18.9.3 Error Analysis of Motion and Structure Computations

Weng, J., Ahuja, N., and Huang, T.S.,
Optimal Motion and Structure Estimation,
PAMI(15), No. 9, September 1993, pp. 864-884.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9309
Earlier: CVPR89(144-152).
IEEE Abstract. IEEE Top Reference. Analysis of a number of factors in motion estimation comparing image error, epipolar error, linear algorithms, sequential, batch, IEKF, etc. See also 3-D Motion Estimation, Understanding, and Prediction from Noisy Image Sequences. BibRef

Weng, J.Y.[Ju-Yang], Huang, T.S., and Ahuja, N.[Narendra],
Motion and Structure from Two Perspective Views: Algorithms, Error Analysis, and Error Estimation,
PAMI(11), No. 5, May 1989, pp. 451-476.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 8905
Earlier:
Motion from Images: Image Matching Parameter Estimation and Intrinsic Stability,
Motion89(359-366). BibRef
And: (Possibly different author order):
Motion and Structure from Point Correspondences: A Robust Algorithm for Planar Case with Error Estimation,
ICPR88(I: 247-251).
WWW Version.
IEEE Top Reference. BibRef
And:
Error Analysis of Motion Parameter Estimation from Image Sequences,
ICCV87(703-707). Motion, Estimation evaluation. An interesting error analysis that indicates that the special case of motion toward (from) the observer is ideal. This depends the least on the Z component of the motion which is the worst (for direction of the motion). For matching: See also Matching Two Perspective Views. BibRef

Hu, X.P., Ahuja, N.,
Mirror Uncertainty and Uniqueness Conditions for Determining Shape and Motion from Orthographic Projection,
IJCV(13), No. 3, December 1994, pp. 295-309. BibRef 9412

Hu, X.P.[Xiao-Ping], Ahuja, N.[Narendra],
Sufficient Conditions for Double or Unique Solution of Motion and Structure,
CVGIP(58), No. 2, September 1993, pp. 161-176.
WWW Version. BibRef 9309
Earlier:
Necessary and sufficient conditions for a unique solution of plane motion and structure,
CAIP93(436-443).
WWW Version. 9309 BibRef

Kanatani, K.I.,
Unbiased Estimation and Statistical Analysis of 3-D Rigid Motion from Two Views,
PAMI(15), No. 1, January 1993, pp. 37-50.
IEEE Abstract. IEEE Top Reference.
WWW Version. Least-squares solution based on epipolar constraint is biased. BibRef 9301

Sohn, W., Kehtarnavaz, N.D.,
Analysis of Camera Movement Errors in Vision-Based Vehicle Tracking,
PAMI(17), No. 1, January 1995, pp. 57-61.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9501
And: Erratum: PAMI(17), No. 2, February 1995, pp. 224-224.
IEEE Top Reference. Analyze the errors from platform movement -- how they affect egomotion computations. BibRef

Kehtarnavaz, N.D., Sohn, W.,
Error Analysis Of Camera Movements In Stereo Vehicle Tracking-Systems,
CVIU(62), No. 3, November 1995, pp. 347-359.
WWW Version. BibRef 9511
Earlier:
Analysis of camera movements in stereo vision-based vehicle tracking,
ICIP94(II: 710-714).
WWW Version. 9411(Texas A&M) BibRef

Lin, Y.C., Tsai, Y.P., Hung, Y.P., Shih, Z.C.,
Comparison Between Immersion-Based and Toboggan-Based Watershed Image Segmentation,
IP(15), No. 3, March 2006, pp. 632-640.
WWW Version. 0604 BibRef

Tsai, C.J., Hung, Y.P., and Hsu, S.C.,
Comparison between Asymptotic Bayesian Approach and Kalman Filter-Based Technique for 3D Reconstruction Using an Image Sequence,
CVPR93(206-211).
IEEE Abstract. IEEE Top Reference. Small motions to get surfaces based on highly textured surfaces (image mapped on a cube or cylinder). BibRef 9300

Daniilidis, K., and Nagel, H.H.,
Analytic Results on Error Sensitivity of Motion Estimation from Two Views,
IVC(8), No. 4, November 1990, pp. 297-303.
Postscript Version. BibRef 9011
Earlier: ECCV90(199-208).
WWW Version. BibRef

Daniilidis, K.[Kostas], and Spetsakis, M.E.[Minas E.],
Understanding Noise Sensitivity in Structure from Motion,
VisNav93(xx-yy). BibRef 9300

Aloimonos, Y., and Brown, C.M.,
Perception of Structure from Motion: I: Optic Flow vs. Discrete Displacements; II: Lower Bound Results,
CVPR86(510-517). Motion, Structure Evaluation. The optic flow field contains much less information than the discrete displacements field. I.e. large motions beat small motions. BibRef 8600

Weldon, Jr., E.J., and Liu, H.,
How Accurately Can Direct Motion Vision Determine Depth,
CVPR91(613-618).
IEEE Abstract. IEEE Top Reference. Using "apparent size" it is about 3%. BibRef 9100

Dutta, R., and Snyder, M.A.,
Robustness of Structure from Binocular Known Motion,
Motion91(81-86). Structure from known motion, analysis of limits on results. Two frames, 40' away, move 4' a 10% error. Motion should be about 6 times a comparable stereo baseline. BibRef 9100

Dutta, R., and Snyder, M.A.,
Robustness of Correspondence-Based Structure from Motion,
ICCV90(106-110).
WWW Version. BibRef 9000
And: DARPA90(299-313). Analysis of rotational motions. Seems to agree with the expected results. BibRef

Bharwani, S.[Seraj], Riseman, E.M., and Hanson, A.R.,
Refinement of Environmental Depth Maps over Multiple Frames,
Motion86(73-80). BibRef 8600
And: DARPA85(413-420). Motion, Structure Evaluation. Multiple frames are used to eliminate ambiguities. Errors are inherent in computing depth from motion, with more estimates, maybe the results are better. BibRef

Thomas, J.I., Hanson, A.R., and Oliensis, J.,
Understanding Noise: The Critical Role of Motion Error in Scene Reconstruction,
ICCV93(325-329).
WWW Version. BibRef 9300
And: DARPA93(691-695). BibRef
And:
The Terms of Error Convariance Matrices and Their Effect on MFSFM,
UMassCS-TR-93-12, February 1993. BibRef

Thomas, J.I., Hanson, A.R.,
Applying Multiframe Reconstruction to Pose Estimation,
UMassCS-TR-93-11, February 1993. BibRef 9302

Maybank, S.J.,
Theory of Reconstruction from Image Motion,
Springer-VerlagBerlin, 1992. BibRef 9200

Maybank, S.J.,
Ambiguity in Reconstruction from Image Correspondences,
IVC(9), No. 2, April 1991, pp. 93-99.
WWW Version. BibRef 9104
Earlier: ECCV90(175-186).
WWW Version. Not much new. BibRef

Matthies, L.H., and Shafer, S.A.,
Error Modelling in Stereo Navigation,
RA(3), No. 3, 1987, pp. 239-248. BibRef 8700
Earlier: CMU-CS-TR-86-140, CMU CS Dept., 1986. The assumption is that motion is in a plane and the 2-D motion can be approximated with some errors. This is similar to the UMass error papers and does not seem to say a lot, except that it is possible. BibRef

Chaudhuri, S., Chatterjee, S.,
Performance Analysis of Total Least Squares Methods in Three-Dimensional Motion Estimation,
RA(7), 1991, pp. 707-714. BibRef 9100

Oliensis, J.[John],
A Critique of Structure-from-Motion Algorithms,
CVIU(80), No. 2, November 2000, pp. 172-214. 0012
WWW Version.
Postscript Version. BibRef
And: Errattum: CVIU(84), No. 3, December 2001, pp. 407-408.
WWW Version. 0207 BibRef

Oliensis, J.[John], Govindu, V.[Venu],
An Experimental Study of Projective Structure from Motion,
PAMI(21), No. 7, July 1999, pp. 665-671.
IEEE Abstract. IEEE Top Reference.
WWW Version.
Postscript Version. Comparison between Euclidean and projective approaches. Euclidean is as accurate as projective. Projective has less trouble with local-minima. BibRef 9907

Oliensis, J.[John],
A New Structure-from-Motion Ambiguity,
PAMI(22), No. 7, July 2000, pp. 685-700.
IEEE Abstract. IEEE Top Reference.
WWW Version.
Postscript Version. 0008 BibRef
Earlier: CVPR99(I: 185-191).
IEEE Abstract. IEEE Top Reference.
WWW Version. In Euclidean structure from motion, with large depth variations. Ambiguity noted in: See also Computing the Camera Heading from Multiple Frames. and See also Optimal Structure from Motion: Local Ambiguities and Global Estimates. Further discussed in: See also Recursive 3-D Visual-Motion Estimation Using Subspace Constraints. now explained. Also appears in See also Direction of Heading from Image Deformations. BibRef

Oliensis, J.[John],
Exact Two-Image Structure from Motion,
PAMI(24), No. 12, December 2002, pp. 1618-1633.
IEEE Abstract. IEEE Top Reference. 0212 BibRef

Jacobs, D.W.[David W.],
Linear Fitting with Missing Data for Structure-from-Motion,
CVIU(82), No. 1, April 2001, pp. 57-81.
WWW Version. 0104 Code, Surface Fitting. Code:
WWW Version. BibRef
Earlier:
Linear Fitting with Missing Data: Applications to Structure from Motion and to Characterizing Intensity Images,
CVPR97(206-212).
IEEE Abstract. IEEE Top Reference.
WWW Version. 9704Problems reduce to fitting surface to data. BibRef

Cheong, L.F.[Loong-Fah], Xiang, T.[Tao],
Characterizing Depth Distortion under Different Generic Motions,
IJCV(44), No. 3, September-October 2001, pp. 199-217.
WWW Version.
WWW Version. 0111 See also Depth distortion under calibration uncertainty. Given the errors in camera calibrations, what are the effects. For lateral motion, although Euclidean reconstruction is difficult, ordinal depth information is obtainable; while for forward motion, depth information (even partial one) is difficult to recover. BibRef

Xiang, T.[Tao], Cheong, L.F.[Loong-Fah],
On the distortion of shape recovery from motion,
IVC(22), No. 10, 1 September 2004, pp. 807-817.
WWW Version. 0409 BibRef

Xiang, T., Cheong, L.F.,
Distortion of Shape from Motion,
BMVC02(Poster Session). 0208 BibRef

Cheong, L.F.[Loong-Fah], Peh, C.H.[Chin-Hwee],
Depth distortion under calibration uncertainty,
CVIU(93), No. 3, March 2004, pp. 221-244.
WWW Version. 0402 See also Characterizing Depth Distortion under Different Generic Motions. BibRef

Cheong, L.F.[Loong-Fah],
Depth Perception Under Motion and Stereo with Implications for 3D TV,
3DTV07(1-4).
WWW Version. 0705 BibRef

Ma, Y.[Yi], Kosecká, J.[Jana], Sastry, S.[Shankar],
Linear Differential Algorithm for Motion Recovery: A Geometric Approach,
IJCV(36), No. 1, January 2000, pp. 71-89.
WWW Version. 9912 BibRef
Earlier:
Motion Recovery from Image Sequences: Discrete Viewpoint vs. Differential Viewpoint,
ECCV98(II: 337).
WWW Version. See also Differential Geometric Approach to Multiple View Geometry in Spaces of Constant Curvature, A. BibRef

Ma, Y.[Yi], Kosecká, J.[Jana], Sastry, S.[Shankar],
Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation,
IJCV(44), No. 3, September-October 2001, pp. 219-249.
WWW Version.
WWW Version. 0111Study the main aspects of motion and structure recovery: the choice of objective function, optimization techniques and sensitivity and robustness issues in the presence of noise. And the interactions. BibRef

Zhang, W.[Wei], Kosecka, J.[Jana],
Ensemble Method for Robust Motion Estimation,
RANSAC06(100).
WWW Version. 0609 BibRef
And:
Nonparametric Estimation of Multiple Structures with Outliers,
WDV06(60-74).
WWW Version. 0705 BibRef

Lingrand, D.[Diane],
An Exhaustive Study of Particular Cases Leading to Robust and Accurate Motion Estimation,
CVIU(85), No. 3, March 2002, pp. 159-188.
WWW Version. 0211 BibRef

Xiang, T.[Tao], Cheong, L.F.[Loong-Fah],
Understanding the Behavior of SFM Algorithms: A Geometric Approach,
IJCV(51), No. 2, February 2003, pp. 111-137.
WWW Version. 0301 BibRef

Cheong, L.F.[Loong-Fah], Li, S.M.[Shi-Miao],
Error Analysis of SFM Under Weak-Perspective Projection,
ACCV06(II:862-871).
WWW Version. 0601 BibRef

Cheong, L.F.[Loong-Fah], Xiang, X.[Xu],
Error Characteristics of SFM with Erroneous Focal Length,
ACCV06(I:714-723).
WWW Version. 0601 BibRef

Roy Chowdhury, A.K.[Amit K.], and Chellappa, R.[Rama],
Stochastic Approximation and Rate-Distortion Analysis for Robust Structure and Motion Estimation,
IJCV(55), No. 1, September 2003, pp. 27-53.
WWW Version. 0307 BibRef
And: UMD--TR4261, June 2001.
WWW Version.
WWW Version. Focus on sources of errors, experimental and theoretical analysis, robust and information-theoretic techniques to characterize the quality of reconstruction. BibRef

Roy Chowdhury, A.K., Chellappa, R.,
An Information Theoretic Criterion for Evaluating the Quality of 3-D Reconstructions from Video,
IP(13), No. 7, July 2004, pp. 960-973.
WWW Version. 0406 BibRef

Roy Chowdhury, A.K.[Amit K.], Chellappa, R.[Rama],
Statistical Analysis of 3d Modeling From Monocular Video Streams,
UMD-- TR4383, July 2002.
WWW Version.
WWW Version. BibRef 0207

Roy Chowdhury, A.K.[Amit K.], Chellappa, R.[Rama],
Face reconstruction from monocular video using uncertainty analysis and a generic model,
CVIU(91), No. 1-2, July-August 2003, pp. 188-213.
WWW Version. 0309 BibRef

Roy Chowdhury, A.K.[Amit K.], Chellappa, R.[Rama],
Statistical bias in 3-D reconstruction from a monocular video,
IP(14), No. 8, August 2005, pp. 1057-1062.
WWW Version. 0508 BibRef
Earlier:
Statistical Bias and the Accuracy of 3d Reconstruction from Video,
UMD-- TR4303, November 2001.
WWW Version.
WWW Version. BibRef

Roy Chowdhury, A.K., Chellappa, R.,
Robust Estimation of Depth and Motion Using Stochastic Approximation,
ICIP01(I: 642-645).
IEEE Abstract. IEEE Top Reference. 0108 BibRef

Agrawal, A.K.[Amit K.], Chellappa, R.[Rama],
Robust Ego-Motion Estimation and 3-D Model Refinement Using Surface Parallax,
IP(15), No. 5, May 2006, pp. 1215-1225.
WWW Version. 0605 BibRef
Earlier:
Ego-Motion Estimation and 3D Model Refinement in Scenes with Varying Illumination,
Motion05(II: 140-146).
WWW Version. 0502 BibRef
Earlier:
Robust ego-motion estimation and 3d model refinement using depth based parallax model,
ICIP04(IV: 2483-2486).
WWW Version. 0505 BibRef

Chen, P.[Pei], Suter, D.[David],
Recovering the Missing Components in a Large Noisy Low-Rank Matrix: Application to SFM,
PAMI(26), No. 8, August 2004, pp. 1051-1063.
IEEE Abstract. IEEE Top Reference. 0407Structure from motion with missing data. See also Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling. See also Linear Fitting with Missing Data for Structure-from-Motion. BibRef

Lu, Y.[Ye], Zhang, J.Z., Wu, Q.M.J., Li, Z.N.[Ze-Nian],
A survey of motion-parallax-based 3-D reconstruction algorithms,
SMC-C(34), No. 4, December 2004, pp. 532-548.
IEEE Abstract. IEEE Top Reference. 0412 Survey, Motion Parallax. BibRef

Zucchelli, M.[Marco], Kosecka, J.[Jana],
Motion bias and structure distortion induced by intrinsic calibration errors,
IVC(26), No. 5, May 2008, pp. 639-646.
WWW Version. 0803 BibRef
Earlier:
Motion bias and structure distortion induced by calibration errors,
BMVC01(Session 7: Geometry &. Structure).
HTML Version. Royal Institute of Technology 0110Structure and motion recovery; Calibration sensitivity; Optical flow BibRef

Nister, D.[David], Kahl, F.[Fredrik], Stewenius, H.[Henrik],
Structure from Motion with Missing Data is NP-Hard,
ICCV07(1-7).
WWW Version. 0710 BibRef

Nister, D.[David], Hartley, R.I.[Richard I.], Stewenius, H.[Henrik],
Using Galois Theory to Prove Structure from Motion Algorithms are Optimal,
CVPR07(1-8).
WWW Version. 0706 BibRef

Jähne, B.[Bernd], Garbe, C.S.,
Towards objective performance analysis for estimation of complex motion: analytic motion modeling, filter optimization, and test sequences,
ICIP03(III: 73-76).
IEEE Abstract. IEEE Top Reference. 0312 BibRef

Betke, M.[Margrit], Naftali, E.[Eran], and Makris, N.C.[Nicholas C.],
Necessary Conditions to Attain Performance Bounds on Structure and Motion Estimates of Rigid Objects,
CVPR01(II:448-455).
IEEE Abstract. IEEE Top Reference. 0110Study Cramer-Rao lower bound issues. Noise level, number of pixels and texture. BibRef

Haddon, J.[John], Forsyth, D.A.[David A.],
Noise in Bilinear Problems,
ICCV01(II: 622-627).
WWW Version. 0106Analysis of noise and its effects. BibRef

Torr, P.H.S.,
An Assessment of Information Criteria for Motion Model Selection,
CVPR97(47-52).
IEEE Abstract. IEEE Top Reference.
WWW Version. 9704Evaluation of criteria. BibRef

Boufama, B., Weinshall, D., Werman, M.,
Shape from Motion Algorithms: A Comparative Analysis of Scaled Orthography and Perspective,
ECCV94(A:197-204).
WWW Version. BibRef 9400

Xuening, S., and Spetsakis, M.E.,
A Comparison of Weighted LS Methods with LS Methods in 3-D Motion Estimation from Stereo Image Sequences,
CVPR93(200-205).
IEEE Abstract. IEEE Top Reference. BibRef 9300