1046:
Harris-Affine detector. The performance changes depending on the type of scene being analyzed. The
Hessian affine detector responds well to textured scenes in which there are a lot of corner-like parts. However, for some structured scenes, like buildings, the Hessian affine detector performs very well. This is complementary to MSER that tends to do better with well structured (segmentable) scenes.
1058:: K. Mikolajczyk maintains a web page that contains Linux binaries of the Hessian-Affine detector in addition to other detectors and descriptors. Matlab code is also available that can be used to illustrate and compute the repeatability of various detectors. Code and images are also available to duplicate the results found in the Mikolajczyk et al. (2005) paper.
549:
1018:
interest points. Furthermore, using these initially detected points, the
Hessian affine detector uses an iterative shape adaptation algorithm to compute the local affine transformation for each interest point. The implementation of this algorithm is almost identical to that of the Harris affine
1045:
Overall, the
Hessian affine detector performs second best to MSER. Like the Harris affine detector, Hessian affine interest regions tend to be more numerous and smaller than other detectors. For a single image, the Hessian affine detector typically identifies more reliable regions than the
1001:
1005:
As discussed in
Mikolajczyk et al.(2005), by choosing points that maximize the determinant of the Hessian, this measure penalizes longer structures that have small second derivatives (signal changes) in a single direction. This type of measure is very similar to the measures used in the
1035:
detectors. Mikolajczyk et al. analyzed both structured images and textured images in their evaluation. Linux binaries of the detectors and their test images are freely available at their webpage. A brief summary of the results of
Mikolajczyk et al. (2005) follow; see
390:
on the second-moment matrix. The
Hessian affine also uses a multiple scale iterative algorithm to spatially localize and select scale and affine invariant points. However, at each individual scale, the Hessian affine detector chooses interest points based on the
400:
1013:
Like the Harris affine algorithm, these interest points based on the
Hessian matrix are also spatially localized using an iterative search based on the Laplacian of Gaussians. Predictably, these interest points are called
821:
763:
826:
306:
653:
592:
1217:
K. Mikolajczyk, T. Tuytelaars, C. Schmid, A. Zisserman, J. Matas, F. Schaffalitzky, T. Kadir and L. Van Gool, A comparison of affine region detectors. In IJCV 65(1/2):43-72, 2005
799:
695:
directions. It's important to note that the derivatives are computed in the current iteration scale and thus are derivatives of an image smoothed by a
Gaussian kernel:
98:
1010:
schemes proposed by
Lindeberg (1998), where either the Laplacian or the determinant of the Hessian were used in blob detection methods with automatic scale selection.
299:
693:
673:
612:
335:. Like other feature detectors, the Hessian affine detector is typically used as a preprocessing step to algorithms that rely on identifiable, characteristic
544:{\displaystyle H(\mathbf {x} )={\begin{bmatrix}L_{xx}(\mathbf {x} )&L_{xy}(\mathbf {x} )\\L_{yx}(\mathbf {x} )&L_{yy}(\mathbf {x} )\\\end{bmatrix}}}
1263:
292:
88:
83:
996:{\displaystyle {\begin{aligned}DET=\sigma _{I}^{2}(L_{xx}L_{yy}(\mathbf {x} )-L_{xy}^{2}(\mathbf {x} ))\\TR=\sigma _{I}(L_{xx}+L_{yy})\end{aligned}}}
1027:
Mikolajczyk et al. (2005) have done a thorough analysis of several state of the art affine region detectors: Harris affine, Hessian affine,
1297:
698:
1228:
J.Matas, O. Chum, M. Urban, and T. Pajdla, Robust wide baseline stereo from maximally stable extremal regions. In BMVC pp. 384–393, 2002.
1130:
Lindeberg, Tony. "Feature detection with automatic scale selection", International
Journal of Computer Vision, 30, 2, pp. 77–116, 1998.
146:
1239:
T.Tuytelaars and L. Van Gool, Matching widely separated views based on affine invariant regions . In IJCV 59(1):61–85, 2004.
1198:
1075:
1064:
1238:
324:
93:
1032:
1028:
355:
351:
237:
141:
1227:
1216:
1037:
1173:
252:
1142:
1129:
1284:– Bibliography of feature (and blob) detectors maintained by USC Institute for Robotics and Intelligent Systems
1114:
108:
136:
1250:
T. Kadir, A. Zisserman, and M. Brady, An affine invariant salient region detector. In ECCV pp. 404–416, 2004.
1249:
766:
367:
347:
216:
103:
1019:
detector; however, the above mentioned Hessian measure replaces all instances of the Harris corner measure.
195:
1275:– Code, test Images, bibliography of Affine Covariant Features maintained by Krystian Mikolajczyk and the
617:
556:
174:
126:
1143:"Shape-adapted smoothing in estimation of 3-D depth cues from affine distortions of local 2-D structure"
280:
275:
242:
772:
19:
336:
804:
At each scale, interest points are those points that simultaneously are local extrema of both the
769:
article, the derivatives must be scaled appropriately by a factor related to the Gaussian kernel:
1091:
371:
211:
131:
1282:
813:
60:
40:
1199:
Mikolajczyk K. and Schmid, C. 2004. Scale & affine invariant interest point detectors.
45:
386:
The Harris affine detector relies on interest points detected at multiple scales using the
1071:: – binary code for Linux, Windows and SunOS from VIREO research group, see more from the
8:
35:
1178:
Encyclopedia of Computer Science and Engineering (Benjamin Wah, ed), John Wiley and Sons
678:
658:
597:
270:
1158:
1115:
Mikolajczyk, K. and Schmid, C. 2002. An affine invariant interest point detector. In
809:
1273:
1055:
1181:
1154:
387:
190:
74:
55:
1185:
342:
The Hessian affine detector is part of the subclass of feature detectors known as
1079:
1068:
328:
169:
155:
1072:
1061:
1007:
392:
332:
117:
50:
26:
1291:
65:
375:
378:
in 2002, based on earlier work in, see also for a more general overview.
805:
261:
812:
of the Hessian matrix. The trace of Hessian matrix is identical to the
358:, edge-based regions (EBR) and intensity-extrema-based (IBR) regions.
1268:
758:{\displaystyle L(\mathbf {x} )=g(\sigma _{I})\otimes I(\mathbf {x} )}
1276:
1096:
1265:– Presentation slides from Mikolajczyk et al. on their 2005 paper.
1117:
Proceedings of the 8th International Conference on Computer Vision
1022:
366:
The Hessian affine detector algorithm is almost identical to the
1140:
247:
426:
381:
824:
775:
701:
681:
661:
620:
600:
559:
403:
1279:
from the Robotics group at the University of Oxford.
995:
793:
757:
687:
667:
647:
606:
586:
543:
1171:
1289:
1023:Robustness to affine and other transformations
655:is the mixed partial second derivative in the
300:
370:. In fact, both algorithms were derived by
307:
293:
1212:
1210:
1201:International Journal on Computer Vision
361:
1270:– Cordelia Schmid's Computer Vision Lab
1039:A comparison of affine region detectors
1290:
1207:
1192:
1108:
1180:. Vol. IV. pp. 2495–2504.
1141:T. Lindeberg and J. Garding (1997).
1123:
1049:
648:{\displaystyle L_{ab}(\mathbf {x} )}
594:is second partial derivative in the
587:{\displaystyle L_{aa}(\mathbf {x} )}
1298:Feature detection (computer vision)
382:How does the Hessian affine differ?
13:
1042:for a more quantitative analysis.
204:Affine invariant feature detection
14:
1309:
1257:
352:maximally stable extremal regions
142:Maximally stable extremal regions
99:Hessian feature strength measures
921:
889:
748:
709:
638:
577:
526:
500:
472:
446:
411:
794:{\displaystyle \sigma _{I}^{2}}
1243:
1232:
1221:
1165:
1134:
986:
954:
928:
925:
917:
893:
885:
856:
752:
744:
735:
722:
713:
705:
642:
634:
581:
573:
530:
522:
504:
496:
476:
468:
450:
442:
415:
407:
321:Hessian affine region detector
1:
1186:10.1002/9780470050118.ecse609
1159:10.1016/S0262-8856(97)01144-X
1102:
767:Harris affine region detector
368:Harris affine region detector
356:Kadir–Brady saliency detector
348:Harris affine region detector
137:Determinant of Hessian (DoH)
132:Difference of Gaussians (DoG)
196:Generalized structure tensor
7:
1085:
175:Generalized Hough transform
127:Laplacian of Gaussian (LoG)
10:
1314:
1172:T. Lindeberg (2008–2009).
1147:Image and Vision Computing
350:, Hessian affine regions,
1056:Affine Covariant Features
1092:Affine shape adaptation
765:. As discussed in the
212:Affine shape adaptation
997:
814:Laplacian of Gaussians
795:
759:
689:
669:
649:
608:
588:
545:
327:used in the fields of
276:Implementation details
1277:Visual Geometry Group
998:
796:
760:
690:
670:
650:
609:
589:
546:
388:Harris corner measure
362:Algorithm description
94:Level curve curvature
1119:, Vancouver, Canada.
1031:, IBR & EBR and
822:
773:
699:
679:
659:
618:
598:
557:
401:
372:Krystian Mikolajczyk
916:
855:
790:
230:Feature description
1078:2017-05-11 at the
1067:2017-05-11 at the
993:
991:
899:
841:
791:
776:
755:
685:
665:
645:
604:
584:
541:
535:
271:Scale-space axioms
1050:Software packages
688:{\displaystyle b}
668:{\displaystyle a}
607:{\displaystyle a}
317:
316:
20:Feature detection
1305:
1252:
1247:
1241:
1236:
1230:
1225:
1219:
1214:
1205:
1196:
1190:
1189:
1169:
1163:
1162:
1138:
1132:
1127:
1121:
1112:
1002:
1000:
999:
994:
992:
985:
984:
969:
968:
953:
952:
924:
915:
910:
892:
884:
883:
871:
870:
854:
849:
800:
798:
797:
792:
789:
784:
764:
762:
761:
756:
751:
734:
733:
712:
694:
692:
691:
686:
674:
672:
671:
666:
654:
652:
651:
646:
641:
633:
632:
613:
611:
610:
605:
593:
591:
590:
585:
580:
572:
571:
550:
548:
547:
542:
540:
539:
529:
521:
520:
503:
495:
494:
475:
467:
466:
449:
441:
440:
414:
344:affine-invariant
325:feature detector
309:
302:
295:
191:Structure tensor
183:Structure tensor
75:Corner detection
16:
15:
1313:
1312:
1308:
1307:
1306:
1304:
1303:
1302:
1288:
1287:
1260:
1255:
1248:
1244:
1237:
1233:
1226:
1222:
1215:
1208:
1197:
1193:
1170:
1166:
1139:
1135:
1128:
1124:
1113:
1109:
1105:
1088:
1080:Wayback Machine
1069:Wayback Machine
1052:
1025:
1016:Hessian–Laplace
990:
989:
977:
973:
961:
957:
948:
944:
932:
931:
920:
911:
903:
888:
876:
872:
863:
859:
850:
845:
825:
823:
820:
819:
785:
780:
774:
771:
770:
747:
729:
725:
708:
700:
697:
696:
680:
677:
676:
660:
657:
656:
637:
625:
621:
619:
616:
615:
599:
596:
595:
576:
564:
560:
558:
555:
554:
534:
533:
525:
513:
509:
507:
499:
487:
483:
480:
479:
471:
459:
455:
453:
445:
433:
429:
422:
421:
410:
402:
399:
398:
395:at that point:
384:
376:Cordelia Schmid
364:
337:interest points
329:computer vision
313:
170:Hough transform
162:Hough transform
156:Ridge detection
84:Harris operator
12:
11:
5:
1311:
1301:
1300:
1286:
1285:
1280:
1271:
1266:
1259:
1258:External links
1256:
1254:
1253:
1242:
1231:
1220:
1206:
1191:
1164:
1153:(6): 415–434.
1133:
1122:
1106:
1104:
1101:
1100:
1099:
1094:
1087:
1084:
1083:
1082:
1059:
1051:
1048:
1024:
1021:
1008:blob detection
988:
983:
980:
976:
972:
967:
964:
960:
956:
951:
947:
943:
940:
937:
934:
933:
930:
927:
923:
919:
914:
909:
906:
902:
898:
895:
891:
887:
882:
879:
875:
869:
866:
862:
858:
853:
848:
844:
840:
837:
834:
831:
828:
827:
788:
783:
779:
754:
750:
746:
743:
740:
737:
732:
728:
724:
721:
718:
715:
711:
707:
704:
684:
664:
644:
640:
636:
631:
628:
624:
614:direction and
603:
583:
579:
575:
570:
567:
563:
538:
532:
528:
524:
519:
516:
512:
508:
506:
502:
498:
493:
490:
486:
482:
481:
478:
474:
470:
465:
462:
458:
454:
452:
448:
444:
439:
436:
432:
428:
427:
425:
420:
417:
413:
409:
406:
393:Hessian matrix
383:
380:
363:
360:
333:image analysis
315:
314:
312:
311:
304:
297:
289:
286:
285:
284:
283:
278:
273:
265:
264:
258:
257:
256:
255:
250:
245:
240:
232:
231:
227:
226:
225:
224:
222:Hessian affine
219:
214:
206:
205:
201:
200:
199:
198:
193:
185:
184:
180:
179:
178:
177:
172:
164:
163:
159:
158:
152:
151:
150:
149:
144:
139:
134:
129:
121:
120:
118:Blob detection
114:
113:
112:
111:
106:
101:
96:
91:
89:Shi and Tomasi
86:
78:
77:
71:
70:
69:
68:
63:
58:
53:
48:
43:
38:
30:
29:
27:Edge detection
23:
22:
9:
6:
4:
3:
2:
1310:
1299:
1296:
1295:
1293:
1283:
1281:
1278:
1274:
1272:
1269:
1267:
1264:
1262:
1261:
1251:
1246:
1240:
1235:
1229:
1224:
1218:
1213:
1211:
1204:
1202:
1195:
1187:
1183:
1179:
1175:
1174:"Scale-space"
1168:
1160:
1156:
1152:
1148:
1144:
1137:
1131:
1126:
1120:
1118:
1111:
1107:
1098:
1095:
1093:
1090:
1089:
1081:
1077:
1074:
1070:
1066:
1063:
1060:
1057:
1054:
1053:
1047:
1043:
1041:
1040:
1034:
1030:
1020:
1017:
1011:
1009:
1003:
981:
978:
974:
970:
965:
962:
958:
949:
945:
941:
938:
935:
912:
907:
904:
900:
896:
880:
877:
873:
867:
864:
860:
851:
846:
842:
838:
835:
832:
829:
817:
815:
811:
807:
802:
786:
781:
777:
768:
741:
738:
730:
726:
719:
716:
702:
682:
662:
629:
626:
622:
601:
568:
565:
561:
551:
536:
517:
514:
510:
491:
488:
484:
463:
460:
456:
437:
434:
430:
423:
418:
404:
396:
394:
389:
379:
377:
373:
369:
359:
357:
353:
349:
345:
340:
338:
334:
330:
326:
322:
310:
305:
303:
298:
296:
291:
290:
288:
287:
282:
279:
277:
274:
272:
269:
268:
267:
266:
263:
260:
259:
254:
251:
249:
246:
244:
241:
239:
236:
235:
234:
233:
229:
228:
223:
220:
218:
217:Harris affine
215:
213:
210:
209:
208:
207:
203:
202:
197:
194:
192:
189:
188:
187:
186:
182:
181:
176:
173:
171:
168:
167:
166:
165:
161:
160:
157:
154:
153:
148:
145:
143:
140:
138:
135:
133:
130:
128:
125:
124:
123:
122:
119:
116:
115:
110:
107:
105:
102:
100:
97:
95:
92:
90:
87:
85:
82:
81:
80:
79:
76:
73:
72:
67:
66:Roberts cross
64:
62:
59:
57:
54:
52:
49:
47:
44:
42:
39:
37:
34:
33:
32:
31:
28:
25:
24:
21:
18:
17:
1245:
1234:
1223:
1203:60(1):63–86.
1200:
1194:
1177:
1167:
1150:
1146:
1136:
1125:
1116:
1110:
1044:
1038:
1026:
1015:
1012:
1004:
818:
803:
552:
397:
385:
365:
343:
341:
320:
318:
221:
46:Differential
806:determinant
346:detectors:
262:Scale space
1103:References
1062:lip-vireo
946:σ
897:−
843:σ
778:σ
739:⊗
727:σ
1292:Category
1097:Isotropy
1086:See also
1076:Archived
1073:homepage
1065:Archived
281:Pyramids
61:Robinson
1033:salient
816:(LoG):
56:Prewitt
41:Deriche
553:where
810:trace
323:is a
104:SUSAN
51:Sobel
36:Canny
1029:MSER
808:and
675:and
374:and
331:and
319:The
248:GLOH
243:SURF
238:SIFT
147:PCBR
109:FAST
1182:doi
1155:doi
253:HOG
1294::
1209:^
1176:.
1151:15
1149:.
1145:.
801:.
354:,
339:.
1188:.
1184::
1161:.
1157::
987:)
982:y
979:y
975:L
971:+
966:x
963:x
959:L
955:(
950:I
942:=
939:R
936:T
929:)
926:)
922:x
918:(
913:2
908:y
905:x
901:L
894:)
890:x
886:(
881:y
878:y
874:L
868:x
865:x
861:L
857:(
852:2
847:I
839:=
836:T
833:E
830:D
787:2
782:I
753:)
749:x
745:(
742:I
736:)
731:I
723:(
720:g
717:=
714:)
710:x
706:(
703:L
683:b
663:a
643:)
639:x
635:(
630:b
627:a
623:L
602:a
582:)
578:x
574:(
569:a
566:a
562:L
537:]
531:)
527:x
523:(
518:y
515:y
511:L
505:)
501:x
497:(
492:x
489:y
485:L
477:)
473:x
469:(
464:y
461:x
457:L
451:)
447:x
443:(
438:x
435:x
431:L
424:[
419:=
416:)
412:x
408:(
405:H
308:e
301:t
294:v
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.