*Akaike, H.[Hirotugu]*,

**A new look at the statistical model identification**,

*AC(19)*, No. 6, 1974, pp. 716-723.

IEEE DOI
**1001**

Measurement of goodness of fit to a statistical model.
BibRef

*Nielsen, L.[Lars]*,
*Sparr, G.[Gunnar]*,

**Projective Area-Invariants as an Extension of the Cross-Ratio**,

*CVGIP(54)*, No. 1, July 1991, pp. 145-159.

Elsevier DOI
BibRef
**9107**

Earlier: A2, A1:

**Shape and mutual cross-ratios with applications to exterior, interior
and relative orientation**,

*ECCV90*(607-609).

Springer DOI
**9004**

BibRef

*Kanatani, K.[Kenichi]*,

**Computational Cross Ratio for Computer Vision**,

*CVGIP(60)*, No. 3, November 1994, pp. 371-381.

DOI Link
BibRef
**9411**

*Kanatani, K.[Kenichi]*,

**Statistical Foundation for Hypothesis Testing of Image Data**,

*CVGIP(60)*, No. 3, November 1994, pp. 382-391.

DOI Link
BibRef
**9411**

*Kanatani, K.[Kenichi]*,

**Geometric Information Criterion for Model Selection**,

*IJCV(26)*, No. 3, March 1998, pp. 171-189.

DOI Link
**9804**

See also Statistical-Analysis of Geometric Computation.
BibRef

*Kanatani, K.[Kenichi]*,

**Uncertainty Modeling and Model Selection for Geometric Inference**,

*PAMI(26)*, No. 10, October 2004, pp. 1307-1319.

IEEE Abstract.
**0409**

Discuss the meaning of statistical methods for geometric inference.
Feature uncertainty from image processing operations.
Derive the geometric AIC and the geometric MDL as counterparts of
Akaike's AIC (

See also new look at the statistical model identification, A. ) and Rissanen's MDL (

See also Universal Prior for Integers and Esitmation by Minimum Description Length, A. ).
BibRef

*Kanatani, K.[Kenichi]*,

**Geometric BIC**,

*IEICE(E93-D)*, No. 1, January 2010, pp. 144-151.

WWW Link.
**1001**

Geometric fitting. Similar to geometric MDL.
BibRef

*Kanatani, K.[Kenichi]*,

**Further improving geometric fitting**,

*3DIM05*(2-13).

IEEE DOI
**0508**

BibRef

*Sapiro, G.*,
*Tannenbaum, A.*,

**Area and Length Preserving Geometric Invariant Scale-Spaces**,

*PAMI(17)*, No. 1, January 1995, pp. 67-72.

IEEE DOI
BibRef
**9501**

Earlier:
*ECCV94*(B:449-458).

Springer DOI

See also Affine Invariant Scale-Space.
BibRef

*Maybank, S.J.*,

**Probabilistic Analysis of the Application of the Cross Ratio to
Model-Based Vision: Misclassification**,

*IJCV(14)*, No. 3, April 1995, pp. 199-210.

Springer DOI
BibRef
**9504**

*Maybank, S.J.*,

**Probabilistic Analysis of the Application of the Cross Ratio
to Model-Based Vision**,

*IJCV(16)*, No. 1, September 1995, pp. 5-33.

Springer DOI
*Evaluation, Cross Ratio*. Analysis of the use of the cross ratio for matching. How does it vary
when the points have Gaussian distributions.
BibRef
**9509**

*Maybank, S.J.*,

**Stochastic Properties of the Cross Ratio**,

*PRL(17)*, No. 3, March 6 1996, pp. 211-217.
BibRef
**9603**

*Maybank, S.J.[Steven J.]*,

**Relation Between 3D Invariants and 2D Invariants**,

*IVC(16)*, No. 1, January 30 1998, pp. 13-20.

Elsevier DOI
**9803**

BibRef

Earlier:
*RVS95*(xx).
BibRef

*Maybank, S.J.[Steven J.]*,

**Error Trade-Offs for the Cross-Ratio in Model Based Vision**,

*Conference*Workshop on Computer Vision for Space Applications 1993,
pp. 350-359. Antibes France.
BibRef
**9300**

*Maybank, S.J.[Steven J.]*,
*Fraile, R.*,

**Minimum description length method for facet matching**,

*PRAI(14)*, 2000, pp. 919-927.
BibRef
**0001**

*Bribiesca, E.[Ernesto]*,

**Measuring 3-D Shape Similarity Using Progressive Transformations**,

*PR(29)*, No. 7, July 1996, pp. 1117-1129.

Elsevier DOI
**9607**

Use Voxel representation.
Measure how much "information" in the representation.
Shape difference is how much work to trransform one to the other.

See also easy measure of compactness for 2D and 3D shapes, An.

See also Digital Elevation Model Data Analysis Using the Contact Surface Area.
BibRef

*Sanchez-Cruz, H.[Hermilo]*,
*Bribiesca, E.[Ernesto]*,

**A method of optimum transformation of 3D objects used as a measure of
shape dissimilarity**,

*IVC(21)*, No. 12, November 2003, pp. 1027-1036.

Elsevier DOI
**0310**

BibRef

*Chetverikov, D.*,
*Lerch, A.*,

**A Matching Algorithm for Motion Analysis of Dense Populations**,

*PRL(11)*, 1990, pp. 743-749.
BibRef
**9000**

*Chetverikov, D.*,
*Lerch, A.*,

**A Multiresolution Algorithm for Rotation-Invariant Matching of
Planar Shapes**,

*PRL(13)*, September 1992, pp. 669-676.
BibRef
**9209**

*Ciuti, V.*,
*Marola, G.*,
*Santerini, D.*,

**An Algorithm for the Localization of Rotated and Scaled Objects**,

*PRL(11)*, 1990, pp. 59-66.
BibRef
**9000**

*Lei, G.*,

**Recognition of Planar Objects in 3-D Space from
Single Perspective Views Using Cross Ratio**,

*RA(6)*, 1990, pp. 432-437.
BibRef
**9000**

*Weinshall, D.[Daphna]*,

**Minimal Decomposition of Model-Based Invariants**,

*JMIV(10)*, No. 1, January 1999, pp. 75-85.

DOI Link
BibRef
**9901**

*Lourakis, M.I.A.*,
*Halkidis, S.T.*,
*Orphanoudakis, S.C.*,

**Matching Disparate Views of Planar Surfaces Using Projective Invariants**,

*IVC(18)*, No. 9, June 2000, pp. 673-683.

Elsevier DOI
**0004**

BibRef

Earlier:
*BMVC98*(I: 94-104).

PS File.
BibRef

*Adán, A.[Antonio]*,
*Cerrada, C.[Carlos]*,
*Feliu, V.[Vicente]*,

**Global shape invariants: a solution for 3D free-form object
discrimination/identification problem**,

*PR(34)*, No. 7, July 2001, pp. 1331-1348.

Elsevier DOI
**0105**

See also Active object recognition based on Fourier descriptors clustering.
BibRef

*Tien, S.C.[Shen-Chi]*,
*Chia, T.L.[Tsorng-Lin]*,
*Lu, Y.B.[Yi-Bin]*,

**Using cross-ratios to model curve data for aircraft recognition**,

*PRL(24)*, No. 12, August 2003, pp. 2047-2060.

Elsevier DOI
**0304**

BibRef

*Dibos, F.[Françoise]*,
*Frosini, P.[Patrizio]*,
*Pasquignon, D.[Denis]*,

**The Use of Size Functions for Comparison of Shapes Through Differential
Invariants**,

*JMIV(21)*, No. 2, September 2004, pp. 107-118.

DOI Link
**0409**

Use size to reduce errors in invariants.
BibRef

Springer DOI

BibRef

*Huynh, D.*,

**The Cross Ratio: A Revisit to its Probability Density Function**,

*BMVC00*(xx-yy).

PDF File.
**0009**

BibRef

*Wang, G.Y.[Guo-Yu]*,
*Houkes, Z.*,
*Regtien, P.P.L.*,
*Korsten, M.J.*,
*Ji, G.*,

**A Statistical Model to Describe Invariants Extracted from a 3-D
Quadric Surface Patch and its Applications in Region-Based Recognition**,

*ICPR98*(Vol I: 668-672).

IEEE DOI
**9808**

BibRef

*Simon, D.A.[David A.]*,
*Kanade, T.[Takeo]*,

**Geometric Constraint Analysis and Synthesis:
Methods for Improving Shape-Based Registration Accuracy**,

*DARPA97*(901-910).
BibRef
**9700**

*Muresan, L.[Lucian]*,

**2D-2D geometric transformation invariant to arbitrary translations,
rotations and scales**,

*CAIP97*(90-97).

Springer DOI
**9709**

BibRef

*Zribi, M.*,
*Fonga, H.*,
*Ghorbel, F.*,

**A Set of Invariant Features for Three-Dimensional Gray Level Objects
by Harmonic Analysis**,

*ICPR96*(I: 549-553).

IEEE DOI
**9608**

(Ecole Nouvelle d'ingenierus, F)
BibRef

*Lei, Z.B.[Zhi-Bin]*,
*Tasdizen, T.[Tolga]*, and
*Cooper, D.B.[David B.]*,

**PIMs and Invariant Parts for Shape Recognition**,

*ICCV98*(827-832).

IEEE DOI
BibRef
**9800**

*Lei, Z.B.[Zhi-Bin]*,
*Keren, D.*,
*Cooper, D.B.*,

**Computationally fast Bayesian recognition of complex objects based on
mutual algebraic invariants**,

*ICIP95*(II: 635-638).

IEEE DOI
**9510**

BibRef

*Cooper, D.B.[David B.]*,
*Lei, Z.B.[Zhi-Bin]*,

**On representation and invariant recognition of complex objects based on
patches and parts**,

*ORCV94*(139-153).

Springer DOI
**9412**

BibRef

*Sanfeliu, A.*,
*Llorens, A.*,
*Emde, W.*,

**Sensibility, Relative Error and Error Probability of Projective
Invariants of Planar Surfaces of 3D Objects**,

*ICPR92*(I:328-331).

IEEE DOI
BibRef
**9200**

*Yu, X.*,
*Bui, T.D.*, and
*Krzyzak, A.*,

**Invariants and Pose Determination**,

*VF91*(623-632).
Based on matching surface patches.
BibRef
**9100**

Chapter on Matching and Recognition Using Volumes, High Level Vision Techniques, Invariants continues in

Invariants, Projective, Perspective .

Last update:Mar 27, 2023 at 09:32:08