li-Min], Coatrieux, J.L.[Jean Louis],
Translation and scale invariants of Tchebichef moments,
PR(40), No. 9, September 2007, pp. 2530-2542.
WWW Version. 0705
Discrete orthogonal moments; Tchebichef polynomials; Translation and scale invariants; Pattern classification; Image normalization BibRef

Rodtook, A.[Annupan], Makhanov, S.S.[Stanislav S.],
A filter bank method to construct rotationally invariant moments for pattern recognition,
PRL(28), No. 12, 1 September 2007, pp. 1492-1500.
WWW Version. 0707
BibRef
And: Corrigendum: PRL(29), No. 1, 1 January 2008, pp. 96.
WWW Version. 0711
Rotationally invariant moments; Wavelet filter bank; Feature selection; The Kullback-Leibler distance; Apriori mining algorithm; Fuzzy C-mean clustering BibRef

Hosny, K.M.[Khalid M.],
Efficient Computation Of Legendre Moments For Gray Level Images,
IJIG(7), No. 4, October 2007, pp. 735-747. 0710
BibRef

Hosny, K.M.[Khalid M.],
Exact Legendre moment computation for gray level images,
PR(40), No. 12, December 2007, pp. 3597-3605.
WWW Version. 0709
Legendre moments; Fast algorithm; Gray level images BibRef

Hosny, K.M.[Khalid M.],
Fast computation of accurate Zernike moments,
RealTimeIP(3), No. 1-2, March 2008, pp. xx-yy.
Springer DOI Link 0804
BibRef

Cohen, M.F., Szeliski, R.S.,
The Moment Camera,
Computer(39), No. 8, August 2006, pp. 40-45.
IEEE DOI Link 0608
BibRef

Xu, D.[Dong], Li, H.[Hua],
Geometric moment invariants,
PR(41), No. 1, January 2008, pp. 240-249.
WWW Version. 0710
BibRef
Earlier:
3-D Affine Moment Invariants Generated by Geometric Primitives,
ICPR06(II: 544-547).
WWW Version. 0609
BibRef
And:
3-D Surface Moment Invariants,
ICPR06(IV: 173-176).
WWW Version. 0609
Geometric primitive; Moment invariant; Similarity transformation; Symbolic computation BibRef

Liu, J.[Jin], Li, D.R.[De-Ren], Tao, W.B.[Wen-Bing], Yan, L.[Li],
An automatic method for generating affine moment invariants,
PRL(28), No. 16, December 2007, pp. 2295-2304.
WWW Version. 0711
Affine invariant; Pattern recognition; Affine transformation; Generating invariants BibRef

Xia, T.[Ting], Zhu, H.[Hongqing], Shu, H.Z.[Hua-Zhong], Haigron, P.[Pascal], Luo, L.M.[Li-Min],
Image description with generalized pseudo-Zernike moments,
JOSA-A(24), No. 1, January 2007, pp. 50-59.
WWW Version. 0801
BibRef

Lin, H., Si, J., Abousleman, G.P.,
Orthogonal Rotation-Invariant Moments for Digital Image Processing,
IP(17), No. 3, March 2008, pp. 272-282.
IEEE DOI Link 0802
BibRef

Al-Rawi, M.[Mohammed],
Fast Zernike moments,
RealTimeIP(3), No. 1-2, March 2008, pp. xx-yy.
Springer DOI Link 0804
BibRef

Hu, H.T.[Hai-Tao], Ping, Z.L.[Zi-Liang],
Computation of orthogonal Fourier-Mellin moments in two coordinate systems,
JOSA-A(26), No. 5, May 2009, pp. 1080-1084.
WWW Version. 0905
BibRef

Singh, C., Walia, E.,
Computation of Zernike moments in improved polar configuration,
IET-IPR(3), No. 4, August 2009, pp. 217-227.
WWW Version. 0909
BibRef

Watanabe, Y.[Yoshihiro], Komuro, T.[Takashi], Ishikawa, M.[Masatoshi],
A High-Speed Vision System for Moment-Based Analysis of Numerous Objects,
ICIP07(V: 177-180).
IEEE DOI Link 0709
BibRef

Wee, C.Y.[Chong-Yaw], Paramesran, R.[Raveendran], Takeda, F.[Fumiaki],
Fast Computation of Zernike Moments For Rice Sorting System,
ICIP07(VI: 165-168).
IEEE DOI Link 0709
BibRef

Raj, P.A.[P. Ananth], Venkataramana, A.,
Fast Computation of Inverse Krawtchouk Moment Transform using Clenshaw's Recurrence Formula,
ICIP07(IV: 37-40).
IEEE DOI Link 0709
BibRef

Aubreton, O.[Olivier], Chong, L.F.[Lew Fock], Voon, L.Y.[Lew Yan], Nongaillard, M.[Matthieu], Cathebras, G.[Guy], Lemaitre, C.[Cédric], Lamalle, B.[Bernard],
Hardware Implementation of Moment Functions in a CMOS Retina: Application to Pattern Recognition,
IbPRIA07(I: 306-313).
Springer DOI Link 0706
BibRef

Ong, L.Y.[Lee-Yeng], Chong, C.W.[Chee-Way], Besar, R.[Rosli],
Scale Invariants of Three-Dimensional Legendre Moments,
ICPR06(III: 141-144).
WWW Version. 0609
BibRef

Amayeh, G.[Gholamreza], Bebis, G.N.[George N.], Erol, A.[Ali], Nicolescu, M.[Mircea],
Peg-Free Hand Shape Verification Using High Order Zernike Moments,
Biometrics06(40).
IEEE DOI Link 0609
BibRef

Amayeh, G.[Gholamreza], Erol, A.[Ali], Bebis, G.N.[George N.], Nicolescu, M.[Mircea],
Accurate and Efficient Computation of High Order Zernike Moments,
ISVC05(462-469).
Springer DOI Link 0512
BibRef

Sladoje, N.[Nataša], Lindblad, J.[Joakim],
Estimation of Moments of Digitized Objects with Fuzzy Borders,
CIAP05(188-195).
Springer DOI Link 0509
BibRef

Bresson, X., Vandergheynst, P., Thiran, J.P.,
Geometric moments in scale-spaces,
ICPR02(II: 418-421).
IEEE DOI Link 0211
BibRef

Tuzikov, A.V.[Alexander V.], Sheynin, S.A.[Stanislav A.], Vasiliev, P.V.[Pavel V.],
Efficient Computation of Body Moments,
CAIP01(201 ff.).
HTML Version. 0210
BibRef

Prismall, S.P., Nixon, M.S., Carter, J.N.,
On Moving Object Reconstruction by Moments,
BMVC02(Reconstruction). 0208
BibRef

Canterakis, N.,
3D Zernike Moments and Zernike Affine Invariants for 3D Image Analysis and Recognition,
SCIA99(Pattern Recognition I). BibRef 9900

Martinez, J., Thomas, F., Staffetti, E.,
A Recursive Updating Rule for Efficient Computation of Linear Moments in Sliding-Window Applications,
ICPR96(II: 295-299).
IEEE DOI Link 9608
(Universidad Politecnica de Cataluna, E) BibRef

Shen, J., Shen, D.,
Orthogonal Legendre Moments and Their Calculation,
ICPR96(II: 241-245).
IEEE DOI Link 9608
(Institute of Geodynamics, F) BibRef

Zhou, F., Kornerup, P.,
Computing moments by prefix sums,
ICIP96(III: 619-622).
IEEE DOI Link 9610
BibRef

Yang, L., Albregtsen, F.,
Fast Computation of Invariant Geometric Moments: A New Method Giving Correct Results,
ICPR94(A:201-204).
IEEE DOI Link BibRef 9400

Li, B.C.[Bing-Cheng], Ma, S.D.[Song De],
Efficient computation of 3D moments,
ICPR94(A:22-26).
IEEE DOI Link 9410
BibRef

Li, B.C.[Bing-Cheng], Shen, J.[Jun],
Fast calculation of local moments and application to range image segmentation,
ICPR92(III:298-301).
IEEE DOI Link 9208
BibRef

Zhu, Q., Poh, L.,
A Transformation-Invariant Recursive Subdivision Method for Shape Analysis,
ICPR88(II: 833-835).
IEEE DOI Link
IEEE Top Reference. BibRef 8800

Chapter on Registration, Matching and Recognition Using Points, Lines, Regions, Areas, Surfaces continues in
Features for Contour Matching .