12.3.1.9.1 Moment Computation, Computation of Moments

Chapter Contents (Back)
Moments, Computation. 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.
Elsevier DOI Fast computation using Delta Method. Moments of contiguous images using a line rather than pixel. BibRef 8700

Teh, C.H.[Cho-Huak], Chin, R.T.[Roland T.],
On Image Analysis by the Methods of Moments,
PAMI(10), No. 4, July 1988, pp. 496-513.
IEEE DOI BibRef 8807
And: CVPR88(556-561).
IEEE DOI A discussion of various moment techniques for descriptions. BibRef

Teh, C.H.[Cho-Huak], Chin, R.T.[Roland T.],
On Digital Approximation of Moment Invariants,
CVGIP(33), No. 3, March 1986, pp. 318-326.
Elsevier DOI 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.
Elsevier DOI 0501
BibRef

Sluzek, A.[Andrzej],
Detecting local features in complex images: A combination of Hough transform and moment-based approximations,
ICARCV08(1323-1328).
IEEE DOI 1109
BibRef

Sluzek, A.[Andrzej], Paradowski, M.[Mariusz],
Detection of Near-Duplicate Patches in Random Images Using Keypoint-Based Features,
ACIVS12(301-312).
Springer DOI 1209
BibRef
Earlier: A2, A1:
Keypoint-Based Detection of Near-Duplicate Image Fragments Using Image Geometry and Topology,
ICCVG10(II: 175-182).
Springer DOI 1009
Retrieve the image with the exact copy of the fragment. 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.
Elsevier DOI 0711
BibRef
Earlier:
3D Object Localization Using Local Shape Features,
ICARCV06(1-6).
IEEE DOI 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.
DOI Link 0903
BibRef
Earlier:
A New Local-Feature Framework for Scale-Invariant Detection of Partially Occluded Objects,
PSIVT06(248-257).
Springer DOI 0612
BibRef

Sluzek, A.[Andrzej],
Large Vocabularies for Keypoint-Based Representation and Matching of Image Patches,
WebScale12(I: 229-238).
Springer DOI 1210

See also Approximation-Based Keypoints in Colour Images: A Tool for Building and Searching Visual Databases. BibRef

Budrikis, Z.L.[Zigmantas L.], Hatamian, M.[Mehdi],
Moment generator,
US_Patent4,745,567, May 17, 1988
WWW Link. 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.
Elsevier DOI 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.
Elsevier DOI BibRef 9003

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

Pan, Y.[Yi],
A Note on Efficient Parallel Algorithms for the Computation of Two-Dimensional Image Moments,
PR(24), No. 9, 1991, pp. 917.
Elsevier DOI 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 DOI BibRef

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

Khotanzad, A.[Alireza], Hong, Y.H.[Yaw Hua],
Rotation Invariant Image Recognition Using Features Selected via a Systematic Method,
PR(23), No. 10, 1990, pp. 1089-1101.
Elsevier DOI 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 0702
BibRef

Dai, M.[Mo], Baylou, P.[Pierre], Najim, M.[Mohamed],
An Efficient Algorithm for Computation of Shape Moments from Run-Length Codes or Chain Codes,
PR(25), No. 10, October 1992, pp. 1119-1128.
Elsevier DOI 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.
Elsevier DOI Compute higher order moments from those of lower order. BibRef 9100

Leu, J.G.[Jia-Guu],
Computing A Shape's Moments from Its Boundary,
PR(24), No. 10, 1991, pp. 949-957.
Elsevier DOI 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.[Mark H.],
A General Approach to Moment Calculation for Polygons and Line Segments,
PR(26), No. 7, July 1993, pp. 1019-1028.
Elsevier DOI Relation between mement of polygonal area and stick figure of lines in 2D plane. BibRef 9307

Philips, W.[Wilfried],
A New Fast Algorithm for Moment Computation,
PR(26), No. 11, November 1993, pp. 1619-1621.
Elsevier DOI Based on discrete analog of Green's theorem. Compare to:
See also Fast Algorithm for the Computation of Moment Invariants. BibRef 9311

Fu, C.W.[Chang-Wu], Yen, J.C.[Jui-Cheng], Chang, S.[Shyang],
Calculation Of Moment Invariants Via Hadamard Transform,
PR(26), No. 2, February 1993, pp. 287-294.
Elsevier DOI Project 2D shape to X and Y 1D. BibRef 9302

Li, B.C.[Bing-Cheng],
The Moment Calculation of Polyhedra,
PR(26), No. 8, August 1993, pp. 1229-1233.
Elsevier DOI 3D polyhedra moments. BibRef 9308

Li, B.C.[Bing-Cheng],
A New Computation of Geometric Moments,
PR(26), No. 1, January 1993, pp. 109-113.
Elsevier DOI BibRef 9301

Li, B.C.[Bing-Cheng], Shen, J.[Jun],
Fast Computation of Moment Invariants,
PR(24), No. 8, 1991, pp. 807-813.
Elsevier DOI Iterative method with no multiplication. BibRef 9100

Li, B.C.[Bing-Cheng], Shen, J.[Jun],
2-Dimensional Local Moment, Surface Fitting and Their Fast Computation,
PR(27), No. 6, June 1994, pp. 785-790.
Elsevier DOI Surface fitting into a moment computation. 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.
Elsevier DOI Patterns are not closed contours. 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.
Elsevier DOI 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 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 DOI 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 DOI 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 0403
BibRef

Keren, D., Subrahmonia, J., Cooper, D.B.,
Robust object recognition based on implicit algebraic curves and surfaces,
CVPR92(791-794).
IEEE DOI 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.
Elsevier DOI 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 9509
BibRef

Chung, K.L.[Kuo-Liang],
Computing Horizontal/Vertical Convex Shapes Moments on Reconfigurable Meshes,
PR(29), No. 10, October 1996, pp. 1713-1717.
Elsevier DOI 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.[Tak-Wai], Lun, D.P.K.[Daniel 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.
Elsevier DOI 9802
2-D moments decomposed into 1D moments. 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 DOI 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.
Elsevier DOI BibRef 9909

Kim, W.Y., Kim, Y.S.,
Robust Rotation Angle Estimator,
PAMI(21), No. 8, August 1999, pp. 768-773.
IEEE DOI 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

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.
Elsevier DOI 0102
BibRef
And: A4, A1, A2, A3: Faster method:
Two new algorithms for efficient computation of Legendre moments,
PR(35), No. 5, May 2002, pp. 1143-1152.
Elsevier DOI 0202
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.
Elsevier DOI 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.
DOI Link 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.
Elsevier DOI 0412
BibRef

Mukundan, R., Ramakrishnan, K.R.,
Moment Functions in Image Analysis: Threoy and Applications,
World Scientific1998, ISBN 978-981-02-3524-6.
HTML Version. Geometric Moments, Complex Moments, Legendre Moments, Zernike Moments, Moment Tensors 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.
Elsevier DOI 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 DOI 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.
Elsevier DOI 0304

See also Automatic Extraction of Control Points for the Registration of Optical Satellite and LiDAR Images. 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.
Elsevier DOI 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. 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.
Elsevier DOI 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 DOI 0106
BibRef
Earlier:
Exact Computation of Area Moments for Spline and Wavelet Curves,
ICPR00(Vol III: 127-130).
IEEE DOI 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.
Elsevier DOI 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.
Elsevier DOI 0309
BibRef

Sheynin, S.A., Tuzikov, A.V.,
Formulae for Polytope Volume and Surface Moments,
ICIP01(III: 720-723).
IEEE DOI 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. 0310
BibRef
Earlier:
Area and Moment Computation for Objects with a Closed Spline Boundary,
CAIP03(33-40).
Springer DOI 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.
Elsevier DOI 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.
Elsevier DOI 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.
Elsevier DOI 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.
DOI Link 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.
Elsevier DOI 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.
Elsevier DOI 0512
BibRef

Martinez, J., Thomas, F.,
Efficient computation of local geometric moments,
IP(11), No. 9, September 2002, pp. 1102-1111.
IEEE DOI 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.
Elsevier DOI 0301
BibRef

Mukundan, R.[Ramakrishnan],
A Comparative Analysis of Radial-tchebichef Moments and Zernike Moments,
BMVC09(xx-yy).
PDF File. 0909
BibRef

Chong, C.W.[Chee-Way], Raveendran, P., Mukundan, R.,
Translation invariants of Zernike moments,
PR(36), No. 8, August 2003, pp. 1765-1773.
Elsevier DOI 0304
Radial moments in polar form. 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 0404
BibRef
Earlier:
Multiresolution moment filters,
ICIP02(I: 393-396).
IEEE DOI 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.
Elsevier DOI 0407
decomposing trig function to obtain various moments.
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.
Elsevier DOI 0407
moment descriptors in terms of central moments. BibRef

Suk, T.[Tomás], Flusser, J.[Jan],
Projective Moment Invariants,
PAMI(26), No. 10, October 2004, pp. 1364-1367.
IEEE Abstract. 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.
Elsevier DOI BibRef 9603
Earlier:
The projective invariants for polygons,
CAIP95(729-734).
Springer DOI 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 0611
BibRef
Earlier:
Construction of Complete and Independent Systems of Rotation Moment Invariants,
CAIP03(41-48).
Springer DOI 0311
BibRef

Suk, T.[Tomas], Flusser, J.[Jan],
Affine moment invariants generated by graph method,
PR(44), No. 9, September 2011, pp. 2047-2056.
Elsevier DOI 1106
BibRef
Earlier:
Graph method for generating affine moment invariants,
ICPR04(II: 192-195).
IEEE DOI 0409
Image moments; Object recognition; Affine transformation; Affine moment invariants; Pseudoinvariants; Graph representation; Irreducibility; Independence BibRef

Mukundan, R.,
Some Computational Aspects of Discrete Orthonormal Moments,
IP(13), No. 8, August 2004, pp. 1055-1059.
IEEE DOI 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.
Elsevier DOI 0412
projection based for 2D wavelet moments. Compute in multiple 1D spaces. 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. 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.
Elsevier DOI 0512
Suitable for VLSI implementation. BibRef

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

Kotoulas, L., Andreadis, I.,
Real-Time Computation of Zernike Moments,
CirSysVideo(15), No. 6, June 2005, pp. 801-809.
IEEE Abstract. 0506
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Kotoulas, L., Andreadis, I.,
Fast Computation of Chebyshev Moments,
CirSysVideo(16), No. 7, July 2006, pp. 884-888.
IEEE DOI 0608
BibRef

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

Kotoulas, L., Andreadis, I.,
Fast Moment Generating Architectures,
CirSysVideo(18), No. 4, April 2008, pp. 533-537.
IEEE DOI 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 0711
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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.
Elsevier DOI 0510
Computation in Order of number of blocks. 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 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.
Elsevier DOI 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.
Elsevier DOI 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.
Elsevier DOI 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 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.
DOI Link 0905
BibRef

Yap, P.T.[Pew-Thian], Paramesran, R.[Raveendran],
Eigenmoments,
PR(40), No. 4, April 2007, pp. 1234-1244.
Elsevier DOI 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 0603
BibRef
And: A1, A2, A4, A3:
Hardware Computation of Moment Functions in a Silicon Retina using Binary Patterns,
ICIP06(3293-3296).
IEEE DOI 0610
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.
Elsevier DOI 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.
Elsevier DOI 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.
Elsevier DOI 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.
DOI Link 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.
Elsevier DOI 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 0909
Moment invariants; Image block representation; Slice moments; Feature extraction; Pattern recognition BibRef

Papakostas, G.A., Karakasis, E.G., Koulouriotis, D.E.,
Accurate and speedy computation of image Legendre moments for computer vision applications,
IVC(28), No. 3, March 2010, pp. 414-423.
Elsevier DOI 1001
Legendre moments; Image Block Representation; Feature extraction; Pattern recognition BibRef

Karakasis, E.G., Papakostas, G.A., Koulouriotis, D.E., Tourassis, V.D.,
Generalized dual Hahn moment invariants,
PR(46), No. 7, July 2013, pp. 1998-2014.
Elsevier DOI 1303
Discrete orthogonal polynomials; Orthogonal moments; Dual Hahn moment invariants; Geometric moments; Pattern recognition; Classification; Weighted 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.
Elsevier DOI 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.
Elsevier DOI 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 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.
Elsevier DOI 0705
Discrete orthogonal moments; Tchebichef polynomials; Translation and scale invariants; Pattern classification; Image normalization Comments:
See also comment on 'Translation and scale invariants of Tchebichef moments' by Hong-Qing Zhu [Pattern Recognition 40 (2007) 2530-2542], A. BibRef

Chen, B.J.[Bei-Jing], Shu, H.Z.[Hua-Zhong], Zhang, H.[Hui], Coatrieux, G., Luo, L.M.[Li-Min], Coatrieux, J.L.,
Combined Invariants to Similarity Transformation and to Blur Using Orthogonal Zernike Moments,
IP(20), No. 2, February 2011, pp. 345-360.
IEEE DOI 1102
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.
Elsevier DOI 0707
BibRef
And: Corrigendum: PRL(29), No. 1, 1 January 2008, pp. 96.
Elsevier DOI 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.
Elsevier DOI 0709
Legendre moments; Fast algorithm; Gray level images BibRef

Hosny, K.M.[Khalid M.],
Fast and low-complexity method for exact computation of 3D Legendre moments,
PRL(32), No. 9, 1 July 2011, pp. 1305-1314.
Elsevier DOI 1101
3D Legendre moments; Symmetry property; Exact computation; Fast algorithm; Translation invariance; Scale invariance BibRef

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

Hosny, K.M.[Khalid M.],
Fast and accurate method for radial moment's computation,
PRL(31), No. 2, 15 January 2010, pp. 143-150.
Elsevier DOI 1001
Radial moments; Geometric moments; Exact computation; Circularly moments; Symmetry property
See also comment on Fast and accurate method for radial moment's computation, A. BibRef

Hosny, K.M.[Khalid M.],
Refined translation and scale Legendre moment invariants,
PRL(31), No. 7, 1 May 2010, pp. 533-538.
Elsevier DOI 1004
Translation invariants; Scale invariants; Legendre moments; Fast computation BibRef

Hosny, K.M.[Khalid M.],
Image representation using accurate orthogonal Gegenbauer moments,
PRL(32), No. 6, 15 April 2011, pp. 795-804.
Elsevier DOI 1103
Gegenbauer moments; Legendre moments; Chebyshev moments; Symmetry property; Fast algorithm; Gray-level images BibRef

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

Xu, D.[Dong], Li, H.[Hua],
Geometric moment invariants,
PR(41), No. 1, January 2008, pp. 240-249.
Elsevier DOI 0710
BibRef
Earlier:
3-D Affine Moment Invariants Generated by Geometric Primitives,
ICPR06(II: 544-547).
IEEE DOI 0609
BibRef
And:
3-D Surface Moment Invariants,
ICPR06(IV: 173-176).
IEEE DOI 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.
Elsevier DOI 0711
Affine invariant; Pattern recognition; Affine transformation; Generating invariants BibRef

Xia, T.[Ting], Zhu, H.Q.[Hong-Qing], 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 Link. 0801
BibRef

Zhang, H., Shu, H.Z., Haigron, P., Li, B.S., Luo, L.M.,
Construction of a complete set of orthogonal Fourier-Mellin moment invariants for pattern recognition applications,
IVC(28), No. 1, Januray 2010, pp. 38-44.
Elsevier DOI 1001
Orthogonal Fourier-Mellin moments; Completeness; Similarity invariants; Moment invariants; Pattern recognition 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 0802
BibRef

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

Al-Rawi, M.S.[Mohammed Sadiq],
Fast computation of pseudo Zernike moments,
RealTimeIP(5), No. 1, March 2010, pp. xx-yy.
Springer DOI 1003
BibRef

Al-Rawi, M.S.[Mohammed S.],
3D (pseudo) Zernike moments: Fast computation via symmetry properties of spherical harmonics and recursive radial polynomials,
ICIP12(2353-2356).
IEEE DOI 1302
BibRef

Al-Rawi, M.S.[Mohammed Sadeq],
Numerical Stability Quality-Factor for Orthogonal Polynomials: Zernike Radial Polynomials Case Study,
ICIAR13(676-686).
Springer DOI 1307
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 Link. 0905
BibRef

Singh, C.[Chandan], Walia, E.[Ekta],
Computation of Zernike moments in improved polar configuration,
IET-IPR(3), No. 4, August 2009, pp. 217-227.
DOI Link 0909
BibRef

Singh, C.[Chandan], Walia, E.[Ekta],
Fast and numerically stable methods for the computation of Zernike moments,
PR(43), No. 7, July 2010, pp. 2497-2506.
Elsevier DOI 1003
Zernike moments; Fast computation; Numerical stability; Accuracy
See also comment on: Fast and numerically stable methods for the computation of Zernike moments, A. BibRef

Singh, C.[Chandan], Walia, E.[Ekta],
Algorithms for fast computation of Zernike moments and their numerical stability,
IVC(29), No. 4, March 2011, pp. 251-259.
Elsevier DOI 1102
Zernike moments; Geometric moments; Quasi-symmetry; Fast computation; Numerical stability BibRef

Chen, Z., Sun, S.K.,
A Zernike Moment Phase-Based Descriptor for Local Image Representation and Matching,
IP(19), No. 1, January 2010, pp. 205-219.
IEEE DOI 1001
BibRef

Walia, E.[Ekta], Singh, C.[Chandan], Goyal, A.[Anjali],
On the fast computation of orthogonal Fourier-Mellin moments with improved numerical stability,
RealTimeIP(7), No. 4, December 2012, pp. 247-256.
WWW Link. 1212
BibRef

Sakaue, K.I.[Ken-Ichi], Iiguni, Y.[Youji],
Moment Invariants of the Weighted Image,
IEICE(E93-D), No. 3, March 2010, pp. 666-670.
WWW Link. 1003
BibRef

Ennahnahi, N., Oumsis, M., Bouhouch, A., Meknassi, M.,
Fast shape description based on a set of moments defined on the unit disc and inspired by three-dimensional spherical harmonics,
IET-IPR(4), No. 2, April 2010, pp. 120-131.
DOI Link 1003
BibRef
Earlier: A1, A3, A2, A4:
A novel moments generation inspired by 3D spherical harmonics for robust 2D shape description,
ICIP09(421-424).
IEEE DOI 0911
BibRef

Flusser, J.[Jan], Zitova, B.[Barbara], Suk, T.[Tomas],
Moments and Moment Invariants in Pattern Recognition,
WileyDecember 2009. ISBN: 978-0-470-69987-4
HTML Version. 0104
Survey, Moments. Buy this book: Moments and Moment Invariants in Pattern Recognition Numerical computation methods. BibRef

Suk, T.[Tomas], Flusser, J.[Jan],
Refined Morphological Methods of Moment Computation,
ICPR10(966-970).
IEEE DOI 1008
BibRef

Zhang, G.J.[Guo-Jun], Luo, Z.[Zhu], Fu, B.[Bo], Li, B.[Bo], Liao, J.P.[Jia-Ping], Fan, X.X.[Xiu-Xiang], Xi, Z.[Zheng],
A symmetry and bi-recursive algorithm of accurately computing Krawtchouk moments,
PRL(31), No. 7, 1 May 2010, pp. 548-554.
Elsevier DOI 1004
Krawtchouk moments; Propagation error; n-Ascending recurrence relation; n-Descending recurrence relation; Diagonal symmetry BibRef

Wang, Y.B.[Yuan-Bin], Bin, Z.[Zhang], Yao, T.S.[Tian-Shun],
Projective invariants of co-moments of 2D images,
PR(43), No. 10, October 2010, pp. 3233-3242.
Elsevier DOI 1007
Moment; Invariant; Co-moment; Projective transformation; Reference points BibRef

Soldea, O.[Octavian], Unel, M.[Mustafa], Ercil, A.[Aytul],
Recursive computation of moments of 2D objects represented by elliptic Fourier descriptors,
PRL(31), No. 11, 1 August 2010, pp. 1428-1436.
Elsevier DOI 1008
Elliptic Fourier descriptors; Moments; Superquadrics; B-spline functions; Bernstein-Bezier representations BibRef

Zhu, H.Q., Liu, M., Shu, H.Z., Zhang, H., Luo, L.,
General form for obtaining discrete orthogonal moments,
IET-IPR(4), No. 5, October 2010, pp. 335-352.
DOI Link 1011
BibRef

Zhu, H.Q.[Hong-Qing], Yang, Y.[Yan], Zhu, X.L.[Xiao-Li], Gui, Z.G.[Zhi-Guo], Shu, H.Z.[Hua-Zhong],
General Form for Obtaining Unit Disc-Based Generalized Orthogonal Moments,
IP(23), No. 12, December 2014, pp. 5455-5469.
IEEE DOI 1412
image recognition BibRef

Shu, H.Z., Zhang, H., Chen, B.J., Haigron, P., Luo, L.M.,
Fast Computation of Tchebichef Moments for Binary and Grayscale Images,
IP(19), No. 12, December 2010, pp. 3171-3180.
IEEE DOI 1011
BibRef

Qin, H.F.[Hua-Feng], Qin, L.[Lan], Li, Y.T.[Yan-Tao],
A comment on: 'Fast and numerically stable methods for the computation of Zernike moments',
PR(44), No. 4, April 2011, pp. 996-997.
Elsevier DOI 1101
Zernike moments; Fast computation; q-Recursive method
See also Fast and numerically stable methods for the computation of Zernike moments. BibRef

Pozo2, J.M.[José María], Villa-Uriol, M.C.[Maria-Cruz], Frangi, A.F.[Alejandro F.],
Efficient 3D Geometric and Zernike Moments Computation from Unstructured Surface Meshes,
PAMI(33), No. 3, March 2011, pp. 471-484.
IEEE DOI 1102

See also Morphodynamic Analysis of Cerebral Aneurysm Pulsation From Time-Resolved Rotational Angiography. Computing 3D moments from mesh data. Computed from the surface, not the full volume. BibRef

Hosny, K.M.[Khalid Mohamed], Shouman, M.A.[Mohamed A.], Salam, H.M.A.[Hayam M. Abdel],
Fast computation of orthogonal Fourier-Mellin moments in polar coordinates,
RealTimeIP(6), No. 2, June 2011, pp. 73-80.
WWW Link. 1101
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Spiliotis, I.M.[Iraklis M.], Boutalis, Y.F.S.[Yi-Fannis S.],
Parameterized real-time moment computation on gray images using block techniques,
RealTimeIP(6), No. 2, June 2011, pp. 81-91.
WWW Link. 1101
BibRef

Chang, K.H., Paramesran, R., Asli, B.H.S., Lim, C.L.,
Efficient Hardware Accelerators for the Computation of Tchebichef Moments,
CirSysVideo(22), No. 3, March 2012, pp. 414-425.
IEEE DOI 1203
BibRef

Singh, C.[Chandan], Upneja, R.[Rahul],
Error analysis and accurate calculation of rotational moments,
PRL(33), No. 12, 1 September 2012, pp. 1614-1622.
Elsevier DOI 1208
Rotational moments; Zernike moments; Pseudo Zernike moments; Orthogonal Fourier-Mellin moments; Rotation invariance; Scale invariance BibRef

Singh, C.[Chandan], Upneja, R.[Rahul],
Accurate Computation of Orthogonal Fourier-Mellin Moments,
JMIV(44), No. 3, November 2012, pp. 411-431.
WWW Link. 1209
BibRef

Singh, C.[Chandan], Upneja, R.[Rahul],
Accuracy and numerical stability of high-order polar harmonic transforms,
IET-IPR(6), No. 6, 2012, pp. 617-626.
DOI Link 1210
BibRef

Singh, C.[Chandan], Upneja, R.[Rahul],
Error Analysis in the Computation of Orthogonal Rotation Invariant Moments,
JMIV(49), No. 1, May 2014, pp. 251-271.
WWW Link. 1404
BibRef

Hickman, M.S.[Mark S.],
Geometric Moments and Their Invariants,
JMIV(44), No. 3, November 2012, pp. 223-235.
WWW Link. 1209
BibRef

Koehl, P.[Patrice],
Fast Recursive Computation of 3D Geometric Moments from Surface Meshes,
PAMI(34), No. 11, November 2012, pp. 2158-2163.
IEEE DOI 1209
Compute 3D moments from unstructured triangulation of the surface. Analytical integration of the moments on tetrahedra of triangles and central point. BibRef

Walia, E.[Ekta], Singh, C.[Chandan], Upneja, R.[Rahul],
A comment on 'Fast and accurate method for radial moment's computation',
PRL(33), No. 16, 1 December 2012, pp. 2224-2225.
Elsevier DOI 1210
Radial moments; Geometric moments; Radial geometric moments
See also Fast and accurate method for radial moment's computation. BibRef

Liu, C., Huang, X.H., Wang, M.,
Fast computation of Zernike moments in polar coordinates,
IET-IPR(6), No. 7, 2012, pp. 996-1004.
DOI Link 1211
BibRef

Karakasis, E.G., Papakostas, G.A., Koulouriotis, D.E., Tourassis, V.D.,
A Unified Methodology for Computing Accurate Quaternion Color Moments and Moment Invariants,
IP(23), No. 2, February 2014, pp. 596-611.
IEEE DOI 1402
BibRef
Earlier: A2, A3, A1, Only:
Computing Orthogonal Moments in Biomedical Imaging,
WSSIP09(1-4).
IEEE DOI 0906
image classification BibRef

Papakostas, G.A., Mertzios, B.G., Karras, D.A.,
Performance of the Orthogonal Moments in Reconstructing Biomedical Images,
WSSIP09(1-4).
IEEE DOI 0906
BibRef

Chen, B.J.[Bei-Jing], Shu, H.Z.[Hua-Zhong], Coatrieux, G.[Gouenou], Chen, G.[Gang], Sun, X.M.[Xing-Ming], Coatrieux, J.L.[Jean Louis],
Color Image Analysis by Quaternion-Type Moments,
JMIV(51), No. 1, January 2015, pp. 124-144.
Springer DOI 1503
BibRef

Chen, B.J.[Bei-Jing], Shu, H.Z.[Hua-Zhong], Zhang, H.[Hui], Chen, G.[Gang], Luo, L.M.[Li-Min],
Color Image Analysis by Quaternion Zernike Moments,
ICPR10(625-628).
IEEE DOI 1008
applied directly to color images. BibRef

Chen, W.[Wei], Cai, Z.C.[Zhan-Chuan],
Orthogonal Polar V Transforms and application to shape retrieval,
JVCIR(34), No. 1, 2016, pp. 146-152.
Elsevier DOI 1601
V-system. Rotation invariant features. BibRef

Deng, A.W.[An-Wen], Wei, C.H.[Chia-Hung], Gwo, C.Y.[Chih-Ying],
Stable, fast computation of high-order Zernike moments using a recursive method,
PR(56), No. 1, 2016, pp. 16-25.
Elsevier DOI 1604
Zernike moments BibRef

Guimarães, J.P.F.[João P. F.], Fontes, A.I.R.[Aluisio I. R.], Rego, J.B.A.[Joilson B. A.], de M. Martins, A.[Allan], Príncipe, J.C.[José C.],
Complex Correntropy: Probabilistic Interpretation and Application to Complex-Valued Data,
SPLetters(24), No. 1, January 2017, pp. 42-45.
IEEE DOI 1702
entropy BibRef

Pee, C.Y.[Chih-Yang], Ong, S.H., Raveendran, P.,
Numerically efficient algorithms for anisotropic scale and translation Tchebichef moment invariants,
PRL(92), No. 1, 2017, pp. 68-74.
Elsevier DOI 1705
Moment invariant BibRef

Pee, C.Y.[Chih-Yang], Ong, S.H., Raveendran, P., Wong, L.K.,
Efficient anisotropic scaling and translation invariants of Tchebichef moments using image normalization,
PRL(169), 2023, pp. 8-16.
Elsevier DOI 2305
Anisotropic scaling and translation invariant, Tchebichef moment, Moment invariant, Image normalization, Pattern classification BibRef

Elkhalil, K., Kammoun, A., Al-Naffouri, T.Y., Alouini, M.S.,
Numerically Stable Evaluation of Moments of Random Gram Matrices With Applications,
SPLetters(24), No. 9, September 2017, pp. 1353-1357.
IEEE DOI 1708
Correlation, Covariance matrices, Eigenvalues and eigenfunctions, Numerical stability, Probability density function, Signal processing, Wireless communication, Gram matrices, Laguerre polynomials, one-sided correlation, positive, moments BibRef

Wang, X.[Xuan], Shi, G.H.[Guang-Hui], Guo, F.X.[Fang-Xia],
A comment on 'Translation and scale invariants of Tchebichef moments' by Hong-Qing Zhu [Pattern Recognition 40 (2007) 2530-2542],
PR(77), 2018, pp. 458-463.
Elsevier DOI 1802
Tchebichef moments, Scaling invariants, Discrete orthogonal moments, Charlier moments
See also Translation and scale invariants of Tchebichef moments. BibRef

Yang, B.[Bo], Flusser, J.[Jan], Kautsky, J.[Jaroslav],
Rotation of 2D orthogonal polynomials,
PRL(102), 2018, pp. 44-49.
Elsevier DOI 1802
Rotation invariants, Orthogonal polynomials, Recurrent relation, Hermite-like polynomials, Hermite moments BibRef

Benrais, L.[Lamine], Baha, N.[Nadia],
Towards an accurate and fast computation of discrete Tchebychev moments for binary and grey-level images,
IET-IPR(12), No. 4, April 2018, pp. 605-611.
DOI Link 1804
BibRef

Abdulhussain, S.H.[Sadiq H.], Ramli, A.R.[Abd Rahman], Al-Haddad, S.A.R.[Syed Abdul Rahman], Mahmmod, B.M.[Basheera M.], Jassim, W.A.[Wissam A.],
Fast Recursive Computation of Krawtchouk Polynomials,
JMIV(60), No. 3, March 2018, pp. 285-303.
Springer DOI 1804
BibRef

Camacho-Bello, C.[César], Rivera-Lopez, J.S.[José S.],
Some computational aspects of Tchebichef moments for higher orders,
PRL(112), 2018, pp. 332-339.
Elsevier DOI 1809
Discrete orthogonal polynomials, Tchebichef polynomials, Tchebichef moments, Recurrence algorithm, Numerical propagations errors BibRef

Bibi, A., Alfadly, M., Ghanem, B.,
Analytic Expressions for Probabilistic Moments of PL-DNN with Gaussian Input,
CVPR18(9099-9107)
IEEE DOI 1812
Perturbation methods, Visualization, Training, Probability density function, Probabilistic logic, Task analysis, Robustness BibRef

Bera, A.[Aneta], Klesk, P.[Przemyslaw], Sychel, D.[Dariusz],
Constant-Time Calculation of Zernike Moments for Detection with Rotational Invariance,
PAMI(41), No. 3, March 2019, pp. 537-551.
IEEE DOI 1902
Feature extraction, Detectors, Task analysis, Indexes, Harmonic analysis, Image segmentation, constant-time feature extraction BibRef

Nwali, M.[Marcel], Liao, S.[Simon],
A new fast algorithm to compute continuous moments defined in a rectangular region,
PR(89), 2019, pp. 151-160.
Elsevier DOI 1902
Real-time moment computing, Legendre moments, Gegenbauer moments, Jacobi moments BibRef

Jahid, T.[Tarik], Karmouni, H.[Hicham], Sayyouri, M.[Mhamed], Hmimid, A.[Abdeslam], Qjidaa, H.[Hassan],
Fast Algorithm of 3D Discrete Image Orthogonal Moments Computation Based on 3D Cuboid,
JMIV(61), No. 4, May 2019, pp. 534-554.
Springer DOI 1904
BibRef

Benouini, R.[Rachid], Batioua, I.[Imad], Zenkouar, K.[Khalid], Zahi, A.[Azeddine], El Fadili, H.[Hakim], Qjidaa, H.[Hassan],
Fast and accurate computation of Racah moment invariants for image classification,
PR(91), 2019, pp. 100-110.
Elsevier DOI 1904
Racah moment invariants, Racah polynomials, Fast algorithm, Accurate computation, Direct method, Recursive method, Pattern recognition BibRef

Li, E.[Erbo], Mo, H.L.[Han-Lin], Xu, D.[Dong], Li, H.[Hua],
Image Projective Invariants,
PAMI(41), No. 5, May 2019, pp. 1144-1157.
IEEE DOI 1904
Feature extraction, Strain, Jacobian matrices, Image retrieval, 3G mobile communication, planar object recognition BibRef

Abdulhussain, S.H.[Sadiq H.], Ramli, A.R.[Abd Rahman], Mahmmod, B.M.[Basheera M.], Saripan, M.I.[M. Iqbal], Al-Haddad, S.A.R., Jassim, W.A.[Wissam A.],
A New Hybrid form of Krawtchouk and Tchebichef Polynomials: Design and Application,
JMIV(61), No. 4, May 2019, pp. 555-570.
Springer DOI 1904
BibRef

Benouini, R.[Rachid], Batioua, I.[Imad], Zenkouar, K.[Khalid], Mrabti, F.[Fatiha], El Fadili, H.[Hakim],
New Set of Generalized Legendre Moment Invariants for Pattern Recognition,
PRL(123), 2019, pp. 39-46.
Elsevier DOI 1906
Moment invariants, Fractional-order legendre polynomials, Image classification, Rotation scale translation invariants, Adaptive feature extraction BibRef

Hosny, K.M.[Khalid M.], Salah, A.[Ahmad], Saleh, H.I.[Hassan I.], Sayed, M.[Mahmoud],
Fast computation of 2D and 3D Legendre moments using multi-core CPUs and GPU parallel architectures,
RealTimeIP(16), No. 6, December 2019, pp. 2027-2041.
Springer DOI 1912
BibRef

Lin, Z.J.[Zhi-Jie], Zhao, Z.[Zhou], Zhang, Z.[Zhu], Zhang, Z.J.[Zi-Jian], Cai, D.[Deng],
Moment Retrieval via Cross-Modal Interaction Networks With Query Reconstruction,
IP(29), 2020, pp. 3750-3762.
IEEE DOI 2002
Moment retrieval, syntactic GCN, multi-head self-attention, multi-stage cross-modal interaction, query reconstruction BibRef

Tang, H.Y.[Hao-Yu], Zhu, J.[Jihua], Liu, M.[Meng], Gao, Z.[Zan], Cheng, Z.Y.[Zhi-Yong],
Frame-Wise Cross-Modal Matching for Video Moment Retrieval,
MultMed(24), 2022, pp. 1338-1349.
IEEE DOI 2204
Predictive models, Location awareness, Feature extraction, Task analysis, Proposals, Semantics, Streaming media, video moment retrieval BibRef

Zeng, Y.W.[Ya-Wen], Cao, D.[Da], Wei, X.C.[Xiao-Chi], Liu, M.[Meng], Zhao, Z.[Zhou], Qin, Z.[Zheng],
Multi-Modal Relational Graph for Cross-Modal Video Moment Retrieval,
CVPR21(2215-2224)
IEEE DOI 2111
Visualization, Semantics, Pattern recognition, Object recognition, Task analysis BibRef

Hjouji, A.[Amal], El-Mekkaouib, J.[Jaouad], Jourhmane, M.[Mostafa], Bouikhalene, B.[Belaid],
New Set of Non-separable Orthogonal Invariant Moments for Image Recognition,
JMIV(62), No. 4, May 2020, pp. 606-624.
Springer DOI 2005
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Kostková, J.[Jitka], Suk, T.[Tomáš], Flusser, J.[Jan],
Affine Invariants of Vector Fields,
PAMI(43), No. 4, April 2021, pp. 1140-1155.
IEEE DOI 2103
BibRef
Earlier:
Affine Moment Invariants of Vector Fields,
ICIP18(1338-1342)
IEEE DOI 1809
Pattern matching, Mathematical model, Strain, Task analysis, Color, Wind speed, Vector field, total affine transformation, vector field moments. Jacobian matrices, Indexes, Strain, Color, Vector field BibRef

Flusser, J.[Jan], Suk, T.[Tomáš], Yang, B.[Bo],
Orthogonal Affine Invariants from Gaussian-Hermite Moments,
CAIP19(II:413-424).
Springer DOI 1909
BibRef

Vargas-Vargas, H.[Horlando], Camacho-Bello, C.[César], Rivera-López, J.S.[José S.], Noriega-Escamilla, A.[Alicia],
Some aspects of fractional-order circular moments for image analysis,
PRL(149), 2021, pp. 99-108.
Elsevier DOI 2108
Radial Moments, Fractional-order moments, fractional-order Zernike moments, Golden-section search BibRef

Bujack, R.[Roxana], Zhang, X.H.[Xin-Hua], Suk, T.[Tomás], Rogers, D.[David],
Systematic generation of moment invariant bases for 2D and 3D tensor fields,
PR(123), 2022, pp. 108313.
Elsevier DOI 2112
Pattern detection, Rotation invariant, Moment invariants, Generator approach, Basis, Flexible, Vector, Tensor BibRef

Wang, C.P.[Chun-Peng], Ma, B.[Bin], Xia, Z.Q.[Zhi-Qiu], Li, J.[Jian], Li, Q.[Qi], Shi, Y.Q.[Yun-Qing],
Stereoscopic Image Description With Trinion Fractional-Order Continuous Orthogonal Moments,
CirSysVideo(32), No. 4, April 2022, pp. 1998-2012.
IEEE DOI 2204
Stereo image processing, Image reconstruction, Harmonic analysis, Transforms, Watermarking, Quaternions, Numerical stability, Trinion, stereoscopic image zero watermarking BibRef

Daoui, A.[Achraf], Karmouni, H.[Hicham], Yamni, M.[Mohamed], Sayyouri, M.[Mhamed], Qjidaa, H.[Hassan],
On computational aspects of high-order dual Hahn moments,
PR(127), 2022, pp. 108596.
Elsevier DOI 2205
High-order dual Hahn polynomials, Orthogonal moments, Numerical stability, Signal and image reconstruction, High-order moments BibRef

Bedratyuk, L.[Leonid], Flusser, J.[Jan], Suk, T.[Tomáš], Kostková, J.[Jitka], Kautsky, J.[Jaroslav],
Non-separable rotation moment invariants,
PR(127), 2022, pp. 108607.
Elsevier DOI 2205
Image recognition, Rotation invariants, Non-separable moments, Appell polynomials, Bi-orthogonality, Recurrent relation BibRef

Qi, S.[Shuren], Zhang, Y.S.[Yu-Shu], Wang, C.[Chao], Zhou, J.T.[Jian-Tao], Cao, X.C.[Xiao-Chun],
A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation,
Surveys(55), No. 1, January 2023, pp. xx-yy.
DOI Link 2212
Survey, Moments. image representation, fast computation, orthogonal moments, Pattern recognition, geometric invariance BibRef

He, B.[Bing], Liu, J.[Jun], Lin, G.[Guancheng], Peng, C.[Cheng], Xi, W.Q.[Wen-Qiang],
Quaternion fractional-order weighted generalized Laguerre-Fourier moments and moment invariants for color image analysis,
SP:IC(114), 2023, pp. 116941.
Elsevier DOI 2305
Orthogonal moments, Fractional-order weighted generalized Laguerre polynomials, Geometric invariance BibRef

Yang, J.W.[Jian-Wei], Zeng, Z.Z.[Ze-Zhi], Kwong, T.[Timothy], Tang, Y.Y.[Yuan Yan], Wang, Y.[Yuepeng],
Local Orthogonal Moments for Local Features,
IP(32), 2023, pp. 3266-3280.
IEEE DOI 2306
Feature extraction, Kernel, Image reconstruction, Task analysis, Sensitivity, Deep learning, Training, orthogonal moment BibRef


Li, D.[Ding], Wu, R.[Rui], Tang, Y.Q.[Yong-Qiang], Zhang, Z.Z.[Zhi-Zhong], Zhang, W.S.[Wen-Sheng],
Multi-scale 2D Representation Learning for weakly-supervised moment retrieval,
ICPR21(8616-8623)
IEEE DOI 2105
Training, Annotations, Benchmark testing, Convolutional neural networks BibRef

Tahiri, M.A.[Mohamed Amine], Karmouni, H.[Hicham], Sayyouri, M.[Mhamed], Qjidaa, H.[Hassan],
Stable Computation of Hahn Polynomials for Higher Polynomial Order,
ISCV20(1-7)
IEEE DOI 2011
polynomials, stable computation, higher polynomial order, standard repetition algorithms, high order Hahn moments, image reconstruction BibRef

Angulo, R.A.R.[Rafael Augusto Rocha], Carpio, J.M.[Juan Martín], Rojas-Domínguez, A.[Alfonso], Ornelas-Rodríguez, M.[Manuel], Puga, H.[Héctor],
A Novel Set of Moment Invariants for Pattern Recognition Applications Based on Jacobi Polynomials,
MCPR20(139-148).
Springer DOI 2007
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Joseph-Rivlin, M., Zvirin, A., Kimmel, R.,
Momenet: Flavor the Moments in Learning to Classify Shapes,
GMDL19(4085-4094)
IEEE DOI 2004
computational complexity, feature extraction, image classification, learning (artificial intelligence), Deep Learning BibRef

Amakdouf, H., Zouhri, A., El Mallahi, M., Tahiri, A., Qjidaa, H.,
Translation Scaling and rotation invariants of 3D Krawtchouk moments,
ISCV18(1-6)
IEEE DOI 1807
feature extraction, image matching, object recognition, polynomials, solid modelling, 3D Krawtchouk moments, Translation scaling and rotation invariants BibRef

Lomov, N., Sidyakin, S.,
Morphological Moments of Binary Images,
PTVSBB17(19-25).
DOI Link 1805
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Bastos, I.L.O.[Igor L. O.], Soares, L.R.[Larissa Rocha], Schwartz, W.R.[William Robson],
Pyramidal Zernike Over Time: A Spatiotemporal Feature Descriptor Based on Zernike Moments,
CIARP17(77-85).
Springer DOI 1802
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Karmouni, H.[Hicham], Jahid, T.[Tarik], Lakhili, Z.[Zouhir], Hmimid, A.[Abdeslam], Sayyouri, M.[Mhamed], f Qjidaa, H.[Hassan], Rezzouk, A.[Abdellah],
Image reconstruction by Krawtchouk moments via digital filter,
ISCV17(1-7)
IEEE DOI 1710
binomial distribution, digital filters, image representation, matrix algebra, polynomials, Krawtchouk moments, Krawtchouk polynomials, binomial functions, BibRef

Zhao, Y.J.[Yan-Jun], Belkasim, S.[Saeid],
Improving stability and invariance of Cartesian Zernike moments,
Southwest12(61-64).
IEEE DOI 1205
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Doretto, G.[Gianfranco], Yao, Y.[Yi],
Region moments: Fast invariant descriptors for detecting small image structures,
CVPR10(3019-3026).
IEEE DOI 1006
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Langbein, M.[Max], Hagen, H.[Hans],
A Generalization of Moment Invariants on 2D Vector Fields to Tensor Fields of Arbitrary Order and Dimension,
ISVC09(II: 1151-1160).
Springer DOI 0911
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Yang, Q.Y.[Qing-Yue], Gao, F.[Fei], Nie, Q.[Qing],
A Modified L-Iterative Algorithm for Fast Computation of Pseudo-Zernike Moments,
CISP09(1-5).
IEEE DOI 0910
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Suthaharan, S.[Shan],
Enhanced Accuracy Moment Invariants for Biometric Recognition and Cryptosystems,
ICIAR09(439-450).
Springer DOI 0907
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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 0709
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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 0709
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Venkataramana, A., Raj, P.A.[P. Ananth],
Recursive Computation of Forward Krawtchouk Moment Transform Using Clenshaw's Recurrence Formula,
NCVPRIPG11(200-203).
IEEE DOI 1205
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ICIP07(IV: 37-40).
IEEE DOI 0709
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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,
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Springer DOI 0706
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Ong, L.Y.[Lee-Yeng], Chong, C.W.[Chee-Way], Besar, R.[Rosli],
Scale Invariants of Three-Dimensional Legendre Moments,
ICPR06(III: 141-144).
IEEE DOI 0609
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Amayeh, G.[Gholamreza], Bebis, G.N.[George N.], Erol, A.[Ali], Nicolescu, M.[Mircea],
Peg-Free Hand Shape Verification Using High Order Zernike Moments,
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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).
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Bresson, X., Vandergheynst, P., Thiran, J.P.,
Geometric moments in scale-spaces,
ICPR02(II: 418-421).
IEEE DOI 0211
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Tuzikov, A.V.[Alexander V.], Sheynin, S.A.[Stanislav A.], Vasiliev, P.V.[Pavel V.],
Efficient Computation of Body Moments,
CAIP01(201 ff.).
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Prismall, S.P., Nixon, M.S., Carter, J.N.,
On Moving Object Reconstruction by Moments,
BMVC02(Reconstruction). 0208
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Canterakis, N.,
3D Zernike Moments and Zernike Affine Invariants for 3D Image Analysis and Recognition,
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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 9608
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Shen, J., Shen, D.,
Orthogonal Legendre Moments and Their Calculation,
ICPR96(II: 241-245).
IEEE DOI 9608
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Zhou, F., Kornerup, P.,
Computing moments by prefix sums,
ICIP96(III: 619-622).
IEEE DOI 9610
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Yang, L., Albregtsen, F.,
Fast Computation of Invariant Geometric Moments: A New Method Giving Correct Results,
ICPR94(A:201-204).
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Li, B.C.[Bing-Cheng], Ma, S.D.[Song De],
Efficient computation of 3D moments,
ICPR94(A:22-26).
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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 9208
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Zhu, Q., Poh, L.,
A Transformation-Invariant Recursive Subdivision Method for Shape Analysis,
ICPR88(II: 833-835).
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Chapter on Registration, Matching and Recognition Using Points, Lines, Regions, Areas, Surfaces continues in
Features for Contour Matching .


Last update:Mar 16, 2024 at 20:36:19