12.3.1.7.1 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.
WWW Link. 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.
WWW Link. 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 Link. 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.
WWW Link. 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.
WWW Link. 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 Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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 Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. BibRef 9301

Li, B.C.[Bing-Cheng], Shen, J.[Jun],
Fast Computation of Moment Invariants,
PR(24), No. 8, 1991, pp. 807-813.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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).
WWW Link. 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 Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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 Link. 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.
WWW Link. 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 Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
WWW Link. 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.
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Efficient hardware architectures for computation of image moments,
RealTimeImg(10), No. 6, December 2004, pp. 371-378.
WWW Link. 0501
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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.
WWW Link. 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.
WWW Link. 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 Link. 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 Link. 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.
WWW Link. 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.
WWW Link. 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 Link. 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 Link. 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.
WWW Link. 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; Computer vision; 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; Computer vision; 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; Computer vision; 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.
WWW Link. 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 Link. 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.
WWW Link. 0705
Discrete orthogonal moments; Tchebichef polynomials; Translation and scale invariants; Pattern classification; Image normalization 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.
WWW Link. 0707
BibRef
And: Corrigendum: PRL(29), No. 1, 1 January 2008, pp. 96.
WWW Link. 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 Link. 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.
WWW Link. 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.
WWW Link. 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
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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
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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
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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

Xiao, B.[Bin], Ma, J.F.[Jian-Feng], Wang, X.[Xuan],
Image analysis by Bessel-Fourier moments,
PR(43), No. 8, August 2010, pp. 2620-2629.
Elsevier DOI 1006
Bessel function; Orthogonal moments; Images reconstruction; Image recognition; Invariant moments 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.S.[Yiannis S.],
Parameterized real-time moment computation on gray images using block techniques,
RealTimeIP(6), No. 2, June 2011, pp. 81-91.
WWW Link. 1101
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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
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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
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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

Upneja, R.[Rahul], Singh, C.[Chandan],
Fast computation of Jacobi-Fourier moments for invariant image recognition,
PR(48), No. 5, 2015, pp. 1836-1843.
Elsevier DOI 1502
Jacobi-Fourier moments See also Comments on 'fast computation of jacobi-Fourier moments for invariant image recognition'. BibRef

Sáez-Landete, J.[José],
Comments on 'fast computation of jacobi-Fourier moments for invariant image recognition',
PR(67), No. 1, 2017, pp. 16-22.
Elsevier DOI 1704
Jacobi polynomials See also Fast computation of Jacobi-Fourier moments for invariant image recognition. 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

Camacho-Bello, C., Toxqui-Quitl, C., Padilla-Vivanco, A., Baez-Rojas, J.J.,
High-precision and fast computation of Jacobi-Fourier moments for image description,
JOSA-A(31), No. 1, January 2014, pp. 124-134.
DOI Link 1402
Image processing BibRef

Hu, H.T.[Hai-Tao], Zhang, Y.D.[Ya-Dong], Shao, C.[Chao], Ju, Q.[Quan],
Orthogonal moments based on exponent functions: Exponent-Fourier moments,
PR(47), No. 8, 2014, pp. 2596-2606.
Elsevier DOI 1405
BibRef
And: A1, A4, A3, Only: Errata and Comments:
Errata and comments on 'Errata and comments on Orthogonal moments based on exponent functions: Exponent-Fourier moments',
PR(52), No. 1, 2016, pp. 471-476.
Elsevier DOI 1601
Exponent-Fourier moments Orthogonal moments BibRef

Xiao, B.[Bin], Li, W.S.[Wei-Sheng], Wang, G.Y.[Guo-Yin],
Errata and comments on 'Orthogonal moments based on exponent functions: Exponent-Fourier moments',
PR(48), No. 4, 2015, pp. 1571-1573.
Elsevier DOI 1502
Orthogonal moments. Comments: See also Orthogonal moments based on exponent functions: Exponent-Fourier moments. 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

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


Zhao, Y.J.[Yan-Jun], Belkasim, S.[Saeid],
Improving stability and invariance of Cartesian Zernike moments,
Southwest12(61-64).
IEEE DOI 1205
BibRef

Doretto, G.[Gianfranco], Yao, Y.[Yi],
Region moments: Fast invariant descriptors for detecting small image structures,
CVPR10(3019-3026).
IEEE DOI 1006
BibRef

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
BibRef

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
BibRef

Suthaharan, S.[Shan],
Enhanced Accuracy Moment Invariants for Biometric Recognition and Cryptosystems,
ICIAR09(439-450).
Springer DOI 0907
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 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 0709
BibRef

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
BibRef
Earlier: A2, A1:
Fast Computation of Inverse Krawtchouk Moment Transform using Clenshaw's Recurrence Formula,
ICIP07(IV: 37-40).
IEEE DOI 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 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).
IEEE DOI 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 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 0512
BibRef

Bresson, X., Vandergheynst, P., Thiran, J.P.,
Geometric moments in scale-spaces,
ICPR02(II: 418-421).
IEEE DOI 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.).
Springer DOI 0210
BibRef

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,
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 9608
(Universidad Politecnica de Cataluna, E) BibRef

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

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

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

Li, B.C.[Bing-Cheng], Ma, S.D.[Song De],
Efficient computation of 3D moments,
ICPR94(A:22-26).
IEEE DOI 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 9208
BibRef

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

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


Last update:Sep 22, 2017 at 21:00:01