*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:
*UMD*TR-3605, January 1996
BibRef

And:
*ARPA96*(1251-1256).
BibRef

And:
*UMD*TR3581, 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

IEEE DOI

Multiclass Kernel Projection Machines. 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 .

Last update:Oct 24, 2021 at 16:35:58