2369:
OBJ CUT is an efficient method that automatically segments an object. The OBJ CUT method is a generic method, and therefore it is applicable to any object category model. Given an image D containing an instance of a known object category, e.g. cows, the OBJ CUT algorithm computes a segmentation of
1703:
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1011:
774:
639:
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Since only one eigenvector, corresponding to the second smallest generalized eigenvalue, is used by the uncut algorithm, efficiency can be dramatically improved if the solve of the corresponding eigenvalue problem is performed in a
3332:
31:
problem is concerned with partitioning an image into multiple regions according to some homogeneity criterion. This article is primarily concerned with graph theoretic approaches to image segmentation applying
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504:
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The set of points in an arbitrary feature space can be represented as a weighted undirected complete graph G = (V, E), where the nodes of the graph are the points in the feature space. The weight
2196:
require only a function that performs a matrix-vector product for a given vector, on every iteration. For image segmentation, the matrix W is typically sparse, with a number of nonzero entries
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2010:
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17:
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3246:
3638:. Clustering Large Data Sets; Third IEEE International Conference on Data Mining (ICDM 2003) Melbourne, Florida: IEEE Computer Society. pp. 59–62.
3774:
1698:{\displaystyle \min \limits _{(S,{\overline {S}})}\operatorname {ncut} (S,{\overline {S}})=\min \limits _{y}{\frac {y^{T}(D-W)y}{y^{T}Dy}}}
66:
Segment the image into homogeneous components, and use the most suitable compression algorithm for each component to improve compression.
3652:
Multiscale
Spectral Image Segmentation Multiscale preconditioning for computing eigenvalues of graph Laplacians in image segmentation
3529:
2757:
2669:
1114:
886:
430:
2655:{\displaystyle E(m,\Theta )=\sum \phi _{x}(D|m_{x})+\phi _{x}(m_{x}|\Theta )+\sum \Psi _{xy}(m_{x},m_{y})+\phi (D|m_{x},m_{y})}
1303:
1215:
1069:
841:
224:. In this context, we can formulate the image segmentation problem as a graph partitioning problem that asks for a partition
3127:
3704:
3608:(1997): "Normalized Cuts and Image Segmentation", IEEE Conference on Computer Vision and Pattern Recognition, pp 731–737
2266:
3730:
3350:
100:
Partition a transportation network makes it possible to identify regions characterized by homogeneous traffic states.
1918:, and allow it to take real values. The relaxed problem can be solved by solving the generalized eigenvalue problem
1828:
2105:
Use the eigenvector with the second smallest eigenvalue to bipartition the graph (e.g. grouping according to sign).
1363:
3717:
1162:
1016:
3548:
Lopez, Clélia; Leclercq, Ludovic; Krishnakumari, Panchamy; Chiabaut, Nicolas; Van Lint, Hans (25 October 2017).
3743:
3618:
2910:
3707:. In Proceedings of the 7th European Conference on Computer Vision, Copenhagen, Denmark, pages 109–124, 2002.
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2342:
3440:
3756:
3040:
3779:
1264:
782:
227:
2859:
2058:
1921:
1714:
3398:
1006:{\displaystyle \operatorname {ncut} (S,{\overline {S}})=2-\operatorname {nassoc} (S,{\overline {S}})}
3497:
1517:
2424:
3216:
320:
149:
1786:
1491:
1425:
2188:, i.e., without explicitly manipulating with or even computing the matrix W, as, e.g., in the
2127:
769:{\displaystyle \operatorname {nassoc} (A,B)={\frac {w(A,A)}{w(A,V)}}+{\frac {w(B,B)}{w(B,V)}}}
3680:. Workshop on Algorithms for Modern Massive Datasets Stanford University and Yahoo! Research.
2961:
2400:
2380:
2273:
method. Computing the eigenvector using an optimally preconditioned matrix-free method takes
1977:
1346:
3757:
The Layout
Consistent Random Field for Recognizing and Segmenting Partially Occluded Objects
634:{\displaystyle \operatorname {ncut} (A,B)={\frac {w(A,B)}{w(A,V)}}+{\frac {w(A,B)}{w(B,V)}}}
119:
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3189:
3100:
293:
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2199:
8:
3746:. In Proceedings of the IEEE International Conference on Computer Vision, Beijing, 2005.
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49:
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2035:
2015:
1901:
1471:
1451:
821:
404:
384:
273:
207:
187:
33:
28:
3635:
Modern preconditioned eigensolvers for spectral image segmentation and graph bisection
3675:
3650:
3633:
3587:
3550:"Revealing the day-to-day regularity of urban congestion patterns with 3D speed maps"
2262:
2189:
3656:
3577:
3569:
3327:{\displaystyle m^{*}=\arg \min \limits _{m}\sum \limits _{i}w_{i}E(m,\Theta _{i})}
2350:
2258:
3660:
3605:
3573:
87:
76:
Automatic segmentation of MRI images for identification of cancerous regions.
3768:
3731:
An
Implicit Shape Model for Combined Object Categorization and Segmentation
3591:
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2269:
is a key technology accelerating the convergence, e.g., in the matrix-free
2261:, leading to slow convergence of iterative eigenvalue solvers, such as the
2121:
3692:
Proceedings of IEEE Conference on
Computer Vision and Pattern Recognition
41:
37:
3395:
The objective function given by equation (2) is determined by computing
2346:
2120:
Solving a standard eigenvalue problem for all eigenvectors (using the
3344:
Given an image D, an object category is chosen, e.g. cows or horses.
2160:
time. This is impractical for image segmentation applications where
2012:, compute the weight of each edge, and summarize the information in
2856:
is called a pairwise term. A unary term consists of the likelihood
3547:
3347:
The corresponding LPS model is matched to D to obtain the samples
2302:
time, which is the optimal complexity, since the eigenvector has
1895:
1258:
90:
data from satellites to identify and measure regions of interest.
3718:
Image
Parsing: Unifying Segmentation, Detection, and Recognition
3632:
Knyazev, Andrew V. (2003). Boley; Dhillon; Ghosh; Kogan (eds.).
2334:
2270:
3744:
Locus: Learning object classes with unsupervised segmentation
3677:
Multiscale
Spectral Graph Partitioning and Image Segmentation
2338:
1898:. To make the problem tractable, we relax the constraints on
317:
have high similarity, and the vertices in two different sets
2849:{\displaystyle \Psi _{xy}(m_{x},m_{y})+\phi (D|m_{x},m_{y})}
928:
measures the total similarity of vertices in the same part.
290:, where, according to some measure, the vertices in any set
2747:{\displaystyle \phi _{x}(D|m_{x})+\phi _{x}(m_{x}|\Theta )}
2257:
For high-resolution images, the second eigenvalue is often
3690:
M. P. Kumar, P. H. S. Torr, and A. Zisserman. Obj cut. In
1149:{\displaystyle \operatorname {nassoc} (S,{\overline {S}})}
921:{\displaystyle \operatorname {nassoc} (S,{\overline {S}})}
499:{\displaystyle w(A,B)=\sum \limits _{i\in A,j\in B}w_{ij}}
3733:. Toward Category-Level Object Recognition 2006: 508–524
3720:. Toward Category-Level Object Recognition 2006: 545–576
2111:
Recursively partition the segmented parts, if necessary.
1338:{\displaystyle \operatorname {ncut} (S,{\overline {S}})}
1250:{\displaystyle \operatorname {ncut} (S,{\overline {S}})}
1104:{\displaystyle \operatorname {ncut} (S,{\overline {S}})}
876:{\displaystyle \operatorname {ncut} (S,{\overline {S}})}
3655:. Fast Manifold Learning Workshop, WM Williamburg, VA.
1261:
problem. However, we can find in polynomial time a cut
3179:{\displaystyle \sum \limits _{i}w_{i}E(m,\Theta _{i})}
2102:
for eigenvectors with the second smallest eigenvalues.
3443:
3401:
3353:
3249:
3219:
3192:
3130:
3103:
3043:
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2672:
2465:
2427:
2403:
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2308:
2279:
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2202:
2166:
2130:
2108:
Decide if the current partition should be subdivided.
2061:
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2018:
1980:
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1572:
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1366:
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measures the similarity between different parts, and
844:
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785:
650:
515:
433:
407:
387:
323:
296:
276:
230:
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106:
55:
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the object, that is, it infers a set of labels
3496:The objective function is minimized using a single
2361:as first proposed in and actually tested in and.
3619:"Spectral Clustering — scikit-learn documentation"
3486:
3429:
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3232:
3205:
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2899:
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2314:
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2217:
2172:
2152:
2094:
2044:
2024:
2004:
1974:Given a set of features, set up a weighted graph
1957:
1910:
1886:
1814:
1774:
1751:
1697:
1552:
1506:
1480:
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1204:
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1005:
920:
875:
830:
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413:
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349:
309:
282:
262:
216:
196:
184:is a function of the similarity between the nodes
176:
138:
3766:
1965:for the second smallest generalized eigenvalue.
3386:{\displaystyle \Theta _{1},\cdots ,\Theta _{s}}
1887:{\displaystyle {\frac {y^{T}(D-W)y}{y^{T}Dy}}}
111:
779:In the normalized cuts approach, for any cut
1746:
1731:
1563:After some algebraic manipulations, we get:
1408:{\displaystyle d(i)=\sum \limits _{j}w_{ij}}
2325:
2115:
1205:{\displaystyle (S^{*},{\overline {S}}^{*})}
1059:{\displaystyle (S^{*},{\overline {S}}^{*})}
3716:Z. Tu, X. Chen, A. L. Yuille, S. C. Zhu:
3581:
2377:Let m be a set of binary labels, and let
3530:Minimum spanning tree-based segmentation
2951:{\displaystyle \phi _{x}(m_{x}|\Theta )}
2907:based on color, and the unary potential
2225:, so such a matrix-vector product takes
46:Segmentation-based object categorization
18:Segmentation based object categorization
3673:
3648:
3631:
3030:{\displaystyle \Psi _{xy}(m_{x},m_{y})}
14:
3767:
3487:{\displaystyle w_{i}=g(\Theta _{i}|Z)}
2978:. A pairwise term consists of a prior
2417:is a shape prior on the labels from a
2180:is the number of pixels in the image.
3775:Object recognition and categorization
3705:Class-specific, top-down segmentation
3500:operation to obtain the segmentation
2754:is called a unary term, and the term
1352:
3729:B. Leibe, A. Leonardis, B. Schiele:
3087:{\displaystyle \phi (D|m_{x},m_{y})}
1894:subject to the constraints above is
48:can be viewed as a specific case of
3508:
3280:
3132:
2343:algebraic multigrid preconditioning
1383:
1293:{\displaystyle (S,{\overline {S}})}
811:{\displaystyle (S,{\overline {S}})}
456:
263:{\displaystyle V_{1},\cdots ,V_{k}}
24:
3464:
3415:
3374:
3355:
3312:
3221:
3164:
2986:
2965:
2942:
2900:{\displaystyle \phi _{x}(D|m_{x})}
2762:
2738:
2568:
2555:
2478:
2440:
2404:
2384:
360:
107:Segmentation using normalized cuts
56:Applications of image segmentation
25:
3791:
2421:(LPS) model). An energy function
2095:{\displaystyle (D-W)y=\lambda Dy}
1958:{\displaystyle (D-W)y=\lambda Dy}
1752:{\displaystyle y_{i}\in \{1,-b\}}
3430:{\displaystyle E(m,\Theta _{i})}
52:applied to image segmentation.
3749:
3736:
3723:
3694:, San Diego, pages 18–25, 2005.
3213:is the weight of the parameter
3710:
3697:
3684:
3667:
3642:
3625:
3611:
3598:
3541:
3481:
3474:
3460:
3424:
3405:
3321:
3302:
3173:
3154:
3081:
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3047:
3024:
2998:
2945:
2938:
2924:
2894:
2880:
2873:
2843:
2816:
2809:
2800:
2774:
2741:
2734:
2720:
2704:
2690:
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2580:
2558:
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2521:
2507:
2500:
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2283:
2241:
2235:
2212:
2206:
2147:
2134:
2074:
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1999:
1987:
1937:
1925:
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1845:
1668:
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1627:
1608:
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1332:
1313:
1287:
1268:
1244:
1225:
1199:
1166:
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981:
963:
944:
915:
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713:
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681:
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593:
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534:
522:
449:
437:
165:
153:
13:
1:
3535:
1553:{\displaystyle w_{ij}=w_{ji}}
3338:
2449:{\displaystyle E(m,\Theta )}
1708:subject to the constraints:
1622:
1592:
1327:
1282:
1239:
1188:
1138:
1093:
1042:
995:
958:
910:
865:
800:
421:be two subsets of vertices.
7:
3674:Knyazev, Andrew V. (2006).
3661:10.13140/RG.2.2.35280.02565
3649:Knyazev, Andrew V. (2006).
3270:
3233:{\displaystyle \Theta _{i}}
2958:based on the distance from
2419:layered pictorial structure
1969:The partitioning algorithm:
1634:
1574:
1300:of small normalized weight
381:) be a weighted graph. Let
350:{\displaystyle V_{i},V_{j}}
112:Graph theoretic formulation
10:
3796:
3703:E. Borenstein, S. Ullman:
3574:10.1038/s41598-017-14237-8
2364:
177:{\displaystyle (i,j)\in E}
3520:Interleaved segmentation
1815:{\displaystyle y^{t}D1=0}
1507:{\displaystyle n\times n}
1468:on the diagonal, and let
1441:{\displaystyle n\times n}
3755:J. M. Winn, J. Shotton:
2326:Software Implementations
2153:{\displaystyle O(n^{3})}
2116:Computational Complexity
2971:{\displaystyle \Theta }
2456:is defined as follows.
2410:{\displaystyle \Theta }
2390:{\displaystyle \Theta }
2005:{\displaystyle G=(V,E)}
82:Mapping and measurement
3759:. CVPR (1) 2006: 37–44
3488:
3431:
3387:
3328:
3234:
3207:
3180:
3118:
3088:
3031:
2972:
2952:
2901:
2850:
2748:
2656:
2450:
2411:
2391:
2316:
2296:
2248:
2219:
2174:
2154:
2124:, for instance) takes
2096:
2046:
2026:
2006:
1959:
1912:
1888:
1816:
1776:
1753:
1699:
1554:
1514:symmetric matrix with
1508:
1482:
1462:
1442:
1409:
1339:
1294:
1251:
1206:
1150:
1105:
1060:
1007:
922:
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832:
812:
770:
635:
500:
415:
395:
351:
311:
284:
264:
218:
198:
178:
140:
139:{\displaystyle w_{ij}}
86:Automatic analysis of
3489:
3432:
3388:
3329:
3235:
3208:
3206:{\displaystyle w_{i}}
3181:
3119:
3117:{\displaystyle m^{*}}
3089:
3032:
2973:
2953:
2902:
2851:
2749:
2657:
2451:
2412:
2397:be a shape parameter(
2392:
2317:
2297:
2249:
2220:
2175:
2155:
2097:
2047:
2027:
2007:
1960:
1913:
1889:
1817:
1777:
1754:
1700:
1555:
1509:
1483:
1463:
1448:diagonal matrix with
1443:
1410:
1340:
1295:
1252:
1207:
1151:
1106:
1061:
1008:
923:
878:
833:
813:
771:
636:
501:
416:
396:
357:have low similarity.
352:
312:
310:{\displaystyle V_{i}}
285:
265:
219:
199:
179:
141:
3742:J. Winn, N. Joijic.
3441:
3399:
3351:
3247:
3217:
3190:
3128:
3101:
3041:
3037:and a contrast term
2982:
2962:
2911:
2860:
2758:
2670:
2463:
2425:
2401:
2381:
2306:
2295:{\displaystyle O(n)}
2277:
2247:{\displaystyle O(n)}
2229:
2218:{\displaystyle O(n)}
2200:
2164:
2128:
2059:
2036:
2016:
1978:
1922:
1902:
1829:
1787:
1763:
1759:, for some constant
1715:
1570:
1518:
1492:
1472:
1452:
1426:
1364:
1304:
1265:
1216:
1163:
1115:
1070:
1017:
935:
887:
842:
822:
783:
648:
513:
431:
405:
385:
321:
294:
274:
228:
208:
188:
150:
120:
3566:2017NatSR...714029L
2194:Matrix-free methods
2186:matrix-free fashion
1347:spectral techniques
50:spectral clustering
3780:Image segmentation
3554:Scientific Reports
3484:
3427:
3383:
3324:
3288:
3278:
3230:
3203:
3176:
3140:
3114:
3097:The best labeling
3084:
3027:
2968:
2948:
2897:
2846:
2744:
2652:
2446:
2407:
2387:
2359:graph partitioning
2355:image segmentation
2312:
2292:
2244:
2215:
2170:
2150:
2092:
2042:
2022:
2002:
1955:
1908:
1884:
1812:
1775:{\displaystyle -b}
1772:
1749:
1695:
1642:
1601:
1550:
1504:
1478:
1458:
1438:
1405:
1391:
1353:The ncut algorithm
1335:
1290:
1247:
1202:
1146:
1101:
1056:
1003:
918:
873:
828:
808:
766:
631:
496:
482:
411:
391:
347:
307:
280:
270:of the vertex set
260:
214:
194:
174:
136:
34:graph partitioning
29:image segmentation
3279:
3269:
3131:
2315:{\displaystyle n}
2263:Lanczos algorithm
2190:Lanczos algorithm
2173:{\displaystyle n}
2045:{\displaystyle W}
2025:{\displaystyle D}
1911:{\displaystyle y}
1882:
1693:
1633:
1625:
1595:
1573:
1481:{\displaystyle W}
1461:{\displaystyle d}
1382:
1330:
1285:
1242:
1191:
1141:
1096:
1045:
998:
961:
913:
868:
831:{\displaystyle G}
803:
764:
717:
629:
582:
455:
414:{\displaystyle B}
394:{\displaystyle A}
283:{\displaystyle V}
217:{\displaystyle j}
197:{\displaystyle i}
72:Medical diagnosis
62:Image compression
16:(Redirected from
3787:
3760:
3753:
3747:
3740:
3734:
3727:
3721:
3714:
3708:
3701:
3695:
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3629:
3623:
3622:
3615:
3609:
3602:
3596:
3595:
3585:
3560:(14029): 14029.
3545:
3509:Other approaches
3493:
3491:
3490:
3485:
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2647:
2635:
2634:
2625:
2605:
2604:
2592:
2591:
2579:
2578:
2554:
2549:
2548:
2536:
2535:
2520:
2519:
2510:
2499:
2498:
2455:
2453:
2452:
2447:
2416:
2414:
2413:
2408:
2396:
2394:
2393:
2388:
2349:problem for the
2345:for solving the
2321:
2319:
2318:
2313:
2301:
2299:
2298:
2293:
2253:
2251:
2250:
2245:
2224:
2222:
2221:
2216:
2179:
2177:
2176:
2171:
2159:
2157:
2156:
2151:
2146:
2145:
2101:
2099:
2098:
2093:
2051:
2049:
2048:
2043:
2031:
2029:
2028:
2023:
2011:
2009:
2008:
2003:
1964:
1962:
1961:
1956:
1917:
1915:
1914:
1909:
1893:
1891:
1890:
1885:
1883:
1881:
1874:
1873:
1863:
1844:
1843:
1833:
1821:
1819:
1818:
1813:
1799:
1798:
1781:
1779:
1778:
1773:
1758:
1756:
1755:
1750:
1727:
1726:
1704:
1702:
1701:
1696:
1694:
1692:
1685:
1684:
1674:
1655:
1654:
1644:
1641:
1626:
1618:
1600:
1596:
1588:
1559:
1557:
1556:
1551:
1549:
1548:
1533:
1532:
1513:
1511:
1510:
1505:
1487:
1485:
1484:
1479:
1467:
1465:
1464:
1459:
1447:
1445:
1444:
1439:
1414:
1412:
1411:
1406:
1404:
1403:
1390:
1344:
1342:
1341:
1336:
1331:
1323:
1299:
1297:
1296:
1291:
1286:
1278:
1256:
1254:
1253:
1248:
1243:
1235:
1211:
1209:
1208:
1203:
1198:
1197:
1192:
1184:
1178:
1177:
1159:Computing a cut
1155:
1153:
1152:
1147:
1142:
1134:
1110:
1108:
1107:
1102:
1097:
1089:
1065:
1063:
1062:
1057:
1052:
1051:
1046:
1038:
1032:
1031:
1012:
1010:
1009:
1004:
999:
991:
962:
954:
927:
925:
924:
919:
914:
906:
882:
880:
879:
874:
869:
861:
837:
835:
834:
829:
817:
815:
814:
809:
804:
796:
775:
773:
772:
767:
765:
763:
743:
723:
718:
716:
696:
676:
640:
638:
637:
632:
630:
628:
608:
588:
583:
581:
561:
541:
505:
503:
502:
497:
495:
494:
481:
420:
418:
417:
412:
400:
398:
397:
392:
356:
354:
353:
348:
346:
345:
333:
332:
316:
314:
313:
308:
306:
305:
289:
287:
286:
281:
269:
267:
266:
261:
259:
258:
240:
239:
223:
221:
220:
215:
203:
201:
200:
195:
183:
181:
180:
175:
145:
143:
142:
137:
135:
134:
21:
3795:
3794:
3790:
3789:
3788:
3786:
3785:
3784:
3765:
3764:
3763:
3754:
3750:
3741:
3737:
3728:
3724:
3715:
3711:
3702:
3698:
3689:
3685:
3672:
3668:
3647:
3643:
3630:
3626:
3617:
3616:
3612:
3604:Jianbo Shi and
3603:
3599:
3546:
3542:
3538:
3514:Jigsaw approach
3511:
3473:
3467:
3463:
3448:
3444:
3442:
3439:
3438:
3418:
3414:
3400:
3397:
3396:
3377:
3373:
3358:
3354:
3352:
3349:
3348:
3341:
3315:
3311:
3293:
3289:
3283:
3273:
3254:
3250:
3248:
3245:
3244:
3224:
3220:
3218:
3215:
3214:
3197:
3193:
3191:
3188:
3187:
3167:
3163:
3145:
3141:
3135:
3129:
3126:
3125:
3108:
3104:
3102:
3099:
3098:
3075:
3071:
3062:
3058:
3053:
3042:
3039:
3038:
3018:
3014:
3005:
3001:
2989:
2985:
2983:
2980:
2979:
2963:
2960:
2959:
2937:
2931:
2927:
2918:
2914:
2912:
2909:
2908:
2888:
2884:
2879:
2867:
2863:
2861:
2858:
2857:
2837:
2833:
2824:
2820:
2815:
2794:
2790:
2781:
2777:
2765:
2761:
2759:
2756:
2755:
2733:
2727:
2723:
2714:
2710:
2698:
2694:
2689:
2677:
2673:
2671:
2668:
2667:
2643:
2639:
2630:
2626:
2621:
2600:
2596:
2587:
2583:
2571:
2567:
2550:
2544:
2540:
2531:
2527:
2515:
2511:
2506:
2494:
2490:
2464:
2461:
2460:
2426:
2423:
2422:
2402:
2399:
2398:
2382:
2379:
2378:
2367:
2351:graph Laplacian
2328:
2307:
2304:
2303:
2278:
2275:
2274:
2267:Preconditioning
2259:ill-conditioned
2230:
2227:
2226:
2201:
2198:
2197:
2165:
2162:
2161:
2141:
2137:
2129:
2126:
2125:
2118:
2060:
2057:
2056:
2037:
2034:
2033:
2017:
2014:
2013:
1979:
1976:
1975:
1923:
1920:
1919:
1903:
1900:
1899:
1869:
1865:
1864:
1839:
1835:
1834:
1832:
1830:
1827:
1826:
1794:
1790:
1788:
1785:
1784:
1764:
1761:
1760:
1722:
1718:
1716:
1713:
1712:
1680:
1676:
1675:
1650:
1646:
1645:
1643:
1637:
1617:
1587:
1577:
1571:
1568:
1567:
1541:
1537:
1525:
1521:
1519:
1516:
1515:
1493:
1490:
1489:
1473:
1470:
1469:
1453:
1450:
1449:
1427:
1424:
1423:
1396:
1392:
1386:
1365:
1362:
1361:
1355:
1322:
1305:
1302:
1301:
1277:
1266:
1263:
1262:
1234:
1217:
1214:
1213:
1212:that minimizes
1193:
1183:
1182:
1173:
1169:
1164:
1161:
1160:
1133:
1116:
1113:
1112:
1111:also maximizes
1088:
1071:
1068:
1067:
1066:that minimizes
1047:
1037:
1036:
1027:
1023:
1018:
1015:
1014:
990:
953:
936:
933:
932:
905:
888:
885:
884:
860:
843:
840:
839:
823:
820:
819:
795:
784:
781:
780:
744:
724:
722:
697:
677:
675:
649:
646:
645:
609:
589:
587:
562:
542:
540:
514:
511:
510:
487:
483:
459:
432:
429:
428:
406:
403:
402:
386:
383:
382:
363:
361:Normalized cuts
341:
337:
328:
324:
322:
319:
318:
301:
297:
295:
292:
291:
275:
272:
271:
254:
250:
235:
231:
229:
226:
225:
209:
206:
205:
189:
186:
185:
151:
148:
147:
127:
123:
121:
118:
117:
114:
109:
58:
23:
22:
15:
12:
11:
5:
3793:
3783:
3782:
3777:
3762:
3761:
3748:
3735:
3722:
3709:
3696:
3683:
3666:
3641:
3624:
3610:
3606:Jitendra Malik
3597:
3539:
3537:
3534:
3533:
3532:
3527:
3524:
3521:
3518:
3517:Image parsing
3515:
3510:
3507:
3506:
3505:
3494:
3483:
3480:
3476:
3470:
3466:
3462:
3459:
3456:
3451:
3447:
3426:
3421:
3417:
3413:
3410:
3407:
3404:
3393:
3380:
3376:
3372:
3369:
3366:
3361:
3357:
3345:
3340:
3337:
3336:
3335:
3323:
3318:
3314:
3310:
3307:
3304:
3301:
3296:
3292:
3286:
3282:
3276:
3272:
3268:
3265:
3262:
3257:
3253:
3227:
3223:
3200:
3196:
3175:
3170:
3166:
3162:
3159:
3156:
3153:
3148:
3144:
3138:
3134:
3111:
3107:
3083:
3078:
3074:
3070:
3065:
3061:
3056:
3052:
3049:
3046:
3026:
3021:
3017:
3013:
3008:
3004:
3000:
2995:
2992:
2988:
2967:
2947:
2944:
2940:
2934:
2930:
2926:
2921:
2917:
2896:
2891:
2887:
2882:
2878:
2875:
2870:
2866:
2845:
2840:
2836:
2832:
2827:
2823:
2818:
2814:
2811:
2808:
2805:
2802:
2797:
2793:
2789:
2784:
2780:
2776:
2771:
2768:
2764:
2743:
2740:
2736:
2730:
2726:
2722:
2717:
2713:
2709:
2706:
2701:
2697:
2692:
2688:
2685:
2680:
2676:
2664:
2663:
2651:
2646:
2642:
2638:
2633:
2629:
2624:
2620:
2617:
2614:
2611:
2608:
2603:
2599:
2595:
2590:
2586:
2582:
2577:
2574:
2570:
2566:
2563:
2560:
2557:
2553:
2547:
2543:
2539:
2534:
2530:
2526:
2523:
2518:
2514:
2509:
2505:
2502:
2497:
2493:
2489:
2486:
2483:
2480:
2477:
2474:
2471:
2468:
2445:
2442:
2439:
2436:
2433:
2430:
2406:
2386:
2366:
2363:
2327:
2324:
2311:
2291:
2288:
2285:
2282:
2243:
2240:
2237:
2234:
2214:
2211:
2208:
2205:
2169:
2149:
2144:
2140:
2136:
2133:
2117:
2114:
2113:
2112:
2109:
2106:
2103:
2091:
2088:
2085:
2082:
2079:
2076:
2073:
2070:
2067:
2064:
2053:
2041:
2021:
2001:
1998:
1995:
1992:
1989:
1986:
1983:
1954:
1951:
1948:
1945:
1942:
1939:
1936:
1933:
1930:
1927:
1907:
1880:
1877:
1872:
1868:
1862:
1859:
1856:
1853:
1850:
1847:
1842:
1838:
1823:
1822:
1811:
1808:
1805:
1802:
1797:
1793:
1782:
1771:
1768:
1748:
1745:
1742:
1739:
1736:
1733:
1730:
1725:
1721:
1706:
1705:
1691:
1688:
1683:
1679:
1673:
1670:
1667:
1664:
1661:
1658:
1653:
1649:
1640:
1636:
1632:
1629:
1624:
1621:
1616:
1613:
1610:
1607:
1604:
1599:
1594:
1591:
1586:
1583:
1580:
1576:
1547:
1544:
1540:
1536:
1531:
1528:
1524:
1503:
1500:
1497:
1477:
1457:
1437:
1434:
1431:
1416:
1415:
1402:
1399:
1395:
1389:
1385:
1381:
1378:
1375:
1372:
1369:
1354:
1351:
1334:
1329:
1326:
1321:
1318:
1315:
1312:
1309:
1289:
1284:
1281:
1276:
1273:
1270:
1246:
1241:
1238:
1233:
1230:
1227:
1224:
1221:
1201:
1196:
1190:
1187:
1181:
1176:
1172:
1168:
1145:
1140:
1137:
1132:
1129:
1126:
1123:
1120:
1100:
1095:
1092:
1087:
1084:
1081:
1078:
1075:
1055:
1050:
1044:
1041:
1035:
1030:
1026:
1022:
1002:
997:
994:
989:
986:
983:
980:
977:
974:
971:
968:
965:
960:
957:
952:
949:
946:
943:
940:
917:
912:
909:
904:
901:
898:
895:
892:
872:
867:
864:
859:
856:
853:
850:
847:
827:
807:
802:
799:
794:
791:
788:
777:
776:
762:
759:
756:
753:
750:
747:
742:
739:
736:
733:
730:
727:
721:
715:
712:
709:
706:
703:
700:
695:
692:
689:
686:
683:
680:
674:
671:
668:
665:
662:
659:
656:
653:
642:
641:
627:
624:
621:
618:
615:
612:
607:
604:
601:
598:
595:
592:
586:
580:
577:
574:
571:
568:
565:
560:
557:
554:
551:
548:
545:
539:
536:
533:
530:
527:
524:
521:
518:
507:
506:
493:
490:
486:
480:
477:
474:
471:
468:
465:
462:
458:
454:
451:
448:
445:
442:
439:
436:
410:
390:
362:
359:
344:
340:
336:
331:
327:
304:
300:
279:
257:
253:
249:
246:
243:
238:
234:
213:
193:
173:
170:
167:
164:
161:
158:
155:
133:
130:
126:
113:
110:
108:
105:
104:
103:
102:
101:
96:Transportation
93:
92:
91:
88:remote sensing
79:
78:
77:
69:
68:
67:
57:
54:
9:
6:
4:
3:
2:
3792:
3781:
3778:
3776:
3773:
3772:
3770:
3758:
3752:
3745:
3739:
3732:
3726:
3719:
3713:
3706:
3700:
3693:
3687:
3679:
3678:
3670:
3662:
3658:
3654:
3653:
3645:
3637:
3636:
3628:
3620:
3614:
3607:
3601:
3593:
3589:
3584:
3579:
3575:
3571:
3567:
3563:
3559:
3555:
3551:
3544:
3540:
3531:
3528:
3525:
3522:
3519:
3516:
3513:
3512:
3503:
3499:
3495:
3478:
3468:
3457:
3454:
3449:
3445:
3419:
3411:
3408:
3402:
3394:
3378:
3370:
3367:
3364:
3359:
3346:
3343:
3342:
3316:
3308:
3305:
3299:
3294:
3290:
3284:
3274:
3266:
3263:
3260:
3255:
3251:
3243:
3242:
3241:
3225:
3198:
3194:
3168:
3160:
3157:
3151:
3146:
3142:
3136:
3109:
3105:
3095:
3076:
3072:
3068:
3063:
3059:
3050:
3044:
3019:
3015:
3011:
3006:
3002:
2993:
2990:
2932:
2928:
2919:
2915:
2889:
2885:
2876:
2868:
2864:
2838:
2834:
2830:
2825:
2821:
2812:
2806:
2803:
2795:
2791:
2787:
2782:
2778:
2769:
2766:
2728:
2724:
2715:
2711:
2707:
2699:
2695:
2686:
2678:
2674:
2644:
2640:
2636:
2631:
2627:
2618:
2612:
2609:
2601:
2597:
2593:
2588:
2584:
2575:
2572:
2564:
2561:
2545:
2541:
2532:
2528:
2524:
2516:
2512:
2503:
2495:
2491:
2487:
2484:
2475:
2472:
2466:
2459:
2458:
2457:
2437:
2434:
2428:
2420:
2375:
2373:
2362:
2360:
2357:via spectral
2356:
2352:
2348:
2344:
2340:
2336:
2332:
2323:
2309:
2286:
2280:
2272:
2268:
2264:
2260:
2255:
2238:
2232:
2209:
2203:
2195:
2191:
2187:
2181:
2167:
2142:
2138:
2131:
2123:
2110:
2107:
2104:
2089:
2086:
2083:
2080:
2077:
2071:
2068:
2065:
2054:
2039:
2019:
1996:
1993:
1990:
1984:
1981:
1973:
1972:
1971:
1970:
1966:
1952:
1949:
1946:
1943:
1940:
1934:
1931:
1928:
1905:
1897:
1878:
1875:
1870:
1866:
1860:
1854:
1851:
1848:
1840:
1836:
1809:
1806:
1803:
1800:
1795:
1791:
1783:
1769:
1766:
1743:
1740:
1737:
1734:
1728:
1723:
1719:
1711:
1710:
1709:
1689:
1686:
1681:
1677:
1671:
1665:
1662:
1659:
1651:
1647:
1638:
1630:
1619:
1614:
1611:
1605:
1602:
1589:
1584:
1581:
1566:
1565:
1564:
1561:
1545:
1542:
1538:
1534:
1529:
1526:
1522:
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2329:
2322:components.
2256:
2182:
2122:QR algorithm
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2353:to perform
1825:Minimizing
146:of an edge
42:maximum cut
38:minimum cut
3769:Categories
3536:References
3526:LayoutCRF
3437:and using
3124:minimizes
2347:eigenvalue
1418:Also, let
3465:Θ
3416:Θ
3375:Θ
3368:⋯
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3339:Algorithm
3313:Θ
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3165:Θ
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3186:, where
1013:, a cut
3583:5656590
3562:Bibcode
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1896:NP-hard
1259:NP-hard
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3523:LOCUS
3498:MINCUT
2335:LOBPCG
2271:LOBPCG
2254:time.
2055:Solve
1488:be an
1422:be an
1345:using
1257:is an
1119:nassoc
976:nassoc
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891:nassoc
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204:and
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