Invariants, Projective, Perspective

Chapter Contents (Back)
Invariants, Three-Dimensional.

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
Some Invariant Linear Methods in Photogrammetry and Model-Matching,
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
DOI Link DARPA98(641-652). BibRef
3D Curve Reconstruction from Uncalibrated Cameras,
ICPR96(I: 323-327).
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.
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

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

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
Computing projective and permutation invariants of points and lines,
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
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.
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

Chung, R.[Ronald],
Relative Viewing Distance: A Correspondence Invariance under Paraperspective Projection,
CVIU(86), No. 1, April 2002, pp. 1-31.
DOI Link 0211

Takerkart, S.[Sylvain], Ralaivola, L.[Liva],
MKPM: A multiclass extension to the kernel projection machine,
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

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).

Vicente, M.A., Gil, P., Reinoso, O., Torres, F.,
Objects Recognition by Means of Projective Invariants Considering Corner-points,
PDF File.
HTML Version. 0209

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:Jul 18, 2024 at 20:50:34