Brill, M.H.[Michael H],
Barrett, E.B.[Eamon B],
Closed-Form Extension of the Anharmonic Ratio to N-Space,
CVGIP(23), No. 1, July 1983, pp. 92-98.
Elsevier DOI Cross ratio of volumes in
N-space is shown to be a projective invariant.
BibRef
8307
Barrett, E.B.,
Payton, P.M.,
Haag, N.N., and
Brill, M.H.,
General Methods for Determining Projective Invariants in Imagery,
CVGIP(53), No. 1, January 1991, pp. 46-65.
Elsevier DOI A set of invariant properties in imagery that are independent of the
imaging system. These properties would then be used for recognition.
Start from the cross ratio (relates point to projections on
lines) to get cross ratios of areas and volumes defined by
image points.
BibRef
9101
Barrett, E.B.,
Payton, P.M.,
Brill, M.H., and
Haag, N.N.,
Invariants Under Image Perspective Transformations:
Theory and Examples,
IJIST(2), 1990, pp. 296-314.
Using projective invariants recognize with differences in tilt, scale and
rotation. Develop corresponding operators for finding curves and planar
objects.
BibRef
9000
Barrett, E.B.,
Brill, M.H.,
Haag, N.N., and
Payton, P.M.,
Invariant Linear Methods in Photogrammetry and Model-Matching,
GICV92(277-292). Chapter 14.
BibRef
9200
And:
Some Invariant Linear Methods in Photogrammetry and Model-Matching,
CVPR92(122-128).
IEEE DOI Addresses a number of tasks, resection, intersection and model matching.
BibRef
Barrett, E.B.[Eamon B.],
Payton, P.M.[Paul M.],
Projectively Invariant Structures in Multi-Sensor Imagery,
SPIE(1771), July 1992, pp. 236-251.
BibRef
9207
Barrett, E.B.[Eamon B.],
Payton, P.M.[Paul M.],
Extension of Three-Dimensional Invariant Methods to
Noncentral-Projection Imaging Systems,
SPIE(1944), 1993, pp. 106-119
Combine colinearity and condition equations of photographic and SAR.
BibRef
9300
Payton, P.M.,
Haines, B.,
Smedley, K.,
Barrett, E.B.,
Machine-Vision Applications of Image Invariants:
Real-Time Processing Experiments,
SPIE(1406), October 1990, pp. 58-71.
Using projective invariants recognize with differences in tilt, scale and
rotation.
BibRef
9010
Barrett, E.B.,
Brill, M.H.,
Haag, N.N., and
Payton, P.M.,
Linear Resection, Intersection, and Perspective-Independent Model-Matching
in Photogrammetry: Theory,
SPIE(1567), July 1991, pp. 142-169.
BibRef
9107
Barrett, E.B.,
Gheen, G., and
Payton, P.M.,
Algorithms for Invariant Model Transfer and Object Reconstruction,
ARPA94(II:1429-1440).
Algorithms to derive invariants from imaging equations.
BibRef
9400
Barrett, E.B.[Eamon B.],
Gheen, G.[Gregory],
Payton, P.M.[Paul M.],
Representation of Three-Dimensional Object Structure as Cross-Ratios of
Determinants of Stereo Image Points,
AIVCV93(47-68).
Derive both epipolar geometry and 3-D object structure from stereo given
corresponding points.
BibRef
9300
Barrett, E.B.[Eamon B.],
Payton, P.M.[Paul M.],
Marra, P.[Peter],
Brill, M.H.,
Geometric Interpretations of Algebraic Invariants in
Images of 3D Scenes,
SPIE(3168), July 1997, pp. xx-yy.
Progression of cross ration theorems from 1 through 3 dimensions.
1-D: points on lines. 2-D: cross ratio of products of areas of triangles
(from 3 points). 3-D: Triangles in image, tetrahedra in the object
cross ratios of products of areas in image and volumes in object.
BibRef
9707
Barrett, E.B.[Eamon B.],
Gheen, G.[Gregory],
Payton, P.M.[Paul M.],
Invariant Methods for Model Transfer and Object Reconstruction
Based on Multiple Reference Images,
SPIE(2421), February 1995, pp. 191-202.
BibRef
9502
Barrett, E.B.[Eamon B.],
Payton, P.M.[Paul M.],
Gheen, G.[Gregory],
Robust Algebraic Invariant Methods with
Applications in Geometry and Imaging,
SPIE(2572), July 1995, pp. 30-42.
BibRef
9507
Barrett, E.B.,
Gheen, G.,
Payton, P.M.,
Lockheed Martin Report: Progress in Image Invariants Research--1995,
ARPA96(129-158).
BibRef
9600
Weinshall, D.,
Model-Based Invariants for 3-D Vision,
IJCV(10), No. 1, February 1993, pp. 27-42.
Springer DOI
BibRef
9302
Earlier:
CVPR93(695-696).
IEEE DOI A linear, incremental algorithm to compute invariants and the
use of invariants in other matching schemes.
BibRef
Weinshall, D.,
A Hierarchy of Invariant Representations of 3D Shape,
WQV93(97-106).
BibRef
9300
Holt, R.J.,
Netravali, A.N.,
Using Affine Invariants on Perspective Projections of Plane Curves,
CVIU(61), No. 1, January 1995, pp. 112-121.
DOI Link
BibRef
9501
Weiss, I.[Isaac],
Model-Based Recognition of 3D Curves from One View,
JMIV(10), No. 2, March 1999, pp. 175-184.
BibRef
9903
Earlier:
DOI Link
DARPA98(641-652).
BibRef
Earlier:
3D Curve Reconstruction from Uncalibrated Cameras,
ICPR96(I: 323-327).
IEEE DOI
9608
BibRef
And:
UMDTR-3605, January 1996
BibRef
And:
ARPA96(1251-1256).
BibRef
And:
UMDTR3581, 1995.
WWW Link.
WWW Link. There are no invariants, but assuming something about the model,
there are some.
BibRef
Weiss, I.[Isaac],
Ray, M.[Manjit],
Model-Based Recognition of 3D Objects from Single Images,
PAMI(23), No. 2, February 2001, pp. 116-128.
IEEE DOI
0102
Invariance based. Consider issues of 3D to 2D projection (loss
of depth) and feature point matching. Use assumptions based on the
particular model or class of models to get invariants that hold
with the projection.
BibRef
Ray, M.[Manjit],
Weiss, I.[Isaac],
Feature-based Single-view 3d Object Recognition in
Optical Images using Invariants,
UMD--TR4172, August 2000.
WWW Link.
WWW Link.
BibRef
0008
Ray, M.[Manjit],
Weiss, I.[Isaac],
Feature-less Single-view 3d Object Recognition in
Range Images using Invariants,
UMD--TR4173, August 2000.
WWW Link.
WWW Link.
BibRef
0008
Weiss, I.[Isaac],
Ray, M.[Manjit],
Model-Based Recognition of 3-D Objects from One View,
ECCV98(II: 716).
Springer DOI
BibRef
9800
And:
UMD--TR3842, October 1997.
Invariants.
WWW Link.
WWW Link.
BibRef
Weiss, I.[Isaac],
Rosenfeld, A.[Azriel],
3D Object Recognition from Multiple and Single Views,
DARPA97(1041-1046).
BibRef
9700
Shan, J.,
Photogrammetric Object Description with Projective Invariants,
PandRS(52), No. 5, October 1997, pp. 222-228.
9711
BibRef
Csurka, G.[Gabriella],
Faugeras, O.D.[Olivier D.],
Computing 3-Dimensional Project Invariants from a Pair of
Images Using the Grassmann-Cayley Algebra,
IVC(16), No. 1, January 30 1998, pp. 3-12.
Elsevier DOI
9803
BibRef
Csurka, G.[Gabriella],
Faugeras, O.D.[Olivier D.],
Algebraic and Geometric Tools to Compute Projective and Permutation
Invariants,
PAMI(21), No. 1, January 1999, pp. 58-64.
IEEE DOI
BibRef
9901
Earlier:
Computing projective and permutation invariants of points and lines,
CAIP97(66-73).
Springer DOI
9709
Computation approaches.
BibRef
Startchik, S.,
Milanese, R.,
Pun, T.,
Projective and Illumination Invariant Representation of
Disjoint Shapes,
IVC(16), No. 9-10, July 1998, pp. 713-723.
Elsevier DOI
9808
BibRef
Earlier:
ECCV98(I: 264).
Springer DOI
BibRef
Choudhury, R.[Ragini],
Srivastava, J.B.,
Chaudhury, S.[Santanu],
Reconstruction-Based Recognition of Scenes with
Translationally Repeated Quadrics,
PAMI(23), No. 6, June 2001, pp. 617-632.
IEEE DOI
0106
Invariant based reconition of a pair of rigidly connected repeated
surfaces. (E.g. similar elements on buildings.)
BibRef
Choudhury, R.[Ragini],
Chaudhury, S.[Santanu],
Srivastava, J.B.,
Reconstruction Based Recognition of Scenes with Multiple Repeated
Components,
CVIU(84), No. 3, December 2001, pp. 325-360.
DOI Link
0207
BibRef
Chung, R.[Ronald],
Relative Viewing Distance: A Correspondence Invariance under
Paraperspective Projection,
CVIU(86), No. 1, April 2002, pp. 1-31.
DOI Link
0211
BibRef
Zheng, B.[Bo],
Takamatsu, J.[Jun],
Ikeuchi, K.[Katsushi],
Multilevel Algebraic Invariants Extraction by Incremental Fitting
Scheme,
ACCV09(I: 190-200).
Springer DOI
0909
BibRef
Yuan, T.Q.A.[Tian-Qi-Ang],
Yan, S.C.[Shui-Cheng],
Tang, X.[Xiaoou],
Perspective Symmetry Invariant and Its Applications,
ICPR06(IV: 65-68).
IEEE DOI
0609
BibRef
Vicente, M.A.,
Gil, P.,
Reinoso, O.,
Torres, F.,
Objects Recognition by Means of Projective Invariants Considering
Corner-points,
WSCG02(SH-129).
PDF File.
HTML Version.
0209
BibRef
Berthilsson, R.,
Densities of Projective Invariants,
SCIA99(Statistical Methods).
BibRef
9900
Naeve, A., and
Eklundh, J.O.,
On Projective Geometry and the Recovery of 3-D Structure,
ICCV87(128-135).
BibRef
8700
And:
TRITA-NA-8608, December 1986.
BibRef
Naeve, A.,
Geometric Modelling: A Projective Approach,
ISRN KTH/NA/P--89/18--SE, 1989.
BibRef
8900
Naeve, A.,
Projective Line Geometry of the Visual Operator,
TRITA-NA-8606, December 1986.
BibRef
8612
Poulo, R.J.,
New Invariants for Three Dimensional Recognition,
CVWS84(158-163).
BibRef
8400
Verri, A.[Alessandro],
Yuille, A.L.[Alan L.],
Perspective Projection Invariants,
MIT AI Memo-832, February 1986.
BibRef
8602
Chapter on Matching and Recognition Using Volumes, High Level Vision Techniques, Invariants continues in
Affine Invariants .