18.6.2 Focus of Expansion and Other Features

Schalkoff, R.J.[Robert J.],
Distributed Parameter Systems Approach to Feature Extraction and Motion Estimation in Image Sequences,
IVC(1), No. 4, November 1983, pp. 227-233.
Elsevier DOI BibRef 8311

Schalkoff, R.J.[Robert J.],
Analysis of the Weak Solution Approach to Image Motion Estimation,
PR(20), No. 2, 1987, pp. 189-197.
Elsevier DOI BibRef 8700
Earlier:
Image Motion Analysis Using the Concept of Weak Solutions to Distributed Parameter Systems,
CVPR83(232-239). The discussion does not compare itself to other techniques. BibRef

Schalkoff, R.J.[Robert J.],
Dynamic Imagery Modeling and Motion Estimation Using Weak Formulations,
PAMI(9), No. 4, July 1987, pp. 578-584. A feature based approach. Unclear where it fits in. BibRef 8707

Subbarao, M.[Muralidhara],
Bounds on Time-to-Collision and Rotational Component from First-Order Derivatives of Image Flow,
CVGIP(50), No. 3, June 1990, pp. 329-341.
Elsevier DOI BibRef 9006
Earlier:
Bounds on Translational and Angular Velocity Components from First Order Derivatives of Image Flow,
AAAI-87(744-748). For rigid motion. BibRef

Negahdaripour, S.[Shahriar], Horn, B.K.P.,
A Direct Method for Locating the Focus of Expansion,
CVGIP(46), No. 3, June 1989, pp. 303-326.
Elsevier DOI BibRef 8906
And: A1 only: MIT AI Memo-939, January 1987. The FOE is in front of the camera, this reduces the ambiguities. Analyze the spatial gradient and change in brightness to get the FOE. BibRef

Negahdaripour, S., and Horn, B.K.P.,
Using Depth-is-Positive Constraint to Recover Translational Motion,
CVWS87(138-144). BibRef 8700

Negahdaripour, S., and Ganesan, V.,
Simple Direct Computation of the FOE with Confidence Measures,
CVPR92(228-235).
IEEE DOI Estimate the FOE (many estimates), compute a new one from these estimates. BibRef 9200

Jain, R.C.[Ramesh C.],
Direct Computation of the Focus of Expansion,
PAMI(5), No. 1, January 1983, pp. 58-64. Log Mapping. BibRef 8301
Earlier:
An Approach for the Direct Computation of the Focus of Expansion,
PRIP82(262-268). The focus of expansion is useful for computing the optic flow. This paper seems to give a method that works for very clean data with a moving observer. The FOE can be outside of the image. BibRef

Jain, R.C.[Ramesh C.],
Complex Logarithmic Mapping and the Focus of Expansion,
Motion83(42-49). Log Mapping. This introduces the mapping that he is using in the other recent (83-84) papers. BibRef 8300

Campani, M.[Marco], Verri, A.[Alessandro],
Motion Analysis from First-Order Properties of Optical Flow,
CVGIP(56), No. 1, July 1992, pp. 90-107.
Elsevier DOI BibRef 9207
Earlier:
Computing Optical Flow from an Overconstrained System of Linear Algebraic Equations,
ICCV90(22-26).
IEEE DOI BibRef
And: A2, A1:
An Algebraic Procedure for the Computation of Optical Flow from First Order Derivatives of the Image Brightness,
Robust90(xx). Piecewise linear vector field. BibRef

Poggio, T.[Tomaso], Verri, A.[Alessandro], Torre, V.[Vincent],
Green Theorems and Qualitative Properties of the Optical Flow,
MIT AI Memo-1289, April 1991.
WWW Link. BibRef 9104

Tistarelli, M., and Sandini, G.,
On the Advantage of Polar and Log-Polar Mapping for Direct Estimation of Time-to-Impact from Optical Flow,
PAMI(15), No. 4, April 1993, pp. 401-410.
IEEE DOI Log Mapping.
See also Dynamic Aspects in Active Vision. Using a Log-Polar sensor the basic computations are easier. Time to impact computations. BibRef 9304

Tistarelli, M., and Sandini, G.,
Direct Estimation of Time-to-Impact from Optical Flow,
Motion91(226-233). Active Vision, Sensor. Log Mapping. Using a CLM like sensor for depth computation. BibRef 9100

Sandini, G., and Tistarelli, M.,
Robust Obstacle Detection Using Optical Flow,
Robust90(xx). BibRef 9000

Pollastri, F.,
Projection Center Calibration by Motion,
PRL(14), No. 12, December 1993, pp. 975-983. BibRef 9312

Li, H.,
Global Interpretation Of Optical Flow Field: A Least-Squares Approach,
ICPR92(I:668-671).
IEEE DOI BibRef 9200

Enkelmann, W.[Wilfried],
Obstacle Detection by Evaluation of Optical Flow Fields from Image Sequences,
IVC(9), No. 3, June 1991, pp. 160-168.
Elsevier DOI BibRef 9106
Earlier: ECCV90(134-138).
Springer DOI 2D optical flow to infer 3D object structure. BibRef

Negahdaripour, S.,
Direct Computation of the FOE with Confidence Measures,
CVIU(64), No. 3, November 1996, pp. 323-350. 9612

DOI Link BibRef

Heikkonen, J.[Jukka],
Recovering 3-D Motion Parameters from Optical Flow Field Using Randomized Hough Transform,
PRL(16), 1995, pp. 971-978. BibRef 9500
Earlier:
Recovering translational motion parameters from image sequences using Randomized Hough Transform,
CAIP93(395-402).
Springer DOI 9309
BibRef

Heikkonen, J.,
Video recording and digital image processing in analyzing air flows,
ICPR92(I:129-132).
IEEE DOI 9208
BibRef

Arnspang, J., Ma, J.,
Image Irradiance Equations for a Zooming Camera,
PRL(10), 1989, pp. 189-194. BibRef 8900

Branca, A., Stella, E., Attolico, G., Distante, A.,
Focus of Expansion Estimation by an Error Backpropagation Neural-Network,
NeurCompApp(6), No. 3, 1997, pp. 142-147. 9803
BibRef

Florack, L.M.J., Niessen, W.J., Nielsen, M.,
The Intrinsic Structure of Optic Flow Incorporating Measurement Duality,
IJCV(27), No. 3, May 1998, pp. 263-286.
DOI Link 9805
BibRef

Nielsen, M.[Mads], Niessen, W.J., Maas, R., Florack, L.M.J., ter Haar Romeny, B.M.,
On the Duality of Scalar and Density Flows,
ScaleSpace97(xx). 9702
BibRef

Olsen, O.F.[Ole Fogh], Nielsen, M.[Mads],
The Generic Structure of the Optic Flow Field,
JMIV(24), No. 1, January 2006, pp. 37-53.
Springer DOI 0605
BibRef
Earlier: A2, A1:
The structure of the optic flow field,
ECCV98(II: 271).
Springer DOI BibRef

Olsen, O.F.[Ole Fogh], Nielsen, M.,
Generic Events for the Gradient Squared with Application to Multi-Scale Segmentation,
ScaleSpace97(xx). 9702
BibRef

McQuirk, I.S., Horn, B.K.P., Lee, H.S., Wyatt, J.L.,
Estimating the Focus of Expansion in Analog VLSI,
IJCV(28), No. 3, July/August 1998, pp. 261-277.
DOI Link 9809
BibRef

Duric, Z.[Zoran], Rosenfeld, A.[Azriel], Duncan, J.[James],
The Applicability of Green's Theorem to Computation of Rate of Approach,
IJCV(31), No. 1, February 1999, pp. 83-98.
DOI Link BibRef 9902
Earlier: A1, A3, A2: ARPA94(II:1209-1217). BibRef

Cucka, P.[Peter], Duric, Z.[Zoran], Rivlin, E.[Ehud], Rosenfeld, A.[Azriel],
Qualitative Description of Camera Motion and Scene Depth from Histograms of Normal Flow,
UMD--TR3925, August 1998. Flow Histogram.
WWW Link. BibRef 9808

Duric, Z.[Zoran], Rivlin, E.[Ehud], Rosenfeld, A.[Azriel],
Quantative Description of Camera Motion from Histograms of Normal Flow,
DARPA98(979-986). BibRef 9800

Duric, Z.[Zoran], Rivlin, E.[Ehud], Rosenfeld, A.[Azriel],
Qualitative Description of Camera Motion from Histograms of Normal Flow,
ICPR00(Vol III: 194-198).
IEEE DOI 0009
BibRef

Menéndez, J.M.[José M.], García, N.[Narciso], Salgado, L.[Luis], Rendón, E.[Enrique],
Model-based analytical FOE determination,
SP:IC(14), No. 10, August 1999, pp. 785-798.
Elsevier DOI BibRef 9908
Earlier:
An algorithm for FOE localization,
ICIP96(III: 811-814).
IEEE DOI 9610
FoE from vector field. BibRef

Srinivasan, S.[Sridhar],
Extracting Structure from Optical Flow Using the Fast Error Search Technique,
IJCV(37), No. 3, June 2000, pp. 203-230.
DOI Link 0008
BibRef
And: UMD--TR3923, August 1998. Fast Partial Search.
WWW Link. BibRef
Earlier:
Fast Partial Search Solution to the 3D SFM Problem,
ICCV99(528-535).
IEEE DOI BibRef
And:
Fast FOE Estimation with Applications to Depth Estimation and View Synthesis,
DARPA98(987-994). FOE estimation from optical flow. BibRef

Yeasin, M.[Mohammed],
Optical Flow in Log-Mapped Image Plane-A New Approach,
PAMI(24), No. 1, January 2002, pp. 125-131.
IEEE DOI 0201
New approach allows for image intensity variations. BibRef

Sazbon, D.[Didi], Rotstein, H.P.[Héctor P.], Rivlin, E.[Ehud],
Finding the focus of expansion and estimating range using optical flow images and a matched filter,
MVA(15), No. 4, October 2004, pp. 229-236.
Springer DOI 0410
BibRef

Xiong, Y.L.[Ya-Lin], Olson, C.F.[Clark F.], Matthies, L.H.[Larry H.],
Computing Depth Maps from Descent Imagery,
MVA(16), No. 3, May 2005, pp. 139-147.
Springer DOI 0505
BibRef
Earlier: CVPR01(I:392-397).
IEEE DOI 0110
Depth maps from descending space probes. BibRef

Wu, F.C., Wang, L., Hu, Z.Y.,
FOE estimation: Can image measurement errors be totally 'corrected' by the geometric method?,
PR(40), No. 7, July 2007, pp. 1971-1980.
Elsevier DOI 0704
FOE estimation; Geometric method; Inherent constraint BibRef

Mochizuki, Y., Imiya, A.,
Spatial reasoning for robot navigation using the Helmholtz-Hodge decomposition of omnidirectional optical flow,
IVCNZ09(1-6).
IEEE DOI 0911
BibRef

Mochizuki, Y.[Yoshihiko], Kameda, Y.[Yusuke], Imiya, A.[Atsushi], Sakai, T.[Tomoya], Imaizumi, T.[Takashi],
An Iterative Method for Superresolution of Optical Flow Derived by Energy Minimisation,
ICPR10(2270-2273).
IEEE DOI 1008
BibRef

Mochizuki, Y.[Yoshihiko], Kameda, Y.[Yusuke], Imiya, A.[Atsushi], Sakai, T.[Tomoya], Imaizumi, T.[Takashi],
Two Step Variational Method for Subpixel Optical Flow Computation,
ISVC09(II: 1109-1118).
Springer DOI 0911
BibRef

Kashu, K.[Koji], Imiya, A.[Atsushi], Sakai, T.[Tomoya],
Subvoxel Super-Resolution of Volumetric Motion Field Using General Order Prior,
ISVC11(II: 270-279).
Springer DOI 1109
BibRef
Earlier:
Multiscale Analysis of Volumetric Motion Field Using General Order Prior,
ISVC10(I: 561-570).
Springer DOI 1011
BibRef

Kashu, K.[Koji], Kameda, Y.[Yusuke], Narita, M.[Masaki], Imiya, A.[Atsushi], Sakai, T.[Tomoya],
Continuity Order of Local Displacement in Volumetric Image Sequence,
WBIR10(48-59).
Springer DOI 1007
BibRef

Kashu, K.[Koji], Kameda, Y.[Yusuke], Imiya, A.[Atsushi], Sakai, T.[Tomoya], Mochizuki, Y.,
Computing the Local Continuity Order of Optical Flow Using Fractional Variational Method,
EMMCVPR09(154-167).
Springer DOI 0908
BibRef

Kameda, Y.[Yusuke], Imiya, A.[Atsushi],
The William Harvey Code: Mathematical Analysis of Optical Flow Computation for Cardiac Motion,
HumMotBook08(4). 0802
BibRef
Earlier:
Classification of Optical Flow by Constraints,
CAIP07(61-68).
Springer DOI 0708
BibRef

Suhr, J.K.[Jae Kyu], Jung, H.G.[Ho Gi], Bae, K.H.[Kwang-Hyuk], Kim, J.H.[Jai-Hie],
Outlier rejection for cameras on intelligent vehicles,
PRL(29), No. 6, 15 April 2008, pp. 828-840.
Elsevier DOI 0803
Outlier rejection; Motion constraint; Focus of expansion; Automobile motion; Intelligent vehicle BibRef

Markussen, B.[Bo], Sporring, J.[Jon], Erleben, K.[Kenny],
Guessing Tangents in Normal Flows,
JMIV(31), No. 2-3, July 2008, pp. 195-205.
WWW Link. 0711
BibRef

Maybank, S.J.,
Approximation to the Fisher-Rao metric for the focus of expansion,
Neurocomputing(71), 2008, pp. 2037-2045.
PDF File. BibRef 0800

Xu, D.H.[Da-Hong], Wang, R.S.[Run-Sheng],
An Improved FoE Model for Image Deblurring,
IJCV(81), No. 2, February 2009, pp. xx-yy.
Springer DOI 0901
BibRef

Gil-Jiménez, P.[Pedro], Gómez-Moreno, H.[Hilario], López-Sastre, R.J.[Roberto J.], Bermejillo-Martín-Romo, A.[Alberto],
Estimating the focus of expansion in a video sequence using the trajectories of interest points,
IVC(50), No. 1, 2016, pp. 14-26.
Elsevier DOI 1606
Focus of expansion BibRef

Skelton, P.S.M.[Phillip S.M.], Finn, A.[Anthony], Brinkworth, R.S.A.[Russell S.A.],
Consistent estimation of rotational optical flow in real environments using a biologically-inspired vision algorithm on embedded hardware,
IVC(92), 2019, pp. 103814.
Elsevier DOI 1912
BibRef
Earlier:
Real-Time Visual Rotational Velocity Estimation Using a Biologically-Inspired Algorithm on Embedded Hardware,
DICTA17(1-8)
IEEE DOI 1804
Optical flow, Biologically inspired, Rotational velocity, Embedded hardware, Robotic sensing. image sequences, motion estimation, real-time systems, biologically-inspired egomotion estimator, BibRef

Aristidou, A.[Andreas], Cameron, J.[Jonathan], Lasenby, J.[Joan],
Predicting Missing Markers to Drive Real-Time Centre of Rotation Estimation,
AMDO08(xx-yy).
Springer DOI 0807
BibRef

Mochizuki, Y.[Yoshihiko], Imiya, A.[Atsushi],
Multiresolution Optical Flow Computation of Spherical Images,
CAIP11(II: 348-355).
Springer DOI 1109
BibRef

Kameda, Y.[Yusuke], Ohnishi, N.[Naoya], Imiya, A.[Atsushi], Sakai, T.[Tomoya],
Optical Flow Computation from an Asynchronised Multiresolution Image Sequence,
ISVC09(I: 403-414).
Springer DOI 0911
BibRef

Kameda, Y.[Yusuke], Imiya, A.[Atsushi], Ohnishi, N.[Naoya],
A Convergence Proof for the Horn-Schunck Optical-Flow Computation Scheme Using Neighborhood Decomposition,
IWCIA08(xx-yy).
Springer DOI 0804
BibRef

Kameda, Y.[Yusuke], Imiya, A.[Atsushi], Sakai, T.[Tomoya],
Hierarchical Properties of Multi-resolution Optical Flow Computation,
CVVT12(II: 576-585).
Springer DOI 1210
BibRef

Ohnishi, N.[Naoya], Kameda, Y.[Yusuke], Imiya, A.[Atsushi], Dorst, L.[Leo], Klette, R.[Reinhard],
Dynamic Multiresolution Optical Flow Computation,
RobVis08(1-15).
Springer DOI 0802
BibRef

Gebert, G., Snyder, D., Lopez, J., Siddiqi, N., Evers, J.,
Optical flow angular rate determination,
ICIP03(I: 949-952).
IEEE DOI 0312
BibRef

Salgian, G.[Garbis], Ballard, D.H.[Dana H.],
Looming Detection in Log-Polar Coordinates,
DARPA98(165-170). BibRef 9800

Fleet, D.J.[David J.], Black, M.J.[Michael J.], Jepson, A.D.[Allan D.],
Motion Feature Detection Using Steerable Flow Fields,
CVPR98(274-281).
IEEE DOI BibRef 9800

Branca, A., Stella, E., and Distante, A.,
Passive Navigation Using Focus of Expansion,
WACV96(64-69).
IEEE DOI 9609
BibRef

Carlsson, S., and Eklundh, J.O.,
Object Detection Using Model Based Prediction and Motion Parallax,
ECCV90(297-306).
Springer DOI Optic flow is not as expected, thus an obstacle. BibRef 9000

Guissin, R., Ullman, S.,
Direct Computation of the Focus of Expansion from Velocity Field Measurements,
Motion91(146-155). Log-Polar. BibRef 9100

Castelow, D.A., Rerolle, A.J.,
A Monocular Ground Plane Estimation System,
BMVC91(xx-yy).
PDF File. 9109
BibRef

Chapter on Optical Flow Field Computations and Use continues in
Obstacle Detection, Time to Collision Techniques .