1711:
1723:), the sequence is now described as well as it needs to be. However, in the field of machine vision, the question of whether the ball is moving to the right or if the observer is moving to the left is unknowable yet critical information. Not even if a static, patterned background were present in the five frames, could we confidently state that the ball was moving to the right, because the pattern might have an infinite distance to the observer.
31:
951:
657:
96:
Sequences of ordered images allow the estimation of motion as either instantaneous image velocities or discrete image displacements. Fleet and Weiss provide a tutorial introduction to gradient based optical flow. John L. Barron, David J. Fleet, and Steven
Beauchemin provide a performance analysis of
1718:
Consider a five-frame clip of a ball moving from the bottom left of a field of vision, to the top right. Motion estimation techniques can determine that on a two dimensional plane the ball is moving up and to the right and vectors describing this motion can be extracted from the sequence of frames.
1680:
have developed as a major aspect of optical flow research. While the optical flow field is superficially similar to a dense motion field derived from the techniques of motion estimation, optical flow is the study of not only the determination of the optical flow field itself, but also of its use in
1644:
Discrete optimization methods – the search space is quantized, and then image matching is addressed through label assignment at every pixel, such that the corresponding deformation minimizes the distance between the source and the target image. The optimal solution is often recovered through
773:
807:
1066:
472:
1738:
Various configurations of optical flow sensors exist. One configuration is an image sensor chip connected to a processor programmed to run an optical flow algorithm. Another configuration uses a vision chip, which is an integrated circuit having both the
1754:
techniques to implement circuits that respond to optical flow, and thus may be appropriate for use in an optical flow sensor. Such circuits may draw inspiration from biological neural circuitry that similarly responds to optical flow.
1579:
of the optical flow algorithms. To find the optical flow another set of equations is needed, given by some additional constraint. All optical flow methods introduce additional conditions for estimating the actual flow.
68:
have further demonstrated the role of the optical flow stimulus for the perception of movement by the observer in the world; perception of the shape, distance and movement of objects in the world; and the control of
671:
416:
946:{\displaystyle {\frac {\partial I}{\partial x}}{\frac {\Delta x}{\Delta t}}+{\frac {\partial I}{\partial y}}{\frac {\Delta y}{\Delta t}}+{\frac {\partial I}{\partial t}}{\frac {\Delta t}{\Delta t}}=0}
962:
2346:
1307:
1268:
1229:
652:{\displaystyle I(x+\Delta x,y+\Delta y,t+\Delta t)=I(x,y,t)+{\frac {\partial I}{\partial x}}\,\Delta x+{\frac {\partial I}{\partial y}}\,\Delta y+{\frac {\partial I}{\partial t}}\,\Delta t+{}}
1769:
applications, primarily where there is a need to measure visual motion or relative motion between the robot and other objects in the vicinity of the robot. The use of optical flow sensors in
1568:
34:
The optic flow experienced by a rotating observer (in this case a fly). The direction and magnitude of optic flow at each location is represented by the direction and length of each arrow.
1508:
1681:
estimating the three-dimensional nature and structure of the scene, as well as the 3D motion of objects and the observer relative to the scene, most of them using the image
Jacobian.
1620:– optimizing a functional based on residuals from the brightness constancy constraint, and a particular regularization term expressing the expected smoothness of the flow field
1699:
of objects and the environment. Since awareness of motion and the generation of mental maps of the structure of our environment are critical components of animal (and human)
1608:
Differential methods of estimating optical flow, based on partial derivatives of the image signal and/or the sought flow field and higher-order partial derivatives, such as:
1747:. In some cases the processing circuitry may be implemented using analog or mixed-signal circuits to enable fast optical flow computation using minimal current consumption.
1109:
147:
1623:
1190:
799:
460:
314:
291:
268:
245:
1345:
204:
1629:
1426:
1399:
1372:
2025:
1149:
1129:
118:
1657:
Many of these, in addition to the current state-of-the-art algorithms are evaluated on the
Middlebury Benchmark Dataset. Other popular benchmark datasets are
53:
between an observer and a scene. Optical flow can also be defined as the distribution of apparent velocities of movement of brightness pattern in an image.
1695:
The application of optical flow includes the problem of inferring not only the motion of the observer and objects in the scene, but also the
76:
The term optical flow is also used by roboticists, encompassing related techniques from image processing and control of navigation including
768:{\displaystyle {\frac {\partial I}{\partial x}}\Delta x+{\frac {\partial I}{\partial y}}\Delta y+{\frac {\partial I}{\partial t}}\Delta t=0}
60:
in the 1940s to describe the visual stimulus provided to animals moving through the world. Gibson stressed the importance of optic flow for
1743:
and the processor on the same die, allowing for a compact implementation. An example of this is a generic optical mouse sensor used in an
2579:
2203:
326:
2585:
157:
approximations of the image signal; that is, they use partial derivatives with respect to the spatial and temporal coordinates.
1061:{\displaystyle {\frac {\partial I}{\partial x}}V_{x}+{\frac {\partial I}{\partial y}}V_{y}+{\frac {\partial I}{\partial t}}=0}
2395:
2213:
2158:"Application of Local Optical Flow Methods to High-Velocity Free-surface Flows: Validation and Application to Stepped Chutes"
2081:
2003:
1864:
1837:
2549:
2385:
1854:
2619:
1827:
1273:
1234:
1195:
2523:
2420:
1519:
1437:
2249:
Baker, Simon; Scharstein, Daniel; Lewis, J. P.; Roth, Stefan; Black, Michael J.; Szeliski, Richard (March 2011).
2490:
2457:
2157:
1575:
1639:– a range of modifications/extensions of Horn–Schunck, using other data terms and other smoothness terms.
1599:
1881:
100:
The optical flow methods try to calculate the motion between two image frames which are taken at times
64:, the ability to discern possibilities for action within the environment. Followers of Gibson and his
17:
1703:, the conversion of this innate ability to a computer capability is similarly crucial in the field of
2514:
Floreano, Dario; Zufferey, Jean-Christophe; Srinivasan, Mandyam V.; Ellington, Charlie, eds. (2009).
2066:
2298:
Baker, Simon; Scharstein, Daniel; Lewis, J. P.; Roth, Stefan; Black, Michael J.; Szeliski, Richard.
1984:
1982:
2118:
1751:
1692:. Optical flow information has been recognized as being useful for controlling micro air vehicles.
1646:
1979:
1770:
1617:
1611:
1074:
123:
2113:
2098:
1797:
1154:
781:
424:
296:
273:
250:
209:
1312:
171:
97:
a number of optical flow techniques. It emphasizes the accuracy and density of measurements.
65:
2172:
1593:
1404:
1377:
1350:
8:
2574:
2327:
2184:
1802:
1782:
1636:
85:
2176:
1762:, as the main sensing component for measuring the motion of the mouse across a surface.
1688:
and tracking, image dominant plane extraction, movement detection, robot navigation and
2554:
2366:
2280:
2131:
2047:
1968:
1650:
1573:
This is an equation in two unknowns and cannot be solved as such. This is known as the
1134:
1114:
665:
By truncating the higher order terms (which performs a linearization) it follows that:
659:
103:
81:
2529:
2519:
2496:
2486:
2463:
2453:
2446:
2426:
2416:
2391:
2370:
2272:
2209:
2077:
1999:
1990:
1960:
1900:
1860:
1833:
1732:
1700:
1677:
1673:
1603:
1589:
70:
1972:
2358:
2262:
2180:
2135:
2123:
2051:
2037:
1950:
1904:
1896:
1685:
77:
46:
2284:
1955:
1938:
1689:
57:
50:
2153:
1704:
2362:
2267:
2250:
153:
position. These methods are called differential since they are based on local
2613:
2533:
2430:
2276:
1792:
1787:
1773:, for stability and obstacle avoidance, is also an area of current research.
1759:
1744:
463:
154:
2500:
2467:
1964:
1807:
1740:
84:, time-to-contact information, focus of expansion calculations, luminance,
2230:
2042:
1939:"Use of speed cues in the detection of moving objects by moving observers"
1829:
Thinking in
Perspective: Critical Essays in the Study of Thought Processes
1710:
27:
Pattern of motion in a visual scene due to relative motion of the observer
2323:
2228:
2199:
1989:
Aires, Kelson R. T.; Santana, Andre M.; Medeiros, Adelardo A. D. (2008).
56:
The concept of optical flow was introduced by the
American psychologist
2127:
1908:
1856:
Electronic
Spatial Sensing for the Blind: Contributions from Perception
61:
2603:
2597:
2591:
2232:
Dense Image
Registration through MRFs and Efficient Linear Programming
2565:
2299:
2229:
B. Glocker; N. Komodakis; G. Tziritas; N. Navab; N. Paragios (2008).
2019:
2017:
2015:
1696:
1684:
Optical flow was used by robotics researchers in many areas such as:
2570:
2513:
1766:
2560:
2097:
Barron, John L.; Fleet, David J. & Beauchemin, Steven (1994).
2012:
2197:
2072:. In Paragios, Nikos; Chen, Yunmei; Faugeras, Olivier D. (eds.).
1614:– regarding image patches and an affine model for the flow field
49:
of objects, surfaces, and edges in a visual scene caused by the
1714:
The optical flow vector of a moving object in a video sequence.
1662:
1598:
Block-based methods – minimizing sum of squared differences or
2566:
Middlebury
Optical flow evaluation and ground truth sequences.
30:
2557:
article on fxguide.com (using optical flow in visual effects)
1658:
150:
1626:– based on a model of the motion of edges in image sequences
411:{\displaystyle I(x,y,t)=I(x+\Delta x,y+\Delta y,t+\Delta t)}
1720:
421:
Assuming the movement to be small, the image constraint at
2594:
Online demo and source code of the Horn and
Schunck method
2347:"Biologically inspired visual sensing and flight control"
2483:
Analog VLSI circuits for the perception of visual motion
2345:
Barrows, G. L.; Chahl, J. S.; Srinivasan, M. V. (2003).
2251:"A Database and Evaluation Methodology for Optical Flow"
2248:
2582:
GPU implementation of a Lucas-Kanade based optical flow
2344:
1880:
Horn, Berthold K.P.; Schunck, Brian G. (August 1981).
1758:
Optical flow sensors are used extensively in computer
1278:
1239:
1200:
2606:
Online demo and source code of the Brox et al. method
2600:
Online demo and source code of the Zach et al. method
2096:
1522:
1440:
1428:
can be written for the derivatives in the following.
1407:
1380:
1353:
1315:
1276:
1237:
1198:
1157:
1137:
1117:
1077:
965:
810:
784:
674:
475:
427:
329:
299:
276:
253:
212:
174:
126:
106:
2297:
1988:
2561:
Optical flow evaluation and ground truth sequences.
2445:
2074:Handbook of Mathematical Models in Computer Vision
1562:
1502:
1420:
1393:
1366:
1339:
1301:
1262:
1223:
1184:
1143:
1123:
1103:
1060:
945:
793:
767:
651:
454:
410:
308:
285:
262:
239:
198:
141:
112:
1302:{\displaystyle {\tfrac {\partial I}{\partial t}}}
1263:{\displaystyle {\tfrac {\partial I}{\partial y}}}
1224:{\displaystyle {\tfrac {\partial I}{\partial x}}}
2611:
2023:
1750:One area of contemporary research is the use of
316:between the two image frames, and the following
1563:{\displaystyle \nabla I\cdot {\vec {V}}=-I_{t}}
2485:. Chichester, England: John Wiley & Sons.
1151:components of the velocity or optical flow of
1853:Warren, David H.; Strelow, Edward R. (1985).
1852:
1825:
1719:For the purposes of video compression (e.g.,
2151:
2147:
2145:
1765:Optical flow sensors are also being used in
1583:
1503:{\displaystyle I_{x}V_{x}+I_{y}V_{y}=-I_{t}}
88:encoding, and stereo disparity measurement.
2588:by CUVI (CUDA Vision & Imaging Library)
1936:
1879:
2064:
168:-D cases are similar) a voxel at location
2266:
2142:
2117:
2041:
2024:Beauchemin, S. S.; Barron, J. L. (1995).
1954:
637:
607:
577:
2255:International Journal of Computer Vision
2106:International Journal of Computer Vision
2099:"Performance of optical flow techniques"
1709:
29:
2480:
2373:– via Cambridge University Press.
14:
2612:
2165:Experimental Thermal and Fluid Science
1921:
1826:Burton, Andrew; Radford, John (1978).
1726:
2410:
2383:
2322:
2065:Fleet, David J.; Weiss, Yair (2006).
1632:– coarse optical flow via correlation
2443:
2185:10.1016/j.expthermflusci.2017.09.010
1992:Optical Flow Using Color Information
1937:Royden, C. S.; Moore, K. D. (2012).
1309:are the derivatives of the image at
24:
2573:- Optical flow estimation through
2452:. Reading, Mass.: Addison-Wesley.
1924:The Perception of the Visual World
1649:algorithms, linear programming or
1523:
1289:
1281:
1250:
1242:
1211:
1203:
1043:
1035:
1010:
1002:
977:
969:
928:
920:
908:
900:
885:
877:
865:
857:
842:
834:
822:
814:
785:
753:
744:
736:
724:
715:
707:
695:
686:
678:
638:
628:
620:
608:
598:
590:
578:
568:
560:
518:
503:
488:
399:
384:
369:
300:
277:
254:
133:
25:
2631:
2543:
2238:. Medical Image Analysis Journal.
2036:(3). ACM New York, USA: 433–466.
2026:"The computation of optical flow"
1347:in the corresponding directions.
66:ecological approach to psychology
2507:
2474:
2437:
2404:
2390:. Lawrence Erlbaum Associates.
2377:
2338:
2316:
2291:
2242:
2222:
2191:
1771:unmanned aerial vehicles (UAVs)
318:brightness constancy constraint
2592:Horn and Schunck Optical Flow:
2448:Analog VLSI and neural systems
2384:Brown, Christopher M. (1987).
2090:
2076:. Springer. pp. 237–257.
2058:
1930:
1915:
1873:
1846:
1819:
1538:
1334:
1316:
1179:
1161:
551:
533:
524:
479:
449:
431:
405:
360:
351:
333:
234:
216:
193:
175:
13:
1:
1813:
91:
1956:10.1016/j.visres.2012.02.006
1901:10.1016/0004-3702(81)90024-2
7:
2415:. Boston, MA: Springer US.
2387:Advances in Computer Vision
1776:
1602:, or maximizing normalized
1600:sum of absolute differences
1104:{\displaystyle V_{x},V_{y}}
45:is the pattern of apparent
10:
2636:
1882:"Determining optical flow"
1730:
164:)-dimensional case (3D or
142:{\displaystyle t+\Delta t}
2620:Motion in computer vision
2580:The French Aerospace Lab:
2516:Flying insects and robots
2481:Stocker, Alan A. (2006).
2363:10.1017/S0001924000011891
2268:10.1007/s11263-010-0390-2
2067:"Optical Flow Estimation"
1998:. ACM New York, NY, USA.
1584:Methods for determination
466:can be developed to get:
2518:. Heidelberg: Springer.
1752:neuromorphic engineering
1731:Not to be confused with
1647:Max-flow min-cut theorem
1592:– inverse of normalized
1185:{\displaystyle I(x,y,t)}
794:{\displaystyle \Delta t}
455:{\displaystyle I(x,y,t)}
309:{\displaystyle \Delta t}
286:{\displaystyle \Delta y}
263:{\displaystyle \Delta x}
240:{\displaystyle I(x,y,t)}
2411:Moini, Alireza (2000).
1889:Artificial Intelligence
1668:
1340:{\displaystyle (x,y,t)}
199:{\displaystyle (x,y,t)}
2198:Glyn W. Humphreys and
1798:Vision processing unit
1715:
1564:
1504:
1422:
1395:
1368:
1341:
1303:
1264:
1225:
1186:
1145:
1125:
1105:
1062:
947:
795:
769:
653:
456:
412:
310:
287:
264:
241:
200:
160:For a (2D +
143:
114:
35:
2444:Mead, Carver (1989).
2304:vision.middlebury.edu
2043:10.1145/212094.212141
2030:ACM Computing Surveys
1922:Gibson, J.J. (1950).
1713:
1565:
1505:
1423:
1421:{\displaystyle I_{t}}
1396:
1394:{\displaystyle I_{y}}
1369:
1367:{\displaystyle I_{x}}
1342:
1304:
1265:
1226:
1187:
1146:
1126:
1106:
1063:
948:
796:
770:
654:
457:
413:
311:
288:
265:
242:
201:
144:
115:
62:affordance perception
33:
2604:Robust Optical Flow:
2571:mrf-registration.net
2351:Aeronautical Journal
2328:"The Image Jacobian"
2208:. Psychology Press.
1624:Buxton–Buxton method
1594:cross-power spectrum
1520:
1438:
1405:
1378:
1351:
1313:
1274:
1235:
1196:
1155:
1135:
1115:
1075:
963:
808:
782:
672:
473:
425:
327:
297:
274:
251:
210:
172:
124:
104:
2598:TV-L1 Optical Flow:
2586:CUDA Implementation
2555:Art of Optical Flow
2177:2018ETFS...90..186Z
1926:. Houghton Mifflin.
1803:Continuity Equation
1783:Ambient optic array
1727:Optical flow sensor
1637:variational methods
1630:Black–Jepson method
1618:Horn–Schunck method
1612:Lucas–Kanade method
247:will have moved by
82:object segmentation
2550:Finding Optic Flow
2128:10.1007/bf01420984
1716:
1651:belief propagation
1560:
1500:
1418:
1391:
1364:
1337:
1299:
1297:
1260:
1258:
1221:
1219:
1182:
1141:
1121:
1101:
1058:
956:which results in
943:
791:
765:
660:higher-order terms
649:
452:
408:
306:
283:
260:
237:
196:
139:
110:
86:motion compensated
36:
2397:978-0-89859-648-9
2357:(1069): 159–268.
2332:QUT Robot Academy
2215:978-0-86377-124-8
2083:978-0-387-26371-7
2005:978-1-59593-753-7
1866:978-90-247-2689-9
1839:978-0-416-85840-2
1733:Optical flowmeter
1678:video compression
1674:Motion estimation
1604:cross-correlation
1590:Phase correlation
1541:
1296:
1257:
1218:
1144:{\displaystyle y}
1124:{\displaystyle x}
1050:
1017:
984:
935:
915:
892:
872:
849:
829:
751:
722:
693:
635:
605:
575:
113:{\displaystyle t}
16:(Redirected from
2627:
2538:
2537:
2511:
2505:
2504:
2478:
2472:
2471:
2451:
2441:
2435:
2434:
2408:
2402:
2401:
2381:
2375:
2374:
2342:
2336:
2335:
2320:
2314:
2313:
2311:
2310:
2295:
2289:
2288:
2270:
2246:
2240:
2239:
2237:
2226:
2220:
2219:
2205:Visual Cognition
2195:
2189:
2188:
2162:
2149:
2140:
2139:
2121:
2103:
2094:
2088:
2087:
2071:
2062:
2056:
2055:
2045:
2021:
2010:
2009:
1997:
1986:
1977:
1976:
1958:
1934:
1928:
1927:
1919:
1913:
1912:
1895:(1–3): 185–203.
1886:
1877:
1871:
1870:
1850:
1844:
1843:
1823:
1686:object detection
1576:aperture problem
1569:
1567:
1566:
1561:
1559:
1558:
1543:
1542:
1534:
1509:
1507:
1506:
1501:
1499:
1498:
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1449:
1427:
1425:
1424:
1419:
1417:
1416:
1400:
1398:
1397:
1392:
1390:
1389:
1373:
1371:
1370:
1365:
1363:
1362:
1346:
1344:
1343:
1338:
1308:
1306:
1305:
1300:
1298:
1295:
1287:
1279:
1269:
1267:
1266:
1261:
1259:
1256:
1248:
1240:
1230:
1228:
1227:
1222:
1220:
1217:
1209:
1201:
1191:
1189:
1188:
1183:
1150:
1148:
1147:
1142:
1130:
1128:
1127:
1122:
1110:
1108:
1107:
1102:
1100:
1099:
1087:
1086:
1067:
1065:
1064:
1059:
1051:
1049:
1041:
1033:
1028:
1027:
1018:
1016:
1008:
1000:
995:
994:
985:
983:
975:
967:
952:
950:
949:
944:
936:
934:
926:
918:
916:
914:
906:
898:
893:
891:
883:
875:
873:
871:
863:
855:
850:
848:
840:
832:
830:
828:
820:
812:
800:
798:
797:
792:
778:or, dividing by
774:
772:
771:
766:
752:
750:
742:
734:
723:
721:
713:
705:
694:
692:
684:
676:
658:
656:
655:
650:
648:
636:
634:
626:
618:
606:
604:
596:
588:
576:
574:
566:
558:
461:
459:
458:
453:
417:
415:
414:
409:
315:
313:
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307:
292:
290:
289:
284:
269:
267:
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261:
246:
244:
243:
238:
205:
203:
202:
197:
148:
146:
145:
140:
119:
117:
116:
111:
78:motion detection
21:
2635:
2634:
2630:
2629:
2628:
2626:
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2624:
2610:
2609:
2546:
2541:
2526:
2512:
2508:
2493:
2479:
2475:
2460:
2442:
2438:
2423:
2409:
2405:
2398:
2382:
2378:
2343:
2339:
2321:
2317:
2308:
2306:
2296:
2292:
2247:
2243:
2235:
2227:
2223:
2216:
2196:
2192:
2160:
2150:
2143:
2101:
2095:
2091:
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1793:Range imaging
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2413:Vision Chips
2412:
2406:
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2324:Corke, Peter
2318:
2307:. Retrieved
2303:
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1932:
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1859:. Springer.
1855:
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1808:Motion field
1764:
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39:Optical flow
38:
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2261:(1): 1–31.
2200:Vicki Bruce
2171:: 186–199.
2154:Chanson, H.
2152:Zhang, G.;
1909:1721.1/6337
2492:0470034882
2459:0201059924
2309:2019-10-18
1814:References
92:Estimation
71:locomotion
43:optic flow
18:Optic flow
2534:495477442
2431:851803922
2371:108782688
2277:0920-5691
2114:CiteSeerX
2112:: 43–77.
1949:: 17–24.
1697:structure
1548:−
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2468:17954003
2202:(1989).
2156:(2018).
1973:52847487
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