1875:
2140:
in image sequences. This application of the condensation algorithm impacts the range of human–computer interactions possible. It has been used to recognize simple gestures of a user at a whiteboard to control actions such as selecting regions of the boards to print or save them. Other extensions
2119:
Since clutter can cause the object probability distribution to split into multiple peaks, each peak represents a hypothesis about the object configuration. Smoothing is a statistical technique of conditioning the distribution based on both past and future measurements once the tracking is complete
59:
in 1998. One of the most interesting facets of the algorithm is that it does not compute on every pixel of the image. Rather, pixels to process are chosen at random, and only a subset of the pixels end up being processed. Multiple hypotheses about what is moving are supported naturally by the
2115:
The basic condensation algorithm is used to track a single object in time. It is possible to extend the condensation algorithm using a single probability distribution to describe the likely states of multiple objects to track multiple objects in a scene at the same time.
1565:
Since object-tracking can be a real-time objective, consideration of algorithm efficiency becomes important. The condensation algorithm is relatively simple when compared to the computational intensity of the
Ricatti equation required for Kalman filtering. The parameter
1420:
60:
probabilistic nature of the approach. The evaluation functions come largely from previous work in the area and include many standard statistical approaches. The original part of this work is the application of particle filter estimation techniques.
1669:
2132:
of mobile robots. Instead of tracking the position of an object in the scene, however, the position of the camera platform is tracked. This allows the camera platform to be globally localized given a visual map of the environment.
1593:
in which the splines are limited to certain configurations. Suitable configurations were found by analytically determining combinations of contours from multiple views, of the object in different poses, and through
1548:
1126:
633:
441:
350:
266:
696:
of each other and the dynamics facilitate the implementation of the condensation algorithm. The first assumption allows the dynamics of the object to be entirely determined by the conditional density
1589:
One way to increase efficiency of the algorithm is by selecting a low degree of freedom model for representing the shape of the object. The model used by Isard 1998 is a linear parameterization of
1660:
1190:
816:
755:
71:
and therefore poorly modeled by the Kalman filter. The condensation algorithm in its most general form requires no assumptions about the probability distributions of the object or measurements.
2063:
1046:
183:
972:
515:
2065:
cannot be directly estimated from the data, requiring assumptions to be made in order to estimate it. Isard 1998 assumes that the clutter which may make the object not visible is a
1271:
67:
to perform object tracking well in the presence of significant background clutter. The presence of clutter tends to produce probability distributions for the object state which are
2015:
1906:
1870:{\displaystyle p(\mathbf {x_{t}} |\mathbf {x_{t-1}} )\propto e^{-{\frac {1}{2}}||B^{-1}((\mathbf {x_{t}} -\mathbf {\bar {x}} )-A(\mathbf {x_{t-1}} -\mathbf {\bar {x}} ))||^{2})}}
1266:
109:
40:
the contour of objects moving in a cluttered environment. Object tracking is one of the more basic and difficult aspects of computer vision and is generally a prerequisite to
1464:
1234:
553:
2087:
687:
2110:
660:
352:
is a representation of the probability of possible conformations for the objects based on previous conformations and measurements. The condensation algorithm is a
853:
1986:
1966:
1946:
1926:
1584:
898:
129:
2120:
in order to reduce the effects of multiple peaks. Smoothing cannot be directly done in real-time since it requires information of future measurements.
2172:
2314:
2406:
Dellaert, F.; Burgard, W.; Fox, D.; Thrun, S. (1999). "Using the CONDENSATION algorithm for robust, vision-based mobile robot localization".
2390:
186:
2624:
2563:
2502:
2431:
1473:
1051:
693:
558:
366:
275:
191:
2161:
80:
2260:
Sminchisescu, C.; Kanaujia, A.; Metaxas, D.N. (November 2007). "BM3E: Discriminative
Density Propagation for Visual Tracking".
44:. Being able to identify which pixels in an image make up the contour of an object is a non-trivial problem. Condensation is a
185:
of the detected features in the images up to and including the current time. The algorithm outputs an estimate to the state
1604:
1586:, which determines the number of samples in the sample set, will clearly hold a trade-off in efficiency versus performance.
1134:
760:
699:
2018:
1595:
2346:
Koller-Meier, Esther B.; Ade, Frank (28 February 2001). "Tracking multiple objects using the
Condensation algorithm".
867:
Form the initial sample set and weights by sampling according to the prior distribution. For example, specify as
2183:
2027:
977:
2607:
Zhou, Shaohua; Krueger, V.; Chellappa, R. (21 May 2002). "Face recognition from video: A CONDENSATION approach".
2475:
Black, M.J.; Jepson, A.D. (14 April 1998). "Recognizing temporal trajectories using the condensation algorithm".
2145:
79:
The condensation algorithm seeks to solve the problem of estimating the conformation of an object described by a
2548:
Proceedings 199 IEEE/IEEJ/JSAI International
Conference on Intelligent Transportation Systems (Cat. No.99TH8383)
1415:{\displaystyle \pi _{t}^{(n)}={\frac {p(\mathbf {z_{t}} |s^{(n)})}{\sum _{j=1}^{N}p(\mathbf {z_{t}} |s^{(j)})}}}
134:
2674:
2408:
Proceedings. 1999 IEEE Computer
Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149)
2157:
903:
446:
52:
68:
45:
1948:
are matrices representing the deterministic and stochastic components of the dynamical model respectively.
2480:
2269:
2066:
1991:
1882:
2225:
Isard, M.; Blake, A (August 1998). "CONDENSATION-- conditional density propagation of visual tracking".
2198:– Condensation is the application of Sampling Importance Resampling (SIR) estimation to contour tracking
1550:
which can be directly used to calculate the mean position of the tracked object, as well as the other
1242:
268:
by applying a nonlinear filter based on factored sampling and can be thought of as a development of a
85:
1551:
1425:
1195:
2485:
520:
2274:
2137:
1663:
868:
2546:
Meier, E.B.; Ade, Frank (1999). "Tracking cars in range images using the CONDENSATION algorithm".
2642:
2630:
2581:
2569:
2520:
2508:
2449:
2437:
2295:
2242:
2129:
2090:
357:
269:
41:
2620:
2559:
2498:
2427:
2386:
2287:
2072:
665:
2095:
2612:
2551:
2490:
2419:
2411:
2378:
2355:
2326:
2279:
2234:
692:
The assumptions that object dynamics form a temporal Markov chain and that observations are
353:
64:
638:
2654:
2593:
2532:
2461:
2195:
33:
2477:
Proceedings Third IEEE International
Conference on Automatic Face and Gesture Recognition
832:
2609:
Proceedings of Fifth IEEE International
Conference on Automatic Face Gesture Recognition
1971:
1951:
1931:
1911:
1569:
883:
114:
37:
2359:
2668:
2331:
819:
2573:
2441:
2373:
Isard, Michael; Blake, Andrew (28 May 2006). "A smoothing filter for condensation".
555:. N is a parameter determining the number of sample sets chosen. A realization of
2634:
2512:
2299:
2246:
2089:
and that any true target measurement is unbiased and normally distributed with
2616:
2238:
823:
2555:
2494:
2415:
1557:
Cumulative weights can instead be used to achieve a more efficient sampling.
2283:
1590:
2291:
2382:
2377:. Lecture Notes in Computer Science. Vol. 1406. pp. 767–781.
2423:
2179:
2168:
818:
must also be selected for the algorithm, and generally includes both
2141:
have also been used for tracking multiple cars in the same scene.
2136:
Extensions of the condensation algorithm have also been used to
2313:
Blake, Andrea; Isard, Michael; Reynard, David (October 1995).
2262:
IEEE Transactions on
Pattern Analysis and Machine Intelligence
1543:{\displaystyle p(\mathbf {x_{t}} |\mathbf {z_{1},...,z_{t}} )}
1121:{\displaystyle p(\mathbf {x_{t}} |\mathbf {z_{1},...,z_{t}} )}
628:{\displaystyle p(\mathbf {x_{t}} |\mathbf {z_{1},...,z_{t}} )}
436:{\displaystyle p(\mathbf {x_{t}} |\mathbf {z_{1},...,z_{t}} )}
345:{\displaystyle p(\mathbf {x_{t}} |\mathbf {z_{1},...,z_{t}} )}
261:{\displaystyle p(\mathbf {x_{t}} |\mathbf {z_{1},...,z_{t}} )}
829:
The algorithm can be summarized by initialization at time
363:
The conditional density of the object at the current time
63:
The algorithm’s creation was inspired by the inability of
51:
The algorithm itself is described in detail by Isard and
1192:
to each element of this new set, to generate a new set
662:
with probability equal to the corresponding element of
1655:{\displaystyle p(\mathbf {x_{t}} |\mathbf {x_{t-1}} )}
1185:{\displaystyle p(\mathbf {x_{t}} |\mathbf {x_{t-1}} )}
811:{\displaystyle p(\mathbf {x_{t}} |\mathbf {x_{t-1}} )}
750:{\displaystyle p(\mathbf {x_{t}} |\mathbf {x_{t-1}} )}
635:
is obtained by sampling with replacement from the set
36:
algorithm. The principal application is to detect and
2098:
2075:
2030:
1994:
1974:
1954:
1934:
1914:
1885:
1672:
1607:
1572:
1476:
1428:
1274:
1245:
1198:
1137:
1054:
980:
906:
886:
835:
763:
702:
668:
641:
561:
523:
449:
369:
278:
194:
137:
117:
88:
1470:
This algorithm outputs the probability distribution
443:
is estimated as a weighted, time-indexed sample set
2156:An implementation of the condensation algorithm in
2144:The condensation algorithm has also been used for
2104:
2081:
2057:
2009:
1980:
1960:
1940:
1920:
1900:
1869:
1654:
1578:
1542:
1458:
1414:
1260:
1228:
1184:
1120:
1040:
966:
892:
847:
810:
757:. The model of the system dynamics determined by
749:
681:
654:
627:
547:
509:
435:
344:
260:
177:
123:
103:
2315:"Learning to track the visual motion of contours"
2001:
1892:
1833:
1788:
1666:with deterministic and stochastic components:
2021:while the object performs typical movements.
1239:To take into account the current observation
8:
2058:{\displaystyle p(\mathbf {z} |\mathbf {x} )}
1453:
1429:
1223:
1199:
1041:{\displaystyle \{\pi _{0}^{(n)},n=1,...,N\}}
1035:
981:
961:
907:
504:
450:
2220:
2218:
2216:
2214:
2212:
2128:The algorithm can be used for vision-based
1601:Isard and Blake model the object dynamics
178:{\displaystyle \mathbf {z_{1},...,z_{t}} }
2484:
2330:
2273:
2097:
2074:
2047:
2042:
2037:
2029:
1996:
1995:
1993:
1973:
1953:
1933:
1913:
1887:
1886:
1884:
1856:
1851:
1845:
1828:
1827:
1811:
1806:
1783:
1782:
1772:
1767:
1752:
1743:
1738:
1728:
1724:
1701:
1696:
1691:
1684:
1679:
1671:
1636:
1631:
1626:
1619:
1614:
1606:
1571:
1530:
1505:
1500:
1495:
1488:
1483:
1475:
1441:
1436:
1427:
1394:
1385:
1378:
1373:
1361:
1350:
1329:
1320:
1313:
1308:
1299:
1284:
1279:
1273:
1251:
1246:
1244:
1211:
1206:
1197:
1166:
1161:
1156:
1149:
1144:
1136:
1108:
1083:
1078:
1073:
1066:
1061:
1053:
993:
988:
979:
967:{\displaystyle \{s_{0}^{(n)},n=1,...,N\}}
919:
914:
905:
885:
871:and set the weights equal to each other.
834:
792:
787:
782:
775:
770:
762:
731:
726:
721:
714:
709:
701:
673:
667:
646:
640:
615:
590:
585:
580:
573:
568:
560:
533:
528:
522:
510:{\displaystyle \{s_{t}^{(n)},n=1,...,N\}}
462:
457:
448:
423:
398:
393:
388:
381:
376:
368:
332:
307:
302:
297:
290:
285:
277:
248:
223:
218:
213:
206:
201:
193:
168:
143:
138:
136:
116:
94:
89:
87:
2227:International Journal of Computer Vision
57:International Journal of Computer Vision
2208:
2178:An example of implementation using the
2650:
2640:
2589:
2579:
2528:
2518:
2457:
2447:
48:that attempts to solve this problem.
7:
1908:is the mean value of the state, and
2010:{\displaystyle \mathbf {\bar {x}} }
1901:{\displaystyle \mathbf {\bar {x}} }
14:
2410:. Vol. 2. pp. 588–594.
2048:
2038:
1998:
1889:
1830:
1818:
1815:
1812:
1808:
1785:
1773:
1769:
1708:
1705:
1702:
1698:
1685:
1681:
1643:
1640:
1637:
1633:
1620:
1616:
1531:
1527:
1523:
1520:
1517:
1514:
1511:
1506:
1502:
1489:
1485:
1379:
1375:
1314:
1310:
1261:{\displaystyle \mathbf {z_{t}} }
1252:
1248:
1173:
1170:
1167:
1163:
1150:
1146:
1109:
1105:
1101:
1098:
1095:
1092:
1089:
1084:
1080:
1067:
1063:
799:
796:
793:
789:
776:
772:
738:
735:
732:
728:
715:
711:
616:
612:
608:
605:
602:
599:
596:
591:
587:
574:
570:
424:
420:
416:
413:
410:
407:
404:
399:
395:
382:
378:
360:of the object and the observer.
333:
329:
325:
322:
319:
316:
313:
308:
304:
291:
287:
249:
245:
241:
238:
235:
232:
229:
224:
220:
207:
203:
169:
165:
161:
158:
155:
152:
149:
144:
140:
104:{\displaystyle \mathbf {x_{t}} }
95:
91:
2348:Robotics and Autonomous Systems
1598:(PCA) on the deforming object.
1459:{\displaystyle \{s_{t}^{(n)}\}}
1229:{\displaystyle \{s_{t}^{(n)}\}}
187:conditional probability density
2052:
2043:
2034:
1862:
1852:
1846:
1842:
1839:
1803:
1794:
1764:
1761:
1744:
1739:
1714:
1692:
1676:
1649:
1627:
1611:
1537:
1496:
1480:
1448:
1442:
1406:
1401:
1395:
1386:
1370:
1341:
1336:
1330:
1321:
1305:
1291:
1285:
1218:
1212:
1179:
1157:
1141:
1115:
1074:
1058:
1000:
994:
926:
920:
805:
783:
767:
744:
722:
706:
622:
581:
565:
548:{\displaystyle \pi _{t}^{(n)}}
540:
534:
469:
463:
430:
389:
373:
339:
298:
282:
255:
214:
198:
1:
2360:10.1016/s0921-8890(00)00114-7
2019:Maximum Likelihood Estimation
1561:Implementation considerations
1048:to generate a realization of
855:and three steps at each time
2332:10.1016/0004-3702(95)00032-1
2182:library can be found on the
1596:principal component analysis
1131:Apply the learned dynamics
2691:
2617:10.1109/AFGR.2002.1004158
2375:Computer Vision — ECCV'98
2556:10.1109/ITSC.1999.821040
2495:10.1109/AFGR.1998.670919
2416:10.1109/CVPR.1999.784976
2138:recognize human gestures
2082:{\displaystyle \lambda }
880:Sample with replacement
682:{\displaystyle \pi _{t}}
55:in a publication in the
2319:Artificial Intelligence
2284:10.1109/tpami.2007.1111
2239:10.1023/A:1008078328650
2173:Mathworks File Exchange
2162:Michael Isard’s website
2105:{\displaystyle \sigma }
1554:of the tracked object.
46:probabilistic algorithm
2106:
2083:
2067:Poisson random process
2059:
2024:The observation model
2011:
1982:
1962:
1942:
1922:
1902:
1871:
1656:
1580:
1544:
1460:
1416:
1366:
1262:
1230:
1186:
1122:
1042:
968:
894:
849:
812:
751:
683:
656:
629:
549:
511:
437:
346:
262:
179:
125:
105:
18:condensation algorithm
2167:An implementation in
2148:in a video sequence.
2107:
2084:
2069:with spatial density
2060:
2012:
1983:
1963:
1943:
1923:
1903:
1872:
1657:
1581:
1545:
1461:
1417:
1346:
1263:
1231:
1187:
1123:
1043:
969:
895:
850:
813:
752:
684:
657:
655:{\displaystyle s_{t}}
630:
550:
512:
438:
347:
263:
180:
131:, given observations
126:
106:
2611:. pp. 221–226.
2550:. pp. 129–134.
2171:can be found on the
2096:
2073:
2028:
1992:
1972:
1952:
1932:
1912:
1883:
1670:
1605:
1570:
1474:
1426:
1272:
1243:
1196:
1135:
1052:
978:
904:
884:
833:
761:
700:
666:
639:
559:
521:
447:
367:
356:since it models the
276:
192:
135:
115:
86:
1664:difference equation
1452:
1295:
1222:
1004:
930:
900:times from the set
875:Iterative procedure
848:{\displaystyle t=0}
544:
473:
2479:. pp. 16–21.
2383:10.1007/BFb0055703
2130:robot localization
2102:
2091:standard deviation
2079:
2055:
2017:are estimated via
2007:
1978:
1958:
1938:
1918:
1898:
1867:
1662:as a second order
1652:
1576:
1540:
1456:
1432:
1412:
1275:
1258:
1226:
1202:
1182:
1118:
1038:
984:
964:
910:
890:
845:
808:
747:
679:
652:
625:
545:
524:
507:
453:
433:
358:joint distribution
342:
270:Monte-Carlo method
258:
175:
121:
101:
75:Algorithm overview
42:object recognition
2392:978-3-540-64569-6
2268:(11): 2030–2044.
2004:
1981:{\displaystyle B}
1961:{\displaystyle A}
1941:{\displaystyle B}
1921:{\displaystyle A}
1895:
1836:
1791:
1736:
1579:{\displaystyle N}
1422:for each element
1410:
974:with probability
893:{\displaystyle N}
124:{\displaystyle t}
2682:
2659:
2658:
2652:
2648:
2646:
2638:
2604:
2598:
2597:
2591:
2587:
2585:
2577:
2543:
2537:
2536:
2530:
2526:
2524:
2516:
2488:
2472:
2466:
2465:
2459:
2455:
2453:
2445:
2403:
2397:
2396:
2370:
2364:
2363:
2343:
2337:
2336:
2334:
2325:(1–2): 179–212.
2310:
2304:
2303:
2277:
2257:
2251:
2250:
2222:
2160:can be found on
2146:face recognition
2111:
2109:
2108:
2103:
2088:
2086:
2085:
2080:
2064:
2062:
2061:
2056:
2051:
2046:
2041:
2016:
2014:
2013:
2008:
2006:
2005:
1997:
1987:
1985:
1984:
1979:
1967:
1965:
1964:
1959:
1947:
1945:
1944:
1939:
1927:
1925:
1924:
1919:
1907:
1905:
1904:
1899:
1897:
1896:
1888:
1876:
1874:
1873:
1868:
1866:
1865:
1861:
1860:
1855:
1849:
1838:
1837:
1829:
1823:
1822:
1821:
1793:
1792:
1784:
1778:
1777:
1776:
1760:
1759:
1747:
1742:
1737:
1729:
1713:
1712:
1711:
1695:
1690:
1689:
1688:
1661:
1659:
1658:
1653:
1648:
1647:
1646:
1630:
1625:
1624:
1623:
1585:
1583:
1582:
1577:
1549:
1547:
1546:
1541:
1536:
1535:
1534:
1510:
1509:
1499:
1494:
1493:
1492:
1465:
1463:
1462:
1457:
1451:
1440:
1421:
1419:
1418:
1413:
1411:
1409:
1405:
1404:
1389:
1384:
1383:
1382:
1365:
1360:
1344:
1340:
1339:
1324:
1319:
1318:
1317:
1300:
1294:
1283:
1267:
1265:
1264:
1259:
1257:
1256:
1255:
1235:
1233:
1232:
1227:
1221:
1210:
1191:
1189:
1188:
1183:
1178:
1177:
1176:
1160:
1155:
1154:
1153:
1127:
1125:
1124:
1119:
1114:
1113:
1112:
1088:
1087:
1077:
1072:
1071:
1070:
1047:
1045:
1044:
1039:
1003:
992:
973:
971:
970:
965:
929:
918:
899:
897:
896:
891:
854:
852:
851:
846:
817:
815:
814:
809:
804:
803:
802:
786:
781:
780:
779:
756:
754:
753:
748:
743:
742:
741:
725:
720:
719:
718:
688:
686:
685:
680:
678:
677:
661:
659:
658:
653:
651:
650:
634:
632:
631:
626:
621:
620:
619:
595:
594:
584:
579:
578:
577:
554:
552:
551:
546:
543:
532:
516:
514:
513:
508:
472:
461:
442:
440:
439:
434:
429:
428:
427:
403:
402:
392:
387:
386:
385:
354:generative model
351:
349:
348:
343:
338:
337:
336:
312:
311:
301:
296:
295:
294:
267:
265:
264:
259:
254:
253:
252:
228:
227:
217:
212:
211:
210:
184:
182:
181:
176:
174:
173:
172:
148:
147:
130:
128:
127:
122:
110:
108:
107:
102:
100:
99:
98:
65:Kalman filtering
2690:
2689:
2685:
2684:
2683:
2681:
2680:
2679:
2675:Computer vision
2665:
2664:
2663:
2662:
2649:
2639:
2627:
2606:
2605:
2601:
2588:
2578:
2566:
2545:
2544:
2540:
2527:
2517:
2505:
2486:10.1.1.154.1402
2474:
2473:
2469:
2456:
2446:
2434:
2405:
2404:
2400:
2393:
2372:
2371:
2367:
2354:(2–3): 93–105.
2345:
2344:
2340:
2312:
2311:
2307:
2259:
2258:
2254:
2224:
2223:
2210:
2205:
2196:Particle filter
2192:
2154:
2126:
2094:
2093:
2071:
2070:
2026:
2025:
1990:
1989:
1970:
1969:
1950:
1949:
1930:
1929:
1910:
1909:
1881:
1880:
1850:
1807:
1768:
1748:
1720:
1697:
1680:
1668:
1667:
1632:
1615:
1603:
1602:
1568:
1567:
1563:
1526:
1501:
1484:
1472:
1471:
1424:
1423:
1390:
1374:
1345:
1325:
1309:
1301:
1270:
1269:
1247:
1241:
1240:
1194:
1193:
1162:
1145:
1133:
1132:
1104:
1079:
1062:
1050:
1049:
976:
975:
902:
901:
882:
881:
877:
865:
831:
830:
788:
771:
759:
758:
727:
710:
698:
697:
669:
664:
663:
642:
637:
636:
611:
586:
569:
557:
556:
519:
518:
445:
444:
419:
394:
377:
365:
364:
328:
303:
286:
274:
273:
244:
219:
202:
190:
189:
164:
139:
133:
132:
113:
112:
90:
84:
83:
77:
34:computer vision
12:
11:
5:
2688:
2686:
2678:
2677:
2667:
2666:
2661:
2660:
2651:|journal=
2625:
2599:
2590:|journal=
2564:
2538:
2529:|journal=
2503:
2467:
2458:|journal=
2432:
2398:
2391:
2365:
2338:
2305:
2275:10.1.1.78.1751
2252:
2207:
2206:
2204:
2201:
2200:
2199:
2191:
2188:
2153:
2150:
2125:
2122:
2101:
2078:
2054:
2050:
2045:
2040:
2036:
2033:
2003:
2000:
1977:
1957:
1937:
1917:
1894:
1891:
1864:
1859:
1854:
1848:
1844:
1841:
1835:
1832:
1826:
1820:
1817:
1814:
1810:
1805:
1802:
1799:
1796:
1790:
1787:
1781:
1775:
1771:
1766:
1763:
1758:
1755:
1751:
1746:
1741:
1735:
1732:
1727:
1723:
1719:
1716:
1710:
1707:
1704:
1700:
1694:
1687:
1683:
1678:
1675:
1651:
1645:
1642:
1639:
1635:
1629:
1622:
1618:
1613:
1610:
1575:
1562:
1559:
1539:
1533:
1529:
1525:
1522:
1519:
1516:
1513:
1508:
1504:
1498:
1491:
1487:
1482:
1479:
1468:
1467:
1455:
1450:
1447:
1444:
1439:
1435:
1431:
1408:
1403:
1400:
1397:
1393:
1388:
1381:
1377:
1372:
1369:
1364:
1359:
1356:
1353:
1349:
1343:
1338:
1335:
1332:
1328:
1323:
1316:
1312:
1307:
1304:
1298:
1293:
1290:
1287:
1282:
1278:
1254:
1250:
1237:
1225:
1220:
1217:
1214:
1209:
1205:
1201:
1181:
1175:
1172:
1169:
1165:
1159:
1152:
1148:
1143:
1140:
1129:
1117:
1111:
1107:
1103:
1100:
1097:
1094:
1091:
1086:
1082:
1076:
1069:
1065:
1060:
1057:
1037:
1034:
1031:
1028:
1025:
1022:
1019:
1016:
1013:
1010:
1007:
1002:
999:
996:
991:
987:
983:
963:
960:
957:
954:
951:
948:
945:
942:
939:
936:
933:
928:
925:
922:
917:
913:
909:
889:
876:
873:
864:
863:Initialization
861:
844:
841:
838:
807:
801:
798:
795:
791:
785:
778:
774:
769:
766:
746:
740:
737:
734:
730:
724:
717:
713:
708:
705:
676:
672:
649:
645:
624:
618:
614:
610:
607:
604:
601:
598:
593:
589:
583:
576:
572:
567:
564:
542:
539:
536:
531:
527:
506:
503:
500:
497:
494:
491:
488:
485:
482:
479:
476:
471:
468:
465:
460:
456:
452:
432:
426:
422:
418:
415:
412:
409:
406:
401:
397:
391:
384:
380:
375:
372:
341:
335:
331:
327:
324:
321:
318:
315:
310:
306:
300:
293:
289:
284:
281:
257:
251:
247:
243:
240:
237:
234:
231:
226:
222:
216:
209:
205:
200:
197:
171:
167:
163:
160:
157:
154:
151:
146:
142:
120:
97:
93:
76:
73:
13:
10:
9:
6:
4:
3:
2:
2687:
2676:
2673:
2672:
2670:
2656:
2644:
2636:
2632:
2628:
2626:0-7695-1602-5
2622:
2618:
2614:
2610:
2603:
2600:
2595:
2583:
2575:
2571:
2567:
2565:0-7803-4975-X
2561:
2557:
2553:
2549:
2542:
2539:
2534:
2522:
2514:
2510:
2506:
2504:0-8186-8344-9
2500:
2496:
2492:
2487:
2482:
2478:
2471:
2468:
2463:
2451:
2443:
2439:
2435:
2433:0-7695-0149-4
2429:
2425:
2421:
2417:
2413:
2409:
2402:
2399:
2394:
2388:
2384:
2380:
2376:
2369:
2366:
2361:
2357:
2353:
2349:
2342:
2339:
2333:
2328:
2324:
2320:
2316:
2309:
2306:
2301:
2297:
2293:
2289:
2285:
2281:
2276:
2271:
2267:
2263:
2256:
2253:
2248:
2244:
2240:
2236:
2232:
2228:
2221:
2219:
2217:
2215:
2213:
2209:
2202:
2197:
2194:
2193:
2189:
2187:
2185:
2184:OpenCV forums
2181:
2176:
2174:
2170:
2165:
2163:
2159:
2151:
2149:
2147:
2142:
2139:
2134:
2131:
2123:
2121:
2117:
2113:
2099:
2092:
2076:
2068:
2031:
2022:
2020:
1975:
1955:
1935:
1915:
1877:
1857:
1824:
1800:
1797:
1779:
1756:
1753:
1749:
1733:
1730:
1725:
1721:
1717:
1673:
1665:
1608:
1599:
1597:
1592:
1587:
1573:
1560:
1558:
1555:
1553:
1477:
1445:
1437:
1433:
1398:
1391:
1367:
1362:
1357:
1354:
1351:
1347:
1333:
1326:
1302:
1296:
1288:
1280:
1276:
1238:
1215:
1207:
1203:
1138:
1130:
1055:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1011:
1008:
1005:
997:
989:
985:
958:
955:
952:
949:
946:
943:
940:
937:
934:
931:
923:
915:
911:
887:
879:
878:
874:
872:
870:
862:
860:
858:
842:
839:
836:
827:
825:
821:
820:deterministic
764:
703:
695:
690:
674:
670:
647:
643:
562:
537:
529:
525:
517:with weights
501:
498:
495:
492:
489:
486:
483:
480:
477:
474:
466:
458:
454:
370:
361:
359:
355:
279:
271:
195:
188:
118:
82:
74:
72:
70:
66:
61:
58:
54:
49:
47:
43:
39:
35:
31:
27:
23:
19:
2608:
2602:
2547:
2541:
2476:
2470:
2407:
2401:
2374:
2368:
2351:
2347:
2341:
2322:
2318:
2308:
2265:
2261:
2255:
2230:
2226:
2177:
2166:
2155:
2143:
2135:
2127:
2124:Applications
2118:
2114:
2023:
1878:
1600:
1588:
1564:
1556:
1469:
866:
856:
828:
691:
362:
78:
62:
56:
50:
29:
25:
21:
17:
15:
2233:(1): 5–28.
694:independent
69:multi-modal
2424:1853/21565
2203:References
826:dynamics.
824:stochastic
28:ity Propag
2653:ignored (
2643:cite book
2592:ignored (
2582:cite book
2531:ignored (
2521:cite book
2481:CiteSeerX
2460:ignored (
2450:cite book
2270:CiteSeerX
2152:Resources
2100:σ
2077:λ
2002:¯
1893:¯
1834:¯
1825:−
1816:−
1798:−
1789:¯
1780:−
1754:−
1726:−
1718:∝
1706:−
1641:−
1591:B-splines
1348:∑
1277:π
1171:−
986:π
797:−
736:−
671:π
526:π
24:ditional
2669:Category
2574:12548469
2442:16130780
2292:17848782
2190:See also
869:Gaussian
111:at time
2635:8505547
2513:5159845
2300:1949783
2247:6821810
1552:moments
32:) is a
2633:
2623:
2572:
2562:
2511:
2501:
2483:
2440:
2430:
2389:
2298:
2290:
2272:
2245:
2180:OpenCV
2169:MATLAB
1988:, and
1879:where
1268:, set
81:vector
2631:S2CID
2570:S2CID
2509:S2CID
2438:S2CID
2296:S2CID
2243:S2CID
53:Blake
38:track
30:ation
2655:help
2621:ISBN
2594:help
2560:ISBN
2533:help
2499:ISBN
2462:help
2428:ISBN
2387:ISBN
2288:PMID
822:and
26:Dens
16:The
2613:doi
2552:doi
2491:doi
2420:hdl
2412:doi
2379:doi
2356:doi
2327:doi
2280:doi
2235:doi
22:Con
2671::
2647::
2645:}}
2641:{{
2629:.
2619:.
2586::
2584:}}
2580:{{
2568:.
2558:.
2525::
2523:}}
2519:{{
2507:.
2497:.
2489:.
2454::
2452:}}
2448:{{
2436:.
2426:.
2418:.
2385:.
2352:34
2350:.
2323:78
2321:.
2317:.
2294:.
2286:.
2278:.
2266:29
2264:.
2241:.
2231:29
2229:.
2211:^
2186:.
2175:.
2164:.
2112:.
1968:,
1928:,
859::
689:.
272:.
2657:)
2637:.
2615::
2596:)
2576:.
2554::
2535:)
2515:.
2493::
2464:)
2444:.
2422::
2414::
2395:.
2381::
2362:.
2358::
2335:.
2329::
2302:.
2282::
2249:.
2237::
2158:C
2053:)
2049:x
2044:|
2039:z
2035:(
2032:p
1999:x
1976:B
1956:A
1936:B
1916:A
1890:x
1863:)
1858:2
1853:|
1847:|
1843:)
1840:)
1831:x
1819:1
1813:t
1809:x
1804:(
1801:A
1795:)
1786:x
1774:t
1770:x
1765:(
1762:(
1757:1
1750:B
1745:|
1740:|
1734:2
1731:1
1722:e
1715:)
1709:1
1703:t
1699:x
1693:|
1686:t
1682:x
1677:(
1674:p
1650:)
1644:1
1638:t
1634:x
1628:|
1621:t
1617:x
1612:(
1609:p
1574:N
1538:)
1532:t
1528:z
1524:,
1521:.
1518:.
1515:.
1512:,
1507:1
1503:z
1497:|
1490:t
1486:x
1481:(
1478:p
1466:.
1454:}
1449:)
1446:n
1443:(
1438:t
1434:s
1430:{
1407:)
1402:)
1399:j
1396:(
1392:s
1387:|
1380:t
1376:z
1371:(
1368:p
1363:N
1358:1
1355:=
1352:j
1342:)
1337:)
1334:n
1331:(
1327:s
1322:|
1315:t
1311:z
1306:(
1303:p
1297:=
1292:)
1289:n
1286:(
1281:t
1253:t
1249:z
1236:.
1224:}
1219:)
1216:n
1213:(
1208:t
1204:s
1200:{
1180:)
1174:1
1168:t
1164:x
1158:|
1151:t
1147:x
1142:(
1139:p
1128:.
1116:)
1110:t
1106:z
1102:,
1099:.
1096:.
1093:.
1090:,
1085:1
1081:z
1075:|
1068:t
1064:x
1059:(
1056:p
1036:}
1033:N
1030:,
1027:.
1024:.
1021:.
1018:,
1015:1
1012:=
1009:n
1006:,
1001:)
998:n
995:(
990:0
982:{
962:}
959:N
956:,
953:.
950:.
947:.
944:,
941:1
938:=
935:n
932:,
927:)
924:n
921:(
916:0
912:s
908:{
888:N
857:t
843:0
840:=
837:t
806:)
800:1
794:t
790:x
784:|
777:t
773:x
768:(
765:p
745:)
739:1
733:t
729:x
723:|
716:t
712:x
707:(
704:p
675:t
648:t
644:s
623:)
617:t
613:z
609:,
606:.
603:.
600:.
597:,
592:1
588:z
582:|
575:t
571:x
566:(
563:p
541:)
538:n
535:(
530:t
505:}
502:N
499:,
496:.
493:.
490:.
487:,
484:1
481:=
478:n
475:,
470:)
467:n
464:(
459:t
455:s
451:{
431:)
425:t
421:z
417:,
414:.
411:.
408:.
405:,
400:1
396:z
390:|
383:t
379:x
374:(
371:p
340:)
334:t
330:z
326:,
323:.
320:.
317:.
314:,
309:1
305:z
299:|
292:t
288:x
283:(
280:p
256:)
250:t
246:z
242:,
239:.
236:.
233:.
230:,
225:1
221:z
215:|
208:t
204:x
199:(
196:p
170:t
166:z
162:,
159:.
156:.
153:.
150:,
145:1
141:z
119:t
96:t
92:x
20:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.