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Condensation algorithm

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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
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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
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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
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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.
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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
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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.
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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.
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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
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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
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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
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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.
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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
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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
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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
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is a representation of the probability of possible conformations for the objects based on previous conformations and measurements. The condensation algorithm is a
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in order to reduce the effects of multiple peaks. Smoothing cannot be directly done in real-time since it requires information of future measurements.
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Dellaert, F.; Burgard, W.; Fox, D.; Thrun, S. (1999). "Using the CONDENSATION algorithm for robust, vision-based mobile robot localization".
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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
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Koller-Meier, Esther B.; Ade, Frank (28 February 2001). "Tracking multiple objects using the Condensation algorithm".
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Form the initial sample set and weights by sampling according to the prior distribution. For example, specify as
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Zhou, Shaohua; Krueger, V.; Chellappa, R. (21 May 2002). "Face recognition from video: A CONDENSATION approach".
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Black, M.J.; Jepson, A.D. (14 April 1998). "Recognizing temporal trajectories using the condensation algorithm".
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The condensation algorithm seeks to solve the problem of estimating the conformation of an object described by a
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Proceedings 199 IEEE/IEEJ/JSAI International Conference on Intelligent Transportation Systems (Cat. No.99TH8383)
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Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149)
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are matrices representing the deterministic and stochastic components of the dynamical model respectively.
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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
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by applying a nonlinear filter based on factored sampling and can be thought of as a development of a
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Meier, E.B.; Ade, Frank (1999). "Tracking cars in range images using the CONDENSATION algorithm".
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The assumptions that object dynamics form a temporal Markov chain and that observations are
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Proceedings Third IEEE International Conference on Automatic Face and Gesture Recognition
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Proceedings of Fifth IEEE International Conference on Automatic Face Gesture Recognition
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Isard, Michael; Blake, Andrew (28 May 2006). "A smoothing filter for condensation".
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and that any true target measurement is unbiased and normally distributed with
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Cumulative weights can instead be used to achieve a more efficient sampling.
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must also be selected for the algorithm, and generally includes both
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have also been used for tracking multiple cars in the same scene.
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Extensions of the condensation algorithm have also been used to
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Blake, Andrea; Isard, Michael; Reynard, David (October 1995).
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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
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The conditional density of the object at the current time
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The algorithm’s creation was inspired by the inability of
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The algorithm itself is described in detail by Isard and
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to each element of this new set, to generate a new set
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with probability equal to the corresponding element of
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is obtained by sampling with replacement from the set
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algorithm. The principal application is to detect and
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This algorithm outputs the probability distribution
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is estimated as a weighted, time-indexed sample set
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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 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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: 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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: 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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:: 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Index

computer vision
track
object recognition
probabilistic algorithm
Blake
Kalman filtering
multi-modal
vector
conditional probability density
Monte-Carlo method
generative model
joint distribution
independent
deterministic
stochastic
Gaussian
moments
B-splines
principal component analysis
difference equation
Maximum Likelihood Estimation
Poisson random process
standard deviation
robot localization
recognize human gestures
face recognition
C
Michael Isard’s website
MATLAB
Mathworks File Exchange

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