13.1.2.1 Invariants, General Issues and Techniques

Chapter Contents (Back)
Object Recognition. Invariants, Theory. Invariants.
See also Matching, Descriptions Using Moments.
See also Invariants, Points.

Klopfenstein, R.W., Carlson, C.R.,
Theory of Shape-Invariant Imaging Systems,
IU87(175-214). BibRef 8700

Cyganski, D., and Orr, J.A.,
Applications of Tensor Theory to Object Recognition and Orientation Determination,
PAMI(7), No. 6, November 1985, pp. 662-673. BibRef 8511

Shepherd, T.S.[Thomas S.], Uttal, W.[William], Dayanand, S.[Sriram], Lovell, R.[Robb],
A Method for Shift, Rotation, and Scale Invariant Pattern Recognition Using the Form and Arrangement of Pattern-Specific Features,
PR(25), No. 4, April 1992, pp. 343-356.
Elsevier DOI BibRef 9204

Spirkovska, L.[Lilly], Reid, M.B.[Max B.],
Robust Position, Scale, and Rotation Invariant Object Recognition Using Higher-Order Neural Networks,
PR(25), No. 9, September 1992, pp. 975-985.
Elsevier DOI BibRef 9209

Yuceer, C., Oflazer, K.,
A Rotation, Scaling, and Translation Invariant Pattern Classification System,
PR(26), No. 5, May 1993, pp. 687-710.
Elsevier DOI BibRef 9305
Earlier: ICPR92(II:422-425).
IEEE DOI 9208
BibRef

Li, C.W., Wu, C.H.,
Introducing Rotation Invariance into the Neocognitron Model for Target Recognition,
PRL(14), No. 12, December 1993, pp. 985-995. BibRef 9312

Lin, Y.T., Fang, N., Cheng, M.C., Chiang, S.M.,
A Modified Homomorphic Approach on Invariant Features of Object Images,
PRL(14), 1993, pp. 453-463. BibRef 9300

Tarr, M.J., Hayward, W., Gauthier, I., Williams, P.,
Is Object Recognition Mediated by Viewpoint Invariant Parts or Viewpoint Dependent Features,
Perception(24), 1995, pp. 4. BibRef 9500

Liu, X.F., Tan, S.H., Srinivasan, V., Ong, S.H., Xie, W.X.,
Fuzzy Pyramid-Based Invariant Object Recognition,
PR(27), No. 5, May 1994, pp. 741-756.
Elsevier DOI BibRef 9405

Liu, X.F., Tan, S.H., Ong, S.H.,
Fuzzy Pyramid Scheme for Distorted Object Recognition,
PR(29), No. 10, October 1996, pp. 1631-1646.
Elsevier DOI Character Recognition. Map Recognition. BibRef 9610

You, S.D., Ford, G.E.,
Network Model for Invariant Object Recognition,
PRL(15), No. 8, August 1994, pp. 761-767. BibRef 9408

Marola, G., Vaccarelli, A.,
An Algebraic-Method for Detection and Recognition of Polyhedral Objects from a Single Image,
PR(27), No. 10, October 1994, pp. 1407-1414. BibRef 9410
Earlier:
Elsevier DOI
An Algebraic Method for Detecting Three-Dimensional Objects in a Picture,
ICPR92(I:415-419).
IEEE DOI BibRef

Keren, D.,
Using Symbolic Computation to Find Algebraic Invariants,
PAMI(16), No. 11, November 1994, pp. 1143-1149.
IEEE DOI Includes the invariant expressions. Used for complicated objects. BibRef 9411

Li, W., Nasrabadi, N.M.,
Invariant Object Recognition Based On A Neural Network of Cascaded RCE Nets,
PRAI(7), 1993, pp. 815-829. BibRef 9300

Bennett, B.M., Hoffman, D.D., and Prakash, C.,
Recognition Polynomials,
JOSA-A(10), No. 4, April 1993, pp. 759-764. BibRef 9304
Earlier:
Object Recognition from a Single View Using Recognition Polynomials,
TR from MBS 92-17, UC Irvine1992. BibRef

Goldberg, R.R.,
Constrained Pose Refinement of Parametric Objects,
IJCV(13), No. 2, October 1994, pp. 181-211.
Springer DOI BibRef 9410

Van Gool, L.J., Moons, T., Pauwels, E.J., Oosterlinck, A.,
Vision and Lies Approach to Invariance,
IVC(13), No. 4, May 1995, pp. 259-277.
Elsevier DOI BibRef 9505

Moons, T., Van Gool, L.J., Pauwels, E.J., Oosterlinck, A.,
Viewpoint Invariant Characteristics of Articulated Objects,
JMIV(6), No. 1, January 1996, pp. 37-57. 9608
BibRef

So, A.T.P.,
Complete Object Recognition Under Projection Distortion,
PRL(16), No. 3, March 1995, pp. 257-265. BibRef 9503

Hemminger, T.L., Pomalaza-Raez, C.A.,
Rotation-Independent and Scale-Independent Pattern-Recognition Through Optimization,
PR(29), No. 3, March 1996, pp. 487-495.
Elsevier DOI BibRef 9603

Marabini, R., Carazo, J.M.,
On a New Computationally Fast Image Invariant Based on Bispectral Projections,
PRL(17), No. 9, August 1 1996, pp. 959-967. 9609
BibRef

Mundy, J.L., Liu, A., Pillow, N., Zisserman, A., Abdallah, S., Utcke, S., Nayar, S.K., Rothwell, C.A.,
An Experimental Comparison of Appearance and Geometric Model Based Recognition,
ORCV96(247) 9611
BibRef

Goldberg, R.R.,
Pose Determination of Parameterized Object Models from a Monocular Image,
IVC(11), No. 1, January-February 1993, pp. 49-62.
Elsevier DOI BibRef 9301

Rubinstein, J., Segman, J., Zeevi, Y.,
Recognition of Distorted Patterns by Invariance Kernels,
PR(24), No. 10, 1991, pp. 959-967.
Elsevier DOI BibRef 9100
Earlier: ICPR90(II: 159-164).
IEEE DOI 9208
BibRef

Brandt, R.D., Lin, F.,
Representations That Uniquely Characterize Images Modulo Translation, Rotation, and Scaling,
PRL(17), No. 9, August 1 1996, pp. 1001-1015. 9609
First basic invariants, then hybrid ones invariant to multiple transformations BibRef

Lin, F., Brandt, R.D.,
Towards Absolute Invariants of Images Under Translation, Rotation, and Dilation,
PRL(14), No 5, May, 1993, pp. 369-379. Phase invariants: Taylor, Hessian, Mellin invariants BibRef 9305

Cole, J.B., Murase, H., Naito, S.,
A Lie Group Theoretical Approach to the Invariance Problem in Feature Extraction and Object Recognition,
PRL(12), 1991, pp. 519-523. BibRef 9100

Bulthoff, H.H.[Heinrich H.], Tarr, M.J., Blanz, V., Zabinski, M.,
To What Extent Do Unique Parts Influence Recognition Across Changes in Viewpoint,
Perception(24), 1995, pp. 3. BibRef 9500

Vetter, T.[Thomas], Poggio, T.[Tomaso], Bulthoff, H.H.[Heinrich H.],
3D Object Recognition: Symmetry and Virtual Views,
MIT AI Memo-1409, December 1992.
WWW Link. BibRef 9212

Bruckstein, A.M., Rivlin, E., Weiss, I.,
Scale-Space Semilocal Invariants,
IVC(15), No. 5, May 1997, pp. 335-344.
Elsevier DOI 9706
BibRef
And:
Recognizing Objects Using Scale Space Local Invariants,
ICPR96(I: 760-764).
IEEE DOI 9608
(Israel Institute of Technology, IL) BibRef

Chandran, V., Carswell, B., Boashash, B., Elgar, S.,
Pattern-Recognition Using Invariants Defined from Higher-Order Spectra: 2-D Image Inputs,
IP(6), No. 5, May 1997, pp. 703-712.
IEEE DOI 9705
BibRef

Kaveti, S., Teoh, E.K., Wang, H.,
Efficient Algorithms for Obtaining Algebraic Invariants from Higher Degree Implicit Polynomials for Recognition of Curved Objects,
PR(31), No. 3, March 1998, pp. 301-313.
Elsevier DOI 9802
BibRef

Morse, B.S.[Bryan S.], Pizer, S.M.[Stephen M.], Puff, D.T.[Derek T.], Gu, C.W.[Chen-Wei],
Zoom-Invariant Vision of Figural Shape,
CVIU(69), No. 1, January 1998, pp. 72-86.
DOI Link
See also Zoom-Invariant Vision of Figural Shape: The Mathematics of Cores. BibRef 9801

Moses, Y.[Yael], Ullman, S.[Shimon],
Generalization to Novel Views: Universal, Class-Based, and Model-Based Processing,
IJCV(29), No. 3, September 1998, pp. 233-253.
DOI Link 9811
BibRef
Earlier:
Limitations of Non Model-Based Recognition Schemes,
ECCV92(820-828).
Springer DOI 9205
BibRef
And: MIT AI Memo-1301, May 1991. BibRef

Shao, Z., Kittler, J.V.,
Shape representation and recognition based on invariant unary and binary relations,
IVC(17), No. 5/6, April 1999, pp. 429-444.
Elsevier DOI BibRef 9904

Guil, N., Gonzalez-Linares, J.M., Zapata, E.L.,
Bidimensional shape detection using an invariant approach,
PR(32), No. 6, June 1999, pp. 1025-1038.
Elsevier DOI BibRef 9906

Alferez, R.[Ronald], Wang, Y.F.[Yuan-Fang],
Geometric and Illumination Invariants for Object Recognition,
PAMI(21), No. 6, June 1999, pp. 505-536.
IEEE DOI Rigid motion, affine transforms, changes in illumination, perspective, and view point changes. Applicable to wavelets, Fourier analysis, and splines. BibRef 9906

Basri, R.[Ronen], Moses, Y.[Yael],
When is it Possible to Identify 3D Objects From Single Images Using Class Constraints?,
IJCV(33), No. 2, September 1999, pp. 95-116.
DOI Link BibRef 9909
Earlier: ICCV98(541-548).
IEEE DOI BibRef

Song, B.S.[Bong Seop], Yun, I.D.[Il Dong], Lee, S.U.[Sang Uk],
A target recognition technique employing geometric invariants,
PR(33), No. 3, March 2000, pp. 413-425.
Elsevier DOI 0001
BibRef

Song, B.S.[Bong Seop], Lee, K.M.[Kyoung Mu], Lee, S.U.[Sang Uk], Yun, I.D.[Il Dong],
3D target recognition based on projective invariant relationships,
JVCIR(14), No. 1, March 2002, pp. 1-21.
Elsevier DOI 0304
BibRef

Roh, K.S.[Kyoung Sig], Kweon, I.S.[In So],
3-D object recognition using a new invariant relationship by single-view,
PR(33), No. 5, May 2000, pp. 741-754.
Elsevier DOI 0003
BibRef

Flusser, J.[Jan], Zitová, B.[Barbara],
Combined Invariants to Linear Filtering and Rotation,
PRAI(13), No. 8, December 1999, pp. 1123. 0005
BibRef

Flusser, J.[Jan], Boldys, J.[Jirí], Zitová, B.[Barbara],
Invariants to Convolution in Arbitrary Dimensions,
JMIV(13), No. 2, October 2000, pp. 101-113.
DOI Link 0101
BibRef

Flusser, J., Zitova, B.,
Invariants to convolution with circularly symmetric PSF,
ICPR04(II: 11-14).
IEEE DOI 0409
BibRef

Liu, Y., Rodrigues, M.A.,
Invariant Geometric Properties of Image Correspondence Vectors as Rigid Constraints to Motion Estimation,
PRAI(13), No. 8, December 1999, pp. 1165. 0005
BibRef

Boutin, M.[Mireille],
Numerically Invariant Signature Curves,
IJCV(40), No. 3, December 2000, pp. 235-248.
DOI Link torsion, object recognition, differential invariant, joint invariant, signature curve, Euclidean group, equi-affine group, numerical approximation 0102
BibRef

Osada, R., Funkhauser, T., Chazalle, B., and Dobkins, D.,
Matching 3D Models with Shape Distribution,
TOG(21), No. 4, October 2002, pp. 807-832. BibRef 0210

Bayro-Corrochano, E.[Eduardo], Banarer, V.[Vladimir],
A Geometric Approach for the Theory and Applications of 3D Projective Invariants,
JMIV(16), No. 2, March 2002, pp. 131-154.
DOI Link 0202
BibRef
Earlier:
Geometric analysis and computing of projective structure and motion,
CIAP99(291-296).
IEEE DOI 9909

See also projective reconstruction of points, lines, quadrics, plane conics and degenerate quadrics using uncalibrated cameras, The. BibRef

Wu, Y.H., Hu, Z.Y.,
The invariant representations of a quadric cone and a twisted cubic,
PAMI(25), No. 10, October 2003, pp. 1329-1332.
IEEE Abstract. 0310
A compact representation for a quadric cone and a first representation for a twisted cubic. BibRef

Civi, H.[Hakan], Christopher, C.[Colin], Ercil, A.[Aytul],
The Classical Theory of Invariants and Object Recognition Using Algebraic Curve and Surfaces,
JMIV(19), No. 3, November 2003, pp. 237-253.
DOI Link 0310
BibRef

Petrou, M.[Maria], Kadyrov, A.[Alexander],
Affine invariant features from the trace transform,
PAMI(26), No. 1, January 2004, pp. 30-44.
IEEE Abstract. 0401
Trace is a generalization of the Radon transform. Apply to retrieval systems. BibRef

Kadyrov, A., Petrou, M.,
Object signatures invariant to affine distortions derived from the Trace transform,
IVC(21), No. 12-13, December 2003, pp. 1135-1143.
Elsevier DOI 0401
BibRef
Earlier:
Object descriptors invariant to affine distortions,
BMVC01(Session 5: Matching & Retrieval).
HTML Version. 0110
BibRef
Earlier: A2, A1:
Features Invariant to Affine Distortions from the Trace Transform,
ICIP01(III: 852-855).
IEEE DOI 0108
University of Surrey BibRef

Kadyrov, A.[Alexander], Petrou, M.[Maria],
The Trace Transform and Its Applications,
PAMI(23), No. 8, August 2001, pp. 811-828.
IEEE DOI 0109
Trace, a generalization of the Radon transform. Use to match images of single objects to retrieve from a database. Robust to scale (errors start at 70% scale), and somewhat to additive noise. Salt-and-Pepper noise is worse, rotations also seem worse than scaling. Compared to:
See also Enhancing CSS-based shape retrieval for objects with shallow concavities. BibRef

Kadyrov, A.[Alexander], Petrou, M.[Maria],
Affine Parameter Estimation from the Trace Transform,
PAMI(28), No. 10, October 2006, pp. 1631-1645.
IEEE DOI 0609
BibRef
Earlier: ICPR02(II: 798-801).
IEEE DOI 0211
BibRef
Earlier:
The Trace Transform as a Tool to Invariant Feature Construction,
ICPR98(Vol II: 1037-1039).
IEEE DOI 9808
Given the images of 2 segmented objects, recover the affine transform between them. BibRef

Kadyrov, A.[Alexander],
Triple features for linear distorted images,
CAIP95(844-849).
Springer DOI 9509
BibRef

Olver, P.J.[Peter J.], Tannenbaum, A.[Allen],
Mathematical Methods in Computer Vision,
Springer-Verlag2003. ISBN 0-387-00497-1.
HTML Version. BibRef 0300

Shahshahani, M.[Mehrdad], Targhi, A.T.[Alireza Tavakoli],
A simple set of numerical invariants for the analysis of images,
IJIST(16), No. 5, 2006, pp. 240-248.
DOI Link 0704
BibRef

Flusser, J.[Jan], Kautsky, J.[Jaroslav], Šroubek, F.[Filip],
Implicit Moment Invariants,
IJCV(86), No. 1, January 2010, pp. xx-yy.
Springer DOI 1001
BibRef
Earlier:
Object Recognition by Implicit Invariants,
CAIP07(856-863).
Springer DOI 0708
BibRef

Kautsky, J.[Jaroslav], Flusser, J.[Jan],
Blur Invariants Constructed From Arbitrary Moments,
IP(20), No. 12, December 2011, pp. 3606-3611.
IEEE DOI 1112
BibRef

Zhang, H., Shu, H., Han, G.N., Coatrieux, G., Luo, L., Coatrieux, J.L.,
Blurred Image Recognition by Legendre Moment Invariants,
IP(19), No. 3, March 2010, pp. 596-611.
IEEE DOI 1003
Construct set of blur invariants for recognition. BibRef

Wang, Z.J.[Zi-Jia], Yang, W.B.[Wen-Bin], Liu, Z.S.[Zhi-Song], Chen, Q.[Qiang], Ni, J.C.[Jia-Cheng], Jia, Z.[Zhen],
Object Centric Point Sets Feature Learning with Matrix Decomposition,
MLCSA22(256-268).
Springer DOI 2307
BibRef

Phillips, C.[Carlos], Siddiqi, K.[Kaleem],
Greyscale Photograph Geometry Informed by Dodging and Burning,
ICCVGIP06(13-24).
Springer DOI 0612
Using different prints from same negative. Invariant features. BibRef

González, J.M., Sebastián, J.M., García, D., Sánchez, F., Angel, L.,
Recognition of 3D Object from One Image Based on Projective and Permutative Invariants,
ICIAR04(I: 705-712).
Springer DOI 0409
BibRef