3764:
simplified vision systems was developed where such regions of interest and scale descriptors were used for directing the focus-of-attention of an active vision system. While the specific technique that was used in these prototypes can be substantially improved with the current knowledge in computer vision, the overall general approach is still valid, for example in the way that local extrema over scales of the scale-normalized
Laplacian operator are nowadays used for providing scale information to other visual processes.
917:-dimensional image) and strong negative responses for bright blobs of similar size. A main problem when applying this operator at a single scale, however, is that the operator response is strongly dependent on the relationship between the size of the blob structures in the image domain and the size of the Gaussian kernel used for pre-smoothing. In order to automatically capture blobs of different (unknown) size in the image domain, a multi-scale approach is therefore necessary.
2368:
than the
Laplacian operator. In (Lindeberg 2013b, 2015) it is shown that the determinant of the Hessian operator performs significantly better than the Laplacian operator or its difference-of-Gaussians approximation, as well as better than the Harris or Harris-Laplace operators, for image-based matching using local SIFT-like or SURF-like image descriptors, leading to higher efficiency values and lower 1-precision scores.
25:
2977:
2367:
A detailed analysis of the selection properties of the determinant of the
Hessian operator and other closely scale-space interest point detectors is given in (Lindeberg 2013a) showing that the determinant of the Hessian operator has better scale selection properties under affine image transformations
1398:
Note that this notion of blob provides a concise and mathematically precise operational definition of the notion of "blob", which directly leads to an efficient and robust algorithm for blob detection. Some basic properties of blobs defined from scale-space maxima of the normalized
Laplacian operator
3812:
associated with the local maximum. However, it is rather straightforward to extend this approach to other types of watershed constructions. For example, by proceeding beyond the first delimiting saddle point a "grey-level blob tree" can be constructed. Moreover, the grey-level blob detection method
3738:
A natural approach to detect blobs is to associate a bright (dark) blob with each local maximum (minimum) in the intensity landscape. A main problem with such an approach, however, is that local extrema are very sensitive to noise. To address this problem, Lindeberg (1993, 1994) studied the problem
2355:
are also defined from an operational differential geometric definitions that leads to blob descriptors that are covariant with translations, rotations and rescalings in the image domain. In terms of scale selection, blobs defined from scale-space extrema of the determinant of the
Hessian (DoH) also
1925:
and can be seen as an approximation of the
Laplacian operator. In a similar fashion as for the Laplacian blob detector, blobs can be detected from scale-space extrema of differences of Gaussians—see (Lindeberg 2012, 2015) for the explicit relation between the difference-of-Gaussian operator and the
389:
that differ in properties, such as brightness or color, compared to surrounding regions. Informally, a blob is a region of an image in which some properties are constant or approximately constant; all the points in a blob can be considered in some sense to be similar to each other. The most common
2637:
The blob descriptors obtained from these blob detectors with automatic scale selection are invariant to translations, rotations and uniform rescalings in the spatial domain. The images that constitute the input to a computer vision system are, however, also subject to perspective distortions. To
3763:
It was proposed that regions of interest and scale descriptors obtained in this way, with associated scale levels defined from the scales at which normalized measures of blob strength assumed their maxima over scales could be used for guiding other early visual processing. An early prototype of
1576:
The scale selection properties of the
Laplacian operator and other closely scale-space interest point detectors are analyzed in detail in (Lindeberg 2013a). In (Lindeberg 2013b, 2015) it is shown that there exist other scale-space interest point detectors, such as the determinant of the Hessian
3824:
This algorithm with its applications in computer vision is described in more detail in
Lindeberg's thesis as well as the monograph on scale-space theory partially based on that work. Earlier presentations of this algorithm can also be found in . More detailed treatments of applications of
2646:
to a blob descriptor, where the shape of the smoothing kernel is iteratively warped to match the local image structure around the blob, or equivalently a local image patch is iteratively warped while the shape of the smoothing kernel remains rotationally symmetric (Lindeberg and
Garding 1997;
3784:
For simplicity, consider the case of detecting bright grey-level blobs and let the notation "higher neighbour" stand for "neighbour pixel having a higher grey-level value". Then, at any stage in the algorithm (carried out in decreasing order of intensity values) is based on the following
3751:
was defined to capture the nested topological structure of level sets in the intensity landscape, in a way that is invariant to affine deformations in the image domain and monotone intensity transformations. By studying how these structures evolve with increasing scales, the notion of
3577:
3387:
2376:
A hybrid operator between the
Laplacian and the determinant of the Hessian blob detectors has also been proposed, where spatial selection is done by the determinant of the Hessian and scale selection is performed with the scale-normalized Laplacian (Mikolajczyk and Schmid 2004):
1392:
2270:
3795:
Else, if it has more than one higher neighbour and if those higher neighbours are parts of different blobs, then it cannot be a part of any blob, and must be background. If any of the higher neighbors are still allowed to grow, clear their flag which allows them to
3656:, if we want this operator to assume its maximum value over spatio-temporal scales at a spatio-temporal scale level reflecting the spatial extent and the temporal duration of an onset Gaussian blob. For the second operator, scale selection properties call for using
2624:
1911:
2669:
4157:
Jean-Francois Mangin, Denis Rivière, Olivier Coulon, Cyril Poupon, Arnaud Cachia, Yann Cointepas, Jean-Baptiste Poline, Denis Le Bihan, Jean Régis, Dimitri Papadopoulos-Orfanos: "Coordinate-based versus structural approaches to brain image analysis".
4066:, PhD thesis, Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden, May 1991. (ISSN 1101-2250. ISRN KTH NA/P--91/8--SE) (The grey-level blob detection algorithm is described in section 7.1)
2356:
have slightly better scale selection properties under non-Euclidean affine transformations than the more commonly used Laplacian operator (Lindeberg 1994, 1998, 2015). In simplified form, the scale-normalized determinant of the Hessian computed from
3743:. A region with spatial extent defined from a watershed analogy was associated with each local maximum, as well a local contrast defined from a so-called delimiting saddle point. A local extremum with extent defined in this way was referred to as a
3854:
There are close relations between this notion and the above-mentioned notion of grey-level blob tree. The maximally stable extremal regions can be seen as making a specific subset of the grey-level blob tree explicit for further processing.
2498:
2647:
Baumberg 2000; Mikolajczyk and Schmid 2004, Lindeberg 2008). In this way, we can define affine-adapted versions of the Laplacian/Difference of Gaussian operator, the determinant of the Hessian and the Hessian-Laplace operator (see also
3199:
The Laplacian operator has been extended to spatio-temporal video data by Lindeberg, leading to the following two spatio-temporal operators, which also constitute models of receptive fields of non-lagged vs. lagged neurons in the LGN:
2057:
3799:
Else, it has one or more higher neighbours, which are all parts of the same blob. If that blob is still allowed to grow then the current region should be included as a part of that blob. Otherwise the region should be set to
434:. In early work in the area, blob detection was used to obtain regions of interest for further processing. These regions could signal the presence of objects or parts of objects in the image domain with application to
633:
3395:
3206:
3780:
the pixels, alternatively connected regions having the same intensity, in decreasing order of the intensity values. Then, comparisons were made between nearest neighbours of either pixels or connected regions.
1016:
2109:
and then detecting scale-space maxima of this operator one obtains another straightforward differential blob detector with automatic scale selection which also responds to saddles (Lindeberg 1994, 1998)
1236:
3946:
Lindeberg (2013) "Image Matching Using Generalized Scale-Space Interest Points", Scale Space and Variational Methods in Computer Vision, Springer Lecture Notes in Computer Science Volume 7893, 2013, pp
3730:, if we want this operator to assume its maximum value over spatio-temporal scales at a spatio-temporal scale level reflecting the spatial extent and the temporal duration of a blinking Gaussian blob.
1695:
1151:
is computed and a point is regarded as a bright (dark) blob if the value at this point is greater (smaller) than the value in all its 26 neighbours. Thus, simultaneous selection of interest points
1555:
2116:
2972:{\displaystyle \det(H_{(x,y,t),\mathrm {norm} }L)=s^{2\gamma _{s}}\tau ^{\gamma _{\tau }}\left(L_{xx}L_{yy}L_{tt}+2L_{xy}L_{xt}L_{yt}-L_{xx}L_{yt}^{2}-L_{yy}L_{xt}^{2}-L_{tt}L_{xy}^{2}\right).}
3196:
will perfectly match the spatial extent and the temporal duration of the blob, with scale selection performed by detecting spatio-temporal scale-space extrema of the differential expression.
2504:
1761:
1071:
364:
820:
751:
3932:
Lindeberg, Tony (2013) "Scale Selection Properties of Generalized Scale-Space Interest Point Detectors", Journal of Mathematical Imaging and Vision, Volume 46, Issue 2, pages 177-210.
2324:
1199:
3728:
3654:
3128:
2663:
The determinant of the Hessian operator has been extended to joint space-time by Willems et al. and Lindeberg, leading to the following scale-normalized differential expression:
1749:
1456:
3046:
3194:
3087:
3687:
3613:
3013:
426:
There are several motivations for studying and developing blob detectors. One main reason is to provide complementary information about regions, which is not obtained from
2353:
1228:
411:, which are based on finding the local maxima and minima of the function. With the more recent terminology used in the field, these detectors can also be referred to as
156:
1633:
1149:
3161:
462:
and to signal the presence of informative image features for appearance-based object recognition based on local image statistics. There is also the related notion of
1577:
operator, that perform better than Laplacian operator or its difference-of-Gaussians approximation for image-based matching using local SIFT-like image descriptors.
1108:
517:
3843:. They studied level sets in the intensity landscape and measured how stable these were along the intensity dimension. Based on this idea, they defined a notion of
2383:
895:
859:
357:
2083:
3965:
T. Lindeberg ``Image matching using generalized scale-space interest points", Journal of Mathematical Imaging and Vision, volume 52, number 1, pages 3-36, 2015.
2107:
1476:
656:
915:
3756:
was introduced. Beyond local contrast and extent, these scale-space blobs also measured how stable image structures are in scale-space, by measuring their
1399:
are that the responses are covariant with translations, rotations and rescalings in the image domain. Thus, if a scale-space maximum is assumed at a point
1948:
350:
3130:
implies better scale selection properties in the sense that the selected scale levels obtained from a spatio-temporal Gaussian blob with spatial extent
146:
141:
1557:
in the rescaled image (Lindeberg 1998). This in practice highly useful property implies that besides the specific topic of Laplacian blob detection,
4103:, (Osaka, Japan), pp. 416--426, Dec. 1990. (See Appendix A.1 for the basic definitions for the watershed-based grey-level blob detection algorithm.)
3993:
Geert Willems, Tinne Tuytelaars and Luc van Gool (2008). "An efficient dense and scale-invariant spatiotemporal-temporal interest point detector".
43:
4127:
Lindeberg, T.: Detecting salient blob-like image structures and their scales with a scale-space primal sketch: A method for focus-of-attention,
529:
3572:{\displaystyle \partial _{tt,\mathrm {norm} }(\nabla _{(x,y),\mathrm {norm} }^{2}L)=s^{\gamma _{s}}\tau ^{\gamma _{\tau }}(L_{xxtt}+L_{yytt}).}
3382:{\displaystyle \partial _{t,\mathrm {norm} }(\nabla _{(x,y),\mathrm {norm} }^{2}L)=s^{\gamma _{s}}\tau ^{\gamma _{\tau }/2}(L_{xxt}+L_{yyt}),}
4480:
3789:
If a region has no higher neighbour, then it is a local maximum and will be the seed of a blob. Set a flag which allows the blob to grow.
397:
Given some property of interest expressed as a function of position on the image, there are two main classes of blob detectors: (i)
933:
3909:
2638:
obtain blob descriptors that are more robust to perspective transformations, a natural approach is to devise a blob detector that is
1387:{\displaystyle ({\hat {x}},{\hat {y}};{\hat {t}})=\operatorname {argmaxminlocal} _{(x,y;t)}((\nabla _{\mathrm {norm} }^{2}L)(x,y;t))}
204:
4227:"Detecting Salient Blob-Like Image Structures and Their Scales with a Scale-Space Primal Sketch: A Method for Focus-of-Attention"
1644:
4142:
Lindeberg, T, Lidberg, Par and Roland, P. E..: "Analysis of Brain Activation Patterns Using a 3-D Scale-Space Primal Sketch",
3825:
grey-level blob detection and the scale-space primal sketch to computer vision and medical image analysis are given in .
3792:
Else, if it has at least one higher neighbour, which is background, then it cannot be part of any blob and must be background.
4366:
4272:
2265:{\displaystyle ({\hat {x}},{\hat {y}};{\hat {t}})=\operatorname {argmaxlocal} _{(x,y;t)}((\det H_{\mathrm {norm} }L)(x,y;t))}
1481:
4436:
4164:
3894:
2619:{\displaystyle {\hat {t}}=\operatorname {argmaxminlocal} _{t}((\nabla _{\mathrm {norm} }^{2}L)({\hat {x}},{\hat {y}};t))}
1906:{\displaystyle \nabla _{\mathrm {norm} }^{2}L(x,y;t)\approx {\frac {t}{\Delta t}}\left(L(x,y;t+\Delta t)-L(x,y;t)\right)}
151:
4087:
3834:
1927:
1566:
295:
199:
61:
1030:
4319:
4226:
4141:
4126:
447:
310:
4344:
4283:
4198:
4098:
763:
664:
3904:
454:
analysis and texture recognition. In more recent work, blob descriptors have found increasingly popular use as
279:
166:
4099:
T. Lindeberg and J.-O. Eklundh, "Scale detection and region extraction from a scale-space primal sketch", in
3899:
2279:
1154:
274:
161:
4320:"Shape-adapted smoothing in estimation of 3-{D} depth cues from affine distortions of local 2-{D} structure"
253:
1939:
3692:
3618:
3092:
1703:
1559:
local maxima/minima of the scale-normalized Laplacian are also used for scale selection in other contexts
1402:
451:
232:
3975:
3814:
3018:
2361:
1752:
1592:
659:
338:
333:
300:
3166:
3051:
77:
3840:
4394:
3889:
3659:
3585:
2985:
455:
416:
3808:
in this algorithm stops once the intensity level falls below the intensity value of the so-called
1921:(DoG) approach. Besides minor technicalities, however, this operator is in essence similar to the
3874:
2643:
2371:
1918:
1586:
269:
189:
4190:
Proceedings of the 9th European Conference on Computer Vision, Springer LNCS volume 3951, part 1
3776:(local extrema with extent) from a watershed analogy, Lindeberg developed an algorithm based on
2629:
This operator has been used for image matching, object recognition as well as texture analysis.
2329:
1204:
4389:
3848:
1751:
can also be computed as the limit case of the difference between two Gaussian smoothed images (
3964:
2493:{\displaystyle ({\hat {x}},{\hat {y}})=\operatorname {argmaxlocal} _{(x,y)}((\det HL)(x,y;t))}
1597:
1113:
3133:
399:
118:
98:
1078:
487:
103:
3747:. Moreover, by proceeding with the watershed analogy beyond the delimiting saddle point, a
864:
828:
8:
4455:
4420:
4403:
4348:
825:
is computed, which usually results in strong positive responses for dark blobs of radius
404:, which are based on derivatives of the function with respect to position, and (ii)
93:
3839:
Matas et al. (2002) were interested in defining image descriptors that are robust under
2065:
1938:
By considering the scale-normalized determinant of the Hessian, also referred to as the
39:
4459:
4407:
4306:
4249:
4044:
2092:
1636:
1570:
1461:
641:
459:
435:
328:
4335:
3945:
4411:
4377:
4362:
4268:
4113:
T. Lindeberg and J.-O. Eklundh, "On the computation of a scale-space primal sketch",
4083:
407:
4253:
4061:
4463:
4451:
4399:
4354:
4331:
4298:
4241:
4213:
4048:
4034:
3998:
3931:
3869:
2052:{\displaystyle \det H_{\mathrm {norm} }L=t^{2}\left(L_{xx}L_{yy}-L_{xy}^{2}\right)}
1562:
900:
446:
analysis, blob descriptors can also be used for peak detection with application to
431:
420:
248:
132:
113:
4358:
4310:
3767:
4185:
4168:
4002:
3884:
3864:
480:
463:
443:
378:
227:
213:
3997:. Springer Lecture Notes in Computer Science. Vol. 5303. pp. 650–663.
3992:
3733:
4156:
3817:
and performed at all levels of scale, resulting in a representation called the
2652:
2086:
1926:
scale-normalized Laplacian operator. This approach is for instance used in the
439:
427:
108:
84:
4302:
4039:
4022:
2372:
The hybrid Laplacian and determinant of the Hessian operator (Hessian-Laplace)
4474:
2648:
386:
123:
2642:. In practice, affine invariant interest points can be obtained by applying
4217:
2357:
1075:(Lindeberg 1994, 1998). Thus, given a discrete two-dimensional input image
628:{\displaystyle g(x,y,t)={\frac {1}{2\pi t}}e^{-{\frac {x^{2}+y^{2}}{2t}}}}
3879:
3847:
and showed how these image descriptors can be used as image features for
3740:
520:
391:
319:
4262:
4076:
2364:
descriptor (Bay et al. 2006) for image matching and object recognition.
1565:, scale-adaptive feature tracking (Bretzner and Lindeberg 1998), in the
4245:
3805:
1917:
In the computer vision literature, this approach is referred to as the
1569:(Lowe 2004) as well as other image descriptors for image matching and
2982:
In the work by Willems et al., a simpler expression corresponding to
1922:
754:
476:
474:
One of the first and also most common blob detectors is based on the
4421:"Robust wide baseline stereo from maximally stable extremum regions"
450:. Another common use of blob descriptors is as main primitives for
3582:
For the first operator, scale selection properties call for using
1011:{\displaystyle \nabla _{\mathrm {norm} }^{2}L=t\,(L_{xx}+L_{yy})}
4418:
3768:
Lindeberg's watershed-based grey-level blob detection algorithm
4183:
4199:"Feature Tracking with Automatic Selection of Spatial Scales"
4064:
Discrete Scale-Space Theory and the Scale-Space Primal Sketch
3734:
Grey-level blobs, grey-level blob trees and scale-space blobs
2632:
3739:
of detecting local maxima with extent at multiple scales in
4378:"Distinctive Image Features from Scale-Invariant Keypoints"
3828:
305:
4353:. Vol. IV. John Wiley and Sons. pp. 2495–2504.
1690:{\displaystyle \partial _{t}L={\frac {1}{2}}\nabla ^{2}L}
4115:
Journal of Visual Communication and Image Representation
922:
multi-scale blob detector with automatic scale selection
4434:
4196:
1700:
it follows that the Laplacian of the Gaussian operator
1580:
415:, or alternatively interest region operators (see also
1458:
then under a rescaling of the image by a scale factor
903:
867:
831:
4437:"Scale and affine invariant interest point detectors"
4101:
Proc. 3rd International Conference on Computer Vision
3695:
3662:
3621:
3588:
3398:
3209:
3169:
3136:
3095:
3054:
3021:
2988:
2672:
2507:
2386:
2332:
2282:
2119:
2095:
2068:
1951:
1764:
1706:
1647:
1600:
1550:{\displaystyle \left(sx_{0},sy_{0};s^{2}t_{0}\right)}
1484:
1464:
1405:
1239:
1207:
1157:
1116:
1081:
1033:
936:
766:
667:
644:
532:
490:
4419:
J. Matas; O. Chum; M. Urban & T. Pajdla (2002).
2360:
is used as the basic interest point operator in the
194:
34:
may be too technical for most readers to understand
4284:"Feature detection with automatic scale selection"
3722:
3681:
3648:
3607:
3571:
3381:
3188:
3155:
3122:
3081:
3040:
3007:
2971:
2618:
2492:
2347:
2318:
2264:
2101:
2077:
2051:
1905:
1743:
1689:
1627:
1549:
1470:
1450:
1386:
1222:
1193:
1143:
1102:
1065:
1010:
909:
889:
853:
814:
745:
650:
627:
511:
2658:
1933:
4472:
4350:Encyclopedia of Computer Science and Engineering
4317:
4184:H. Bay; T. Tuytelaars & L. van Gool (2006).
3976:T. Lindeberg ``Scale invariant feature transform
2673:
2454:
2208:
1952:
1110:a three-dimensional discrete scale-space volume
4023:"Spatio-temporal scale selection in video data"
4020:
1066:{\displaystyle \nabla _{\mathrm {norm} }^{2}L}
184:
4016:
4014:
4012:
466:to signal the presence of elongated objects.
358:
4281:
4260:
4224:
469:
385:methods are aimed at detecting regions in a
3988:
3986:
3960:
3958:
3956:
3954:
3941:
3939:
3927:
3925:
4375:
4027:Journal of Mathematical Imaging and Vision
4009:
3048:was used. In Lindeberg, it was shown that
2633:Affine-adapted differential blob detectors
815:{\displaystyle \nabla ^{2}L=L_{xx}+L_{yy}}
746:{\displaystyle L(x,y;t)\ =g(x,y,t)*f(x,y)}
365:
351:
4393:
4342:
4038:
3969:
3804:Compared to other watershed methods, the
1478:, there will be a scale-space maximum at
972:
62:Learn how and when to remove this message
46:, without removing the technical details.
4444:International Journal of Computer Vision
4382:International Journal of Computer Vision
4291:International Journal of Computer Vision
4234:International Journal of Computer Vision
4129:International Journal of Computer Vision
3983:
3951:
3936:
3922:
3829:Maximally stable extremal regions (MSER)
4206:Computer Vision and Image Understanding
4197:L. Bretzner & T. Lindeberg (1998).
2319:{\displaystyle ({\hat {x}},{\hat {y}})}
1194:{\displaystyle ({\hat {x}},{\hat {y}})}
4473:
3995:European Conference on Computer Vision
1027:simultaneously local maxima/minima of
390:method for blob detection is by using
4264:Scale-Space Theory in Computer Vision
4079:Scale-Space Theory in Computer Vision
44:make it understandable to non-experts
1581:The difference of Gaussians approach
1073:with respect to both space and scale
18:
16:A particular task in computer vision
4481:Feature detection (computer vision)
4318:Lindeberg, T.; Garding, J. (1997).
4160:Artificial Intelligence in Medicine
3895:Feature detection (computer vision)
3723:{\displaystyle \gamma _{\tau }=3/4}
3649:{\displaystyle \gamma _{\tau }=1/2}
3123:{\displaystyle \gamma _{\tau }=5/4}
2640:invariant to affine transformations
1744:{\displaystyle \nabla ^{2}L(x,y,t)}
1451:{\displaystyle (x_{0},y_{0};t_{0})}
926:scale-normalized Laplacian operator
753:. Then, the result of applying the
13:
4456:10.1023/B:VISI.0000027790.02288.f2
4435:K. Mikolajczyk; C. Schmid (2004).
4404:10.1023/B:VISI.0000029664.99615.94
4186:"SURF: Speeded Up Robust Features"
4177:
4081:, Kluwer Academic Publishers, 1994
3465:
3462:
3459:
3456:
3433:
3423:
3420:
3417:
3414:
3400:
3273:
3270:
3267:
3264:
3241:
3231:
3228:
3225:
3222:
3211:
2718:
2715:
2712:
2709:
2557:
2554:
2551:
2548:
2543:
2226:
2223:
2220:
2217:
2089:of the scale-space representation
1970:
1967:
1964:
1961:
1930:(SIFT) algorithm—see Lowe (2004).
1862:
1824:
1780:
1777:
1774:
1771:
1766:
1708:
1675:
1649:
1343:
1340:
1337:
1334:
1329:
1049:
1046:
1043:
1040:
1035:
952:
949:
946:
943:
938:
920:A straightforward way to obtain a
768:
262:Affine invariant feature detection
14:
4492:
4428:British Machine Vision Conference
4146:, vol 7, no 3, pp 166--194, 1999.
3978:, Scholarpedia, 7(5):10491, 2012.
3845:maximally stable extremal regions
3835:Maximally stable extremal regions
3041:{\displaystyle \gamma _{\tau }=1}
1928:scale-invariant feature transform
1567:scale-invariant feature transform
200:Maximally stable extremal regions
157:Hessian feature strength measures
4117:, vol. 2, pp. 55--78, Mar. 1991.
23:
4150:
4135:
4120:
4107:
3189:{\displaystyle \tau =\tau _{0}}
3082:{\displaystyle \gamma _{s}=5/4}
4092:
4070:
4055:
3905:Hessian affine region detector
3563:
3519:
3479:
3449:
3437:
3429:
3373:
3335:
3287:
3257:
3245:
3237:
2727:
2702:
2684:
2676:
2659:Spatio-temporal blob detectors
2613:
2610:
2598:
2583:
2574:
2571:
2539:
2536:
2514:
2487:
2484:
2466:
2463:
2451:
2448:
2440:
2428:
2417:
2411:
2396:
2387:
2339:
2313:
2307:
2292:
2283:
2259:
2256:
2238:
2235:
2205:
2202:
2194:
2176:
2165:
2159:
2144:
2129:
2120:
1934:The determinant of the Hessian
1895:
1877:
1868:
1841:
1812:
1794:
1738:
1720:
1622:
1604:
1445:
1406:
1381:
1378:
1360:
1357:
1325:
1322:
1314:
1296:
1285:
1279:
1264:
1249:
1240:
1214:
1188:
1182:
1167:
1158:
1138:
1120:
1097:
1085:
1005:
973:
861:(for a two-dimensional image,
740:
728:
719:
701:
689:
671:
554:
536:
506:
494:
1:
4359:10.1002/9780470050118.ecse609
4336:10.1016/S0262-8856(97)01144-X
3915:
3900:Harris affine region detector
3772:For the purpose of detecting
3682:{\displaystyle \gamma _{s}=1}
3608:{\displaystyle \gamma _{s}=1}
3008:{\displaystyle \gamma _{s}=1}
195:Determinant of Hessian (DoH)
190:Difference of Gaussians (DoG)
4003:10.1007/978-3-540-88688-4_48
484:(LoG). Given an input image
442:. In other domains, such as
254:Generalized structure tensor
7:
3858:
3841:perspective transformations
1753:scale space representations
1025:, that are points that are
233:Generalized Hough transform
185:Laplacian of Gaussian (LoG)
10:
4497:
4347:. In Wah, Benjamin (ed.).
4324:Image and Vision Computing
3832:
3815:scale space representation
2348:{\displaystyle {\hat {t}}}
1593:scale space representation
1584:
1230:is performed according to
1223:{\displaystyle {\hat {t}}}
660:scale space representation
4040:10.1007/s10851-017-0766-9
3819:scale-space primal sketch
1023:scale-space maxima/minima
470:The Laplacian of Gaussian
4131:, 11(3), 283--318, 1993.
3890:Interest point detection
1628:{\displaystyle L(x,y,t)}
1144:{\displaystyle L(x,y,t)}
417:interest point detection
413:interest point operators
4303:10.1023/A:1008045108935
4021:Tony Lindeberg (2018).
3875:Affine shape adaptation
3810:delimiting saddle point
3156:{\displaystyle s=s_{0}}
2644:affine shape adaptation
1919:difference of Gaussians
1591:From the fact that the
1587:Difference of Gaussians
406:methods based on local
270:Affine shape adaptation
4343:Lindeberg, T. (2008).
4218:10.1006/cviu.1998.0650
4167:July 21, 2011, at the
3785:classification rules:
3724:
3683:
3650:
3609:
3573:
3383:
3190:
3157:
3124:
3083:
3042:
3009:
2973:
2620:
2494:
2349:
2320:
2266:
2103:
2079:
2053:
1907:
1745:
1691:
1629:
1551:
1472:
1452:
1388:
1224:
1195:
1145:
1104:
1103:{\displaystyle f(x,y)}
1067:
1012:
911:
891:
855:
816:
747:
652:
629:
513:
512:{\displaystyle f(x,y)}
334:Implementation details
4282:T. Lindeberg (1998).
4261:T. Lindeberg (1994).
4225:T. Lindeberg (1993).
4162:30(2): 177-197 (2004)
4062:Lindeberg, T. (1991)
3725:
3684:
3651:
3610:
3574:
3384:
3191:
3158:
3125:
3084:
3043:
3010:
2974:
2621:
2495:
2350:
2321:
2267:
2104:
2080:
2054:
1940:Monge–Ampère operator
1908:
1746:
1692:
1630:
1552:
1473:
1453:
1389:
1225:
1196:
1146:
1105:
1068:
1013:
912:
892:
890:{\textstyle r^{2}=dt}
856:
854:{\textstyle r^{2}=2t}
817:
748:
653:
630:
523:by a Gaussian kernel
514:
152:Level curve curvature
3758:scale-space lifetime
3749:grey-level blob tree
3693:
3660:
3619:
3586:
3396:
3207:
3167:
3163:and temporal extent
3134:
3093:
3052:
3019:
2986:
2670:
2505:
2384:
2330:
2280:
2117:
2093:
2066:
1949:
1762:
1704:
1645:
1598:
1482:
1462:
1403:
1237:
1205:
1155:
1114:
1079:
1031:
934:
901:
865:
829:
764:
665:
642:
530:
488:
4430:. pp. 384–393.
4376:D. G. Lowe (2004).
4192:. pp. 404–417.
4144:Human Brain Mapping
3475:
3283:
2960:
2926:
2892:
2567:
2043:
1790:
1353:
1059:
962:
924:is to consider the
638:at a certain scale
288:Feature description
4246:10.1007/BF01469346
3813:was embedded in a
3720:
3679:
3646:
3605:
3569:
3432:
3379:
3240:
3186:
3153:
3120:
3079:
3038:
3005:
2969:
2943:
2909:
2875:
2616:
2542:
2490:
2345:
2316:
2262:
2099:
2078:{\displaystyle HL}
2075:
2049:
2026:
1903:
1765:
1741:
1687:
1637:diffusion equation
1625:
1571:object recognition
1547:
1468:
1448:
1384:
1328:
1220:
1191:
1141:
1100:
1063:
1034:
1008:
937:
907:
887:
851:
812:
743:
648:
625:
509:
458:for wide baseline
436:object recognition
329:Scale-space axioms
4368:978-0-470-05011-8
4274:978-0-7923-9418-1
4077:Lindeberg, Tony,
3754:scale-space blobs
2601:
2586:
2517:
2414:
2399:
2342:
2310:
2295:
2162:
2147:
2132:
2102:{\displaystyle L}
1831:
1672:
1471:{\displaystyle s}
1282:
1267:
1252:
1217:
1185:
1170:
694:
651:{\displaystyle t}
621:
576:
375:
374:
78:Feature detection
72:
71:
64:
4488:
4467:
4441:
4431:
4425:
4415:
4397:
4372:
4339:
4314:
4288:
4278:
4257:
4231:
4221:
4203:
4193:
4171:
4154:
4148:
4139:
4133:
4124:
4118:
4111:
4105:
4096:
4090:
4074:
4068:
4059:
4053:
4052:
4042:
4018:
4007:
4006:
3990:
3981:
3973:
3967:
3962:
3949:
3943:
3934:
3929:
3870:Corner detection
3774:grey-level blobs
3729:
3727:
3726:
3721:
3716:
3705:
3704:
3688:
3686:
3685:
3680:
3672:
3671:
3655:
3653:
3652:
3647:
3642:
3631:
3630:
3614:
3612:
3611:
3606:
3598:
3597:
3578:
3576:
3575:
3570:
3562:
3561:
3540:
3539:
3518:
3517:
3516:
3515:
3501:
3500:
3499:
3498:
3474:
3469:
3468:
3428:
3427:
3426:
3388:
3386:
3385:
3380:
3372:
3371:
3353:
3352:
3334:
3333:
3329:
3324:
3323:
3309:
3308:
3307:
3306:
3282:
3277:
3276:
3236:
3235:
3234:
3195:
3193:
3192:
3187:
3185:
3184:
3162:
3160:
3159:
3154:
3152:
3151:
3129:
3127:
3126:
3121:
3116:
3105:
3104:
3088:
3086:
3085:
3080:
3075:
3064:
3063:
3047:
3045:
3044:
3039:
3031:
3030:
3014:
3012:
3011:
3006:
2998:
2997:
2978:
2976:
2975:
2970:
2965:
2961:
2959:
2954:
2942:
2941:
2925:
2920:
2908:
2907:
2891:
2886:
2874:
2873:
2858:
2857:
2845:
2844:
2832:
2831:
2813:
2812:
2800:
2799:
2787:
2786:
2769:
2768:
2767:
2766:
2752:
2751:
2750:
2749:
2723:
2722:
2721:
2625:
2623:
2622:
2617:
2603:
2602:
2594:
2588:
2587:
2579:
2566:
2561:
2560:
2532:
2531:
2519:
2518:
2510:
2499:
2497:
2496:
2491:
2444:
2443:
2416:
2415:
2407:
2401:
2400:
2392:
2354:
2352:
2351:
2346:
2344:
2343:
2335:
2325:
2323:
2322:
2317:
2312:
2311:
2303:
2297:
2296:
2288:
2276:The blob points
2271:
2269:
2268:
2263:
2231:
2230:
2229:
2198:
2197:
2164:
2163:
2155:
2149:
2148:
2140:
2134:
2133:
2125:
2108:
2106:
2105:
2100:
2084:
2082:
2081:
2076:
2058:
2056:
2055:
2050:
2048:
2044:
2042:
2037:
2022:
2021:
2009:
2008:
1991:
1990:
1975:
1974:
1973:
1912:
1910:
1909:
1904:
1902:
1898:
1832:
1830:
1819:
1789:
1784:
1783:
1750:
1748:
1747:
1742:
1716:
1715:
1696:
1694:
1693:
1688:
1683:
1682:
1673:
1665:
1657:
1656:
1634:
1632:
1631:
1626:
1563:corner detection
1556:
1554:
1553:
1548:
1546:
1542:
1541:
1540:
1531:
1530:
1518:
1517:
1502:
1501:
1477:
1475:
1474:
1469:
1457:
1455:
1454:
1449:
1444:
1443:
1431:
1430:
1418:
1417:
1393:
1391:
1390:
1385:
1352:
1347:
1346:
1318:
1317:
1284:
1283:
1275:
1269:
1268:
1260:
1254:
1253:
1245:
1229:
1227:
1226:
1221:
1219:
1218:
1210:
1200:
1198:
1197:
1192:
1187:
1186:
1178:
1172:
1171:
1163:
1150:
1148:
1147:
1142:
1109:
1107:
1106:
1101:
1072:
1070:
1069:
1064:
1058:
1053:
1052:
1017:
1015:
1014:
1009:
1004:
1003:
988:
987:
961:
956:
955:
916:
914:
913:
908:
896:
894:
893:
888:
877:
876:
860:
858:
857:
852:
841:
840:
821:
819:
818:
813:
811:
810:
795:
794:
776:
775:
752:
750:
749:
744:
692:
657:
655:
654:
649:
634:
632:
631:
626:
624:
623:
622:
620:
612:
611:
610:
598:
597:
587:
577:
575:
561:
519:, this image is
518:
516:
515:
510:
432:corner detectors
421:corner detection
367:
360:
353:
249:Structure tensor
241:Structure tensor
133:Corner detection
74:
73:
67:
60:
56:
53:
47:
27:
26:
19:
4496:
4495:
4491:
4490:
4489:
4487:
4486:
4485:
4471:
4470:
4439:
4423:
4369:
4287:(abstract page)
4286:
4275:
4230:(abstract page)
4229:
4202:(abstract page)
4201:
4180:
4178:Further reading
4175:
4174:
4169:Wayback Machine
4155:
4151:
4140:
4136:
4125:
4121:
4112:
4108:
4097:
4093:
4075:
4071:
4060:
4056:
4019:
4010:
3991:
3984:
3974:
3970:
3963:
3952:
3944:
3937:
3930:
3923:
3918:
3885:Ridge detection
3865:Blob extraction
3861:
3849:stereo matching
3837:
3831:
3770:
3745:grey-level blob
3736:
3712:
3700:
3696:
3694:
3691:
3690:
3667:
3663:
3661:
3658:
3657:
3638:
3626:
3622:
3620:
3617:
3616:
3593:
3589:
3587:
3584:
3583:
3548:
3544:
3526:
3522:
3511:
3507:
3506:
3502:
3494:
3490:
3489:
3485:
3470:
3455:
3436:
3413:
3403:
3399:
3397:
3394:
3393:
3361:
3357:
3342:
3338:
3325:
3319:
3315:
3314:
3310:
3302:
3298:
3297:
3293:
3278:
3263:
3244:
3221:
3214:
3210:
3208:
3205:
3204:
3180:
3176:
3168:
3165:
3164:
3147:
3143:
3135:
3132:
3131:
3112:
3100:
3096:
3094:
3091:
3090:
3071:
3059:
3055:
3053:
3050:
3049:
3026:
3022:
3020:
3017:
3016:
2993:
2989:
2987:
2984:
2983:
2955:
2947:
2934:
2930:
2921:
2913:
2900:
2896:
2887:
2879:
2866:
2862:
2850:
2846:
2837:
2833:
2824:
2820:
2805:
2801:
2792:
2788:
2779:
2775:
2774:
2770:
2762:
2758:
2757:
2753:
2745:
2741:
2737:
2733:
2708:
2683:
2679:
2671:
2668:
2667:
2661:
2635:
2593:
2592:
2578:
2577:
2562:
2547:
2546:
2527:
2523:
2509:
2508:
2506:
2503:
2502:
2427:
2423:
2406:
2405:
2391:
2390:
2385:
2382:
2381:
2374:
2334:
2333:
2331:
2328:
2327:
2302:
2301:
2287:
2286:
2281:
2278:
2277:
2216:
2215:
2211:
2175:
2171:
2154:
2153:
2139:
2138:
2124:
2123:
2118:
2115:
2114:
2094:
2091:
2090:
2067:
2064:
2063:
2038:
2030:
2014:
2010:
2001:
1997:
1996:
1992:
1986:
1982:
1960:
1959:
1955:
1950:
1947:
1946:
1936:
1837:
1833:
1823:
1818:
1785:
1770:
1769:
1763:
1760:
1759:
1711:
1707:
1705:
1702:
1701:
1678:
1674:
1664:
1652:
1648:
1646:
1643:
1642:
1599:
1596:
1595:
1589:
1583:
1536:
1532:
1526:
1522:
1513:
1509:
1497:
1493:
1489:
1485:
1483:
1480:
1479:
1463:
1460:
1459:
1439:
1435:
1426:
1422:
1413:
1409:
1404:
1401:
1400:
1348:
1333:
1332:
1295:
1291:
1274:
1273:
1259:
1258:
1244:
1243:
1238:
1235:
1234:
1209:
1208:
1206:
1203:
1202:
1177:
1176:
1162:
1161:
1156:
1153:
1152:
1115:
1112:
1111:
1080:
1077:
1076:
1054:
1039:
1038:
1032:
1029:
1028:
996:
992:
980:
976:
957:
942:
941:
935:
932:
931:
902:
899:
898:
872:
868:
866:
863:
862:
836:
832:
830:
827:
826:
803:
799:
787:
783:
771:
767:
765:
762:
761:
666:
663:
662:
643:
640:
639:
613:
606:
602:
593:
589:
588:
586:
582:
578:
565:
560:
531:
528:
527:
489:
486:
485:
472:
464:ridge detection
460:stereo matching
456:interest points
379:computer vision
371:
228:Hough transform
220:Hough transform
214:Ridge detection
142:Harris operator
68:
57:
51:
48:
40:help improve it
37:
28:
24:
17:
12:
11:
5:
4494:
4484:
4483:
4469:
4468:
4432:
4416:
4395:10.1.1.73.2924
4373:
4367:
4340:
4330:(6): 415–434.
4315:
4279:
4273:
4258:
4240:(3): 283–318.
4222:
4212:(3): 385–392.
4194:
4179:
4176:
4173:
4172:
4149:
4134:
4119:
4106:
4091:
4069:
4054:
4033:(4): 525–562.
4008:
3982:
3968:
3950:
3935:
3920:
3919:
3917:
3914:
3913:
3912:
3907:
3902:
3897:
3892:
3887:
3882:
3877:
3872:
3867:
3860:
3857:
3833:Main article:
3830:
3827:
3802:
3801:
3797:
3793:
3790:
3769:
3766:
3735:
3732:
3719:
3715:
3711:
3708:
3703:
3699:
3678:
3675:
3670:
3666:
3645:
3641:
3637:
3634:
3629:
3625:
3604:
3601:
3596:
3592:
3580:
3579:
3568:
3565:
3560:
3557:
3554:
3551:
3547:
3543:
3538:
3535:
3532:
3529:
3525:
3521:
3514:
3510:
3505:
3497:
3493:
3488:
3484:
3481:
3478:
3473:
3467:
3464:
3461:
3458:
3454:
3451:
3448:
3445:
3442:
3439:
3435:
3431:
3425:
3422:
3419:
3416:
3412:
3409:
3406:
3402:
3390:
3389:
3378:
3375:
3370:
3367:
3364:
3360:
3356:
3351:
3348:
3345:
3341:
3337:
3332:
3328:
3322:
3318:
3313:
3305:
3301:
3296:
3292:
3289:
3286:
3281:
3275:
3272:
3269:
3266:
3262:
3259:
3256:
3253:
3250:
3247:
3243:
3239:
3233:
3230:
3227:
3224:
3220:
3217:
3213:
3183:
3179:
3175:
3172:
3150:
3146:
3142:
3139:
3119:
3115:
3111:
3108:
3103:
3099:
3078:
3074:
3070:
3067:
3062:
3058:
3037:
3034:
3029:
3025:
3004:
3001:
2996:
2992:
2980:
2979:
2968:
2964:
2958:
2953:
2950:
2946:
2940:
2937:
2933:
2929:
2924:
2919:
2916:
2912:
2906:
2903:
2899:
2895:
2890:
2885:
2882:
2878:
2872:
2869:
2865:
2861:
2856:
2853:
2849:
2843:
2840:
2836:
2830:
2827:
2823:
2819:
2816:
2811:
2808:
2804:
2798:
2795:
2791:
2785:
2782:
2778:
2773:
2765:
2761:
2756:
2748:
2744:
2740:
2736:
2732:
2729:
2726:
2720:
2717:
2714:
2711:
2707:
2704:
2701:
2698:
2695:
2692:
2689:
2686:
2682:
2678:
2675:
2660:
2657:
2653:Hessian-Affine
2634:
2631:
2627:
2626:
2615:
2612:
2609:
2606:
2600:
2597:
2591:
2585:
2582:
2576:
2573:
2570:
2565:
2559:
2556:
2553:
2550:
2545:
2541:
2538:
2535:
2530:
2526:
2525:argmaxminlocal
2522:
2516:
2513:
2500:
2489:
2486:
2483:
2480:
2477:
2474:
2471:
2468:
2465:
2462:
2459:
2456:
2453:
2450:
2447:
2442:
2439:
2436:
2433:
2430:
2426:
2422:
2419:
2413:
2410:
2404:
2398:
2395:
2389:
2373:
2370:
2341:
2338:
2315:
2309:
2306:
2300:
2294:
2291:
2285:
2274:
2273:
2261:
2258:
2255:
2252:
2249:
2246:
2243:
2240:
2237:
2234:
2228:
2225:
2222:
2219:
2214:
2210:
2207:
2204:
2201:
2196:
2193:
2190:
2187:
2184:
2181:
2178:
2174:
2170:
2167:
2161:
2158:
2152:
2146:
2143:
2137:
2131:
2128:
2122:
2098:
2087:Hessian matrix
2074:
2071:
2060:
2059:
2047:
2041:
2036:
2033:
2029:
2025:
2020:
2017:
2013:
2007:
2004:
2000:
1995:
1989:
1985:
1981:
1978:
1972:
1969:
1966:
1963:
1958:
1954:
1935:
1932:
1915:
1914:
1901:
1897:
1894:
1891:
1888:
1885:
1882:
1879:
1876:
1873:
1870:
1867:
1864:
1861:
1858:
1855:
1852:
1849:
1846:
1843:
1840:
1836:
1829:
1826:
1822:
1817:
1814:
1811:
1808:
1805:
1802:
1799:
1796:
1793:
1788:
1782:
1779:
1776:
1773:
1768:
1740:
1737:
1734:
1731:
1728:
1725:
1722:
1719:
1714:
1710:
1698:
1697:
1686:
1681:
1677:
1671:
1668:
1663:
1660:
1655:
1651:
1635:satisfies the
1624:
1621:
1618:
1615:
1612:
1609:
1606:
1603:
1585:Main article:
1582:
1579:
1545:
1539:
1535:
1529:
1525:
1521:
1516:
1512:
1508:
1505:
1500:
1496:
1492:
1488:
1467:
1447:
1442:
1438:
1434:
1429:
1425:
1421:
1416:
1412:
1408:
1396:
1395:
1383:
1380:
1377:
1374:
1371:
1368:
1365:
1362:
1359:
1356:
1351:
1345:
1342:
1339:
1336:
1331:
1327:
1324:
1321:
1316:
1313:
1310:
1307:
1304:
1301:
1298:
1294:
1293:argmaxminlocal
1290:
1287:
1281:
1278:
1272:
1266:
1263:
1257:
1251:
1248:
1242:
1216:
1213:
1190:
1184:
1181:
1175:
1169:
1166:
1160:
1140:
1137:
1134:
1131:
1128:
1125:
1122:
1119:
1099:
1096:
1093:
1090:
1087:
1084:
1062:
1057:
1051:
1048:
1045:
1042:
1037:
1021:and to detect
1019:
1018:
1007:
1002:
999:
995:
991:
986:
983:
979:
975:
971:
968:
965:
960:
954:
951:
948:
945:
940:
910:{\textstyle d}
906:
886:
883:
880:
875:
871:
850:
847:
844:
839:
835:
823:
822:
809:
806:
802:
798:
793:
790:
786:
782:
779:
774:
770:
742:
739:
736:
733:
730:
727:
724:
721:
718:
715:
712:
709:
706:
703:
700:
697:
691:
688:
685:
682:
679:
676:
673:
670:
647:
636:
635:
619:
616:
609:
605:
601:
596:
592:
585:
581:
574:
571:
568:
564:
559:
556:
553:
550:
547:
544:
541:
538:
535:
508:
505:
502:
499:
496:
493:
471:
468:
438:and/or object
428:edge detectors
383:blob detection
373:
372:
370:
369:
362:
355:
347:
344:
343:
342:
341:
336:
331:
323:
322:
316:
315:
314:
313:
308:
303:
298:
290:
289:
285:
284:
283:
282:
280:Hessian affine
277:
272:
264:
263:
259:
258:
257:
256:
251:
243:
242:
238:
237:
236:
235:
230:
222:
221:
217:
216:
210:
209:
208:
207:
202:
197:
192:
187:
179:
178:
176:Blob detection
172:
171:
170:
169:
164:
159:
154:
149:
147:Shi and Tomasi
144:
136:
135:
129:
128:
127:
126:
121:
116:
111:
106:
101:
96:
88:
87:
85:Edge detection
81:
80:
70:
69:
52:September 2009
31:
29:
22:
15:
9:
6:
4:
3:
2:
4493:
4482:
4479:
4478:
4476:
4465:
4461:
4457:
4453:
4449:
4445:
4438:
4433:
4429:
4422:
4417:
4413:
4409:
4405:
4401:
4396:
4391:
4388:(2): 91–110.
4387:
4383:
4379:
4374:
4370:
4364:
4360:
4356:
4352:
4351:
4346:
4345:"Scale-space"
4341:
4337:
4333:
4329:
4325:
4321:
4316:
4312:
4308:
4304:
4300:
4297:(2): 77–116.
4296:
4292:
4285:
4280:
4276:
4270:
4266:
4265:
4259:
4255:
4251:
4247:
4243:
4239:
4235:
4228:
4223:
4219:
4215:
4211:
4207:
4200:
4195:
4191:
4187:
4182:
4181:
4170:
4166:
4163:
4161:
4153:
4147:
4145:
4138:
4132:
4130:
4123:
4116:
4110:
4104:
4102:
4095:
4089:
4088:0-7923-9418-6
4085:
4082:
4080:
4073:
4067:
4065:
4058:
4050:
4046:
4041:
4036:
4032:
4028:
4024:
4017:
4015:
4013:
4004:
4000:
3996:
3989:
3987:
3980:
3979:
3972:
3966:
3961:
3959:
3957:
3955:
3948:
3942:
3940:
3933:
3928:
3926:
3921:
3911:
3908:
3906:
3903:
3901:
3898:
3896:
3893:
3891:
3888:
3886:
3883:
3881:
3878:
3876:
3873:
3871:
3868:
3866:
3863:
3862:
3856:
3852:
3850:
3846:
3842:
3836:
3826:
3822:
3820:
3816:
3811:
3807:
3798:
3794:
3791:
3788:
3787:
3786:
3782:
3779:
3775:
3765:
3761:
3759:
3755:
3750:
3746:
3742:
3731:
3717:
3713:
3709:
3706:
3701:
3697:
3676:
3673:
3668:
3664:
3643:
3639:
3635:
3632:
3627:
3623:
3602:
3599:
3594:
3590:
3566:
3558:
3555:
3552:
3549:
3545:
3541:
3536:
3533:
3530:
3527:
3523:
3512:
3508:
3503:
3495:
3491:
3486:
3482:
3476:
3471:
3452:
3446:
3443:
3440:
3410:
3407:
3404:
3392:
3391:
3376:
3368:
3365:
3362:
3358:
3354:
3349:
3346:
3343:
3339:
3330:
3326:
3320:
3316:
3311:
3303:
3299:
3294:
3290:
3284:
3279:
3260:
3254:
3251:
3248:
3218:
3215:
3203:
3202:
3201:
3197:
3181:
3177:
3173:
3170:
3148:
3144:
3140:
3137:
3117:
3113:
3109:
3106:
3101:
3097:
3076:
3072:
3068:
3065:
3060:
3056:
3035:
3032:
3027:
3023:
3002:
2999:
2994:
2990:
2966:
2962:
2956:
2951:
2948:
2944:
2938:
2935:
2931:
2927:
2922:
2917:
2914:
2910:
2904:
2901:
2897:
2893:
2888:
2883:
2880:
2876:
2870:
2867:
2863:
2859:
2854:
2851:
2847:
2841:
2838:
2834:
2828:
2825:
2821:
2817:
2814:
2809:
2806:
2802:
2796:
2793:
2789:
2783:
2780:
2776:
2771:
2763:
2759:
2754:
2746:
2742:
2738:
2734:
2730:
2724:
2705:
2699:
2696:
2693:
2690:
2687:
2680:
2666:
2665:
2664:
2656:
2654:
2650:
2649:Harris-Affine
2645:
2641:
2630:
2607:
2604:
2595:
2589:
2580:
2568:
2563:
2533:
2528:
2524:
2520:
2511:
2501:
2481:
2478:
2475:
2472:
2469:
2460:
2457:
2445:
2437:
2434:
2431:
2424:
2420:
2408:
2402:
2393:
2380:
2379:
2378:
2369:
2365:
2363:
2359:
2358:Haar wavelets
2336:
2304:
2298:
2289:
2253:
2250:
2247:
2244:
2241:
2232:
2212:
2199:
2191:
2188:
2185:
2182:
2179:
2172:
2168:
2156:
2150:
2141:
2135:
2126:
2113:
2112:
2111:
2096:
2088:
2072:
2069:
2045:
2039:
2034:
2031:
2027:
2023:
2018:
2015:
2011:
2005:
2002:
1998:
1993:
1987:
1983:
1979:
1976:
1956:
1945:
1944:
1943:
1941:
1931:
1929:
1924:
1920:
1899:
1892:
1889:
1886:
1883:
1880:
1874:
1871:
1865:
1859:
1856:
1853:
1850:
1847:
1844:
1838:
1834:
1827:
1820:
1815:
1809:
1806:
1803:
1800:
1797:
1791:
1786:
1758:
1757:
1756:
1754:
1735:
1732:
1729:
1726:
1723:
1717:
1712:
1684:
1679:
1669:
1666:
1661:
1658:
1653:
1641:
1640:
1639:
1638:
1619:
1616:
1613:
1610:
1607:
1601:
1594:
1588:
1578:
1574:
1572:
1568:
1564:
1561:, such as in
1560:
1543:
1537:
1533:
1527:
1523:
1519:
1514:
1510:
1506:
1503:
1498:
1494:
1490:
1486:
1465:
1440:
1436:
1432:
1427:
1423:
1419:
1414:
1410:
1375:
1372:
1369:
1366:
1363:
1354:
1349:
1319:
1311:
1308:
1305:
1302:
1299:
1292:
1288:
1276:
1270:
1261:
1255:
1246:
1233:
1232:
1231:
1211:
1179:
1173:
1164:
1135:
1132:
1129:
1126:
1123:
1117:
1094:
1091:
1088:
1082:
1074:
1060:
1055:
1024:
1000:
997:
993:
989:
984:
981:
977:
969:
966:
963:
958:
930:
929:
928:
927:
923:
918:
904:
884:
881:
878:
873:
869:
848:
845:
842:
837:
833:
807:
804:
800:
796:
791:
788:
784:
780:
777:
772:
760:
759:
758:
756:
737:
734:
731:
725:
722:
716:
713:
710:
707:
704:
698:
695:
686:
683:
680:
677:
674:
668:
661:
645:
617:
614:
607:
603:
599:
594:
590:
583:
579:
572:
569:
566:
562:
557:
551:
548:
545:
542:
539:
533:
526:
525:
524:
522:
503:
500:
497:
491:
483:
482:
478:
467:
465:
461:
457:
453:
449:
445:
441:
437:
433:
429:
424:
422:
418:
414:
410:
409:
403:
401:
395:
393:
388:
387:digital image
384:
380:
368:
363:
361:
356:
354:
349:
348:
346:
345:
340:
337:
335:
332:
330:
327:
326:
325:
324:
321:
318:
317:
312:
309:
307:
304:
302:
299:
297:
294:
293:
292:
291:
287:
286:
281:
278:
276:
275:Harris affine
273:
271:
268:
267:
266:
265:
261:
260:
255:
252:
250:
247:
246:
245:
244:
240:
239:
234:
231:
229:
226:
225:
224:
223:
219:
218:
215:
212:
211:
206:
203:
201:
198:
196:
193:
191:
188:
186:
183:
182:
181:
180:
177:
174:
173:
168:
165:
163:
160:
158:
155:
153:
150:
148:
145:
143:
140:
139:
138:
137:
134:
131:
130:
125:
124:Roberts cross
122:
120:
117:
115:
112:
110:
107:
105:
102:
100:
97:
95:
92:
91:
90:
89:
86:
83:
82:
79:
76:
75:
66:
63:
55:
45:
41:
35:
32:This article
30:
21:
20:
4450:(1): 63–86.
4447:
4443:
4427:
4385:
4381:
4349:
4327:
4323:
4294:
4290:
4267:. Springer.
4263:
4237:
4233:
4209:
4205:
4189:
4159:
4152:
4143:
4137:
4128:
4122:
4114:
4109:
4100:
4094:
4078:
4072:
4063:
4057:
4030:
4026:
3994:
3977:
3971:
3853:
3844:
3838:
3823:
3818:
3809:
3803:
3783:
3777:
3773:
3771:
3762:
3757:
3753:
3748:
3744:
3737:
3581:
3198:
2981:
2662:
2639:
2636:
2628:
2375:
2366:
2275:
2085:denotes the
2061:
1937:
1916:
1699:
1590:
1575:
1558:
1397:
1026:
1022:
1020:
925:
921:
919:
824:
637:
475:
473:
448:segmentation
425:
412:
405:
400:differential
398:
396:
382:
376:
175:
104:Differential
58:
49:
33:
3880:Scale space
3800:background.
3778:pre-sorting
3741:scale space
2425:argmaxlocal
2326:and scales
2173:argmaxlocal
1201:and scales
392:convolution
320:Scale space
3916:References
658:to give a
4412:221242327
4390:CiteSeerX
3702:τ
3698:γ
3665:γ
3628:τ
3624:γ
3591:γ
3513:τ
3509:γ
3504:τ
3492:γ
3434:∇
3401:∂
3321:τ
3317:γ
3312:τ
3300:γ
3242:∇
3212:∂
3178:τ
3171:τ
3102:τ
3098:γ
3057:γ
3028:τ
3024:γ
2991:γ
2928:−
2894:−
2860:−
2764:τ
2760:γ
2755:τ
2743:γ
2599:^
2584:^
2544:∇
2534:
2515:^
2446:
2412:^
2397:^
2340:^
2308:^
2293:^
2200:
2160:^
2145:^
2130:^
2024:−
1923:Laplacian
1872:−
1863:Δ
1825:Δ
1816:≈
1767:∇
1709:∇
1676:∇
1650:∂
1330:∇
1320:
1280:^
1265:^
1250:^
1215:^
1183:^
1168:^
1036:∇
939:∇
769:∇
757:operator
755:Laplacian
723:∗
584:−
570:π
521:convolved
477:Laplacian
444:histogram
4475:Category
4254:11998035
4165:Archived
3947:355-367.
3859:See also
3806:flooding
481:Gaussian
440:tracking
339:Pyramids
119:Robinson
4464:1704741
4049:4430109
479:of the
452:texture
408:extrema
402:methods
114:Prewitt
99:Deriche
38:Please
4462:
4410:
4392:
4365:
4311:723210
4309:
4271:
4252:
4086:
4047:
2062:where
897:for a
693:
4460:S2CID
4440:(PDF)
4424:(PDF)
4408:S2CID
4307:S2CID
4250:S2CID
4045:S2CID
3796:grow.
162:SUSAN
109:Sobel
94:Canny
4363:ISBN
4269:ISBN
4084:ISBN
3910:PCBR
3689:and
3615:and
3089:and
3015:and
2651:and
2362:SURF
419:and
306:GLOH
301:SURF
296:SIFT
205:PCBR
167:FAST
4452:doi
4400:doi
4355:doi
4332:doi
4299:doi
4242:doi
4214:doi
4035:doi
3999:doi
2674:det
2655:).
2455:det
2209:det
1953:det
430:or
423:).
377:In
311:HOG
42:to
4477::
4458:.
4448:60
4446:.
4442:.
4426:.
4406:.
4398:.
4386:60
4384:.
4380:.
4361:.
4328:15
4326:.
4322:.
4305:.
4295:30
4293:.
4289:.
4248:.
4238:11
4236:.
4232:.
4210:71
4208:.
4204:.
4188:.
4043:.
4031:60
4029:.
4025:.
4011:^
3985:^
3953:^
3938:^
3924:^
3851:.
3821:.
3760:.
1942:,
1755:)
1573:.
394:.
381:,
4466:.
4454::
4414:.
4402::
4371:.
4357::
4338:.
4334::
4313:.
4301::
4277:.
4256:.
4244::
4220:.
4216::
4051:.
4037::
4005:.
4001::
3718:4
3714:/
3710:3
3707:=
3677:1
3674:=
3669:s
3644:2
3640:/
3636:1
3633:=
3603:1
3600:=
3595:s
3567:.
3564:)
3559:t
3556:t
3553:y
3550:y
3546:L
3542:+
3537:t
3534:t
3531:x
3528:x
3524:L
3520:(
3496:s
3487:s
3483:=
3480:)
3477:L
3472:2
3466:m
3463:r
3460:o
3457:n
3453:,
3450:)
3447:y
3444:,
3441:x
3438:(
3430:(
3424:m
3421:r
3418:o
3415:n
3411:,
3408:t
3405:t
3377:,
3374:)
3369:t
3366:y
3363:y
3359:L
3355:+
3350:t
3347:x
3344:x
3340:L
3336:(
3331:2
3327:/
3304:s
3295:s
3291:=
3288:)
3285:L
3280:2
3274:m
3271:r
3268:o
3265:n
3261:,
3258:)
3255:y
3252:,
3249:x
3246:(
3238:(
3232:m
3229:r
3226:o
3223:n
3219:,
3216:t
3182:0
3174:=
3149:0
3145:s
3141:=
3138:s
3118:4
3114:/
3110:5
3107:=
3077:4
3073:/
3069:5
3066:=
3061:s
3036:1
3033:=
3003:1
3000:=
2995:s
2967:.
2963:)
2957:2
2952:y
2949:x
2945:L
2939:t
2936:t
2932:L
2923:2
2918:t
2915:x
2911:L
2905:y
2902:y
2898:L
2889:2
2884:t
2881:y
2877:L
2871:x
2868:x
2864:L
2855:t
2852:y
2848:L
2842:t
2839:x
2835:L
2829:y
2826:x
2822:L
2818:2
2815:+
2810:t
2807:t
2803:L
2797:y
2794:y
2790:L
2784:x
2781:x
2777:L
2772:(
2747:s
2739:2
2735:s
2731:=
2728:)
2725:L
2719:m
2716:r
2713:o
2710:n
2706:,
2703:)
2700:t
2697:,
2694:y
2691:,
2688:x
2685:(
2681:H
2677:(
2614:)
2611:)
2608:t
2605:;
2596:y
2590:,
2581:x
2575:(
2572:)
2569:L
2564:2
2558:m
2555:r
2552:o
2549:n
2540:(
2537:(
2529:t
2521:=
2512:t
2488:)
2485:)
2482:t
2479:;
2476:y
2473:,
2470:x
2467:(
2464:)
2461:L
2458:H
2452:(
2449:(
2441:)
2438:y
2435:,
2432:x
2429:(
2421:=
2418:)
2409:y
2403:,
2394:x
2388:(
2337:t
2314:)
2305:y
2299:,
2290:x
2284:(
2272:.
2260:)
2257:)
2254:t
2251:;
2248:y
2245:,
2242:x
2239:(
2236:)
2233:L
2227:m
2224:r
2221:o
2218:n
2213:H
2206:(
2203:(
2195:)
2192:t
2189:;
2186:y
2183:,
2180:x
2177:(
2169:=
2166:)
2157:t
2151:;
2142:y
2136:,
2127:x
2121:(
2097:L
2073:L
2070:H
2046:)
2040:2
2035:y
2032:x
2028:L
2019:y
2016:y
2012:L
2006:x
2003:x
1999:L
1994:(
1988:2
1984:t
1980:=
1977:L
1971:m
1968:r
1965:o
1962:n
1957:H
1913:.
1900:)
1896:)
1893:t
1890:;
1887:y
1884:,
1881:x
1878:(
1875:L
1869:)
1866:t
1860:+
1857:t
1854:;
1851:y
1848:,
1845:x
1842:(
1839:L
1835:(
1828:t
1821:t
1813:)
1810:t
1807:;
1804:y
1801:,
1798:x
1795:(
1792:L
1787:2
1781:m
1778:r
1775:o
1772:n
1739:)
1736:t
1733:,
1730:y
1727:,
1724:x
1721:(
1718:L
1713:2
1685:L
1680:2
1670:2
1667:1
1662:=
1659:L
1654:t
1623:)
1620:t
1617:,
1614:y
1611:,
1608:x
1605:(
1602:L
1544:)
1538:0
1534:t
1528:2
1524:s
1520:;
1515:0
1511:y
1507:s
1504:,
1499:0
1495:x
1491:s
1487:(
1466:s
1446:)
1441:0
1437:t
1433:;
1428:0
1424:y
1420:,
1415:0
1411:x
1407:(
1394:.
1382:)
1379:)
1376:t
1373:;
1370:y
1367:,
1364:x
1361:(
1358:)
1355:L
1350:2
1344:m
1341:r
1338:o
1335:n
1326:(
1323:(
1315:)
1312:t
1309:;
1306:y
1303:,
1300:x
1297:(
1289:=
1286:)
1277:t
1271:;
1262:y
1256:,
1247:x
1241:(
1212:t
1189:)
1180:y
1174:,
1165:x
1159:(
1139:)
1136:t
1133:,
1130:y
1127:,
1124:x
1121:(
1118:L
1098:)
1095:y
1092:,
1089:x
1086:(
1083:f
1061:L
1056:2
1050:m
1047:r
1044:o
1041:n
1006:)
1001:y
998:y
994:L
990:+
985:x
982:x
978:L
974:(
970:t
967:=
964:L
959:2
953:m
950:r
947:o
944:n
905:d
885:t
882:d
879:=
874:2
870:r
849:t
846:2
843:=
838:2
834:r
808:y
805:y
801:L
797:+
792:x
789:x
785:L
781:=
778:L
773:2
741:)
738:y
735:,
732:x
729:(
726:f
720:)
717:t
714:,
711:y
708:,
705:x
702:(
699:g
696:=
690:)
687:t
684:;
681:y
678:,
675:x
672:(
669:L
646:t
618:t
615:2
608:2
604:y
600:+
595:2
591:x
580:e
573:t
567:2
563:1
558:=
555:)
552:t
549:,
546:y
543:,
540:x
537:(
534:g
507:)
504:y
501:,
498:x
495:(
492:f
366:e
359:t
352:v
65:)
59:(
54:)
50:(
36:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.