1111:, since they can be designed for a number of dilations and rotations. However, in general, expansion is not applied for Gabor wavelets, since this requires computation of bi-orthogonal wavelets, which may be very time-consuming. Therefore, usually, a filter bank consisting of Gabor filters with various scales and rotations is created. The filters are convolved with the signal, resulting in a so-called Gabor space. This process is closely related to processes in the primary
75:
1124:
Gaussian kernel in the Gabor function with a time-causal and time-recursive kernel referred to as the time-causal limit kernel. In this way, time-frequency analysis based on the resulting complex-valued extension of the time-causal limit kernel makes it possible to capture essentially similar transformations of a temporal signal as the Gabor filter can, and as can be described by the
Heisenberg group, see for further details.
158:
25:
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465:
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gray and colour), since text is rich in high frequency components, whereas pictures are relatively smooth in nature. It has also been applied for facial expression recognition Gabor filters have also been widely used in pattern analysis applications. For example, it has been used to study the directionality distribution inside the porous spongy
865:
665:
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In document image processing, Gabor features are ideal for identifying the script of a word in a multilingual document. Gabor filters with different frequencies and with orientations in different directions have been used to localize and extract text-only regions from complex document images (both
1123:
When processing temporal signals, data from the future cannot be accessed, which leads to problems if attempting to use Gabor functions for processing real-time signals that depend on the temporal dimension. A time-causal analogue of the Gabor filter has been developed in based on replacing the
102:
analysis, which essentially means that it analyzes whether there is any specific frequency content in the image in specific directions in a localized region around the point or region of analysis. Frequency and orientation representations of Gabor filters are claimed by many contemporary vision
263:
676:
476:
1458:
1295:
1574:. Relations between activations for a specific spatial location are very distinctive between objects in an image. Furthermore, important activations can be extracted from the Gabor space in order to create a sparse object representation.
1102:
Demonstration of a Gabor filter applied to
Chinese OCR. Four orientations are shown on the right 0°, 45°, 90° and 135°. The original character picture and the superposition of all four orientations are shown on the
1132:
A set of Gabor filters with different frequencies and orientations may be helpful for extracting useful features from an image. In the discrete domain, two-dimensional Gabor filters are given by,
981:
923:
460:{\displaystyle g(x,y;\lambda ,\theta ,\psi ,\sigma ,\gamma )=\exp \left(-{\frac {x'^{2}+\gamma ^{2}y'^{2}}{2\sigma ^{2}}}\right)\exp \left(i\left(2\pi {\frac {x'}{\lambda }}+\psi \right)\right)}
860:{\displaystyle g(x,y;\lambda ,\theta ,\psi ,\sigma ,\gamma )=\exp \left(-{\frac {x'^{2}+\gamma ^{2}y'^{2}}{2\sigma ^{2}}}\right)\sin \left(2\pi {\frac {x'}{\lambda }}+\psi \right)}
660:{\displaystyle g(x,y;\lambda ,\theta ,\psi ,\sigma ,\gamma )=\exp \left(-{\frac {x'^{2}+\gamma ^{2}y'^{2}}{2\sigma ^{2}}}\right)\cos \left(2\pi {\frac {x'}{\lambda }}+\psi \right)}
1115:. Jones and Palmer showed that the real part of the complex Gabor function is a good fit to the receptive field weight functions found in simple cells in a cat's striate cortex.
1301:
1138:
3351:
Daugman, John G. (1985-07-01). "Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters".
1004:
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1496:
94:, who first proposed it as a 1D filter. The Gabor filter was first generalized to 2D by Gösta Granlund, by adding a reference direction. The Gabor filter is a
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3536:
3965:
Gdyczynski, C.M.; Manbachi, A.; et al. (2014). "On estimating the directionality distribution in pedicle trabecular bone from micro-CT images".
3294:
107:. They have been found to be particularly appropriate for texture representation and discrimination. In the spatial domain, a 2D Gabor filter is a
43:
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Olshausen, B. A. & Field, D. J. (1996). "Emergence of simple-cell receptive-field properties by learning a sparse code for natural images".
238:
of the
Fourier transform of the harmonic function (sinusoidal function) and the Fourier transform of the Gaussian function. The filter has a
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3D surface tracking and approximation using Gabor filters, Jesper Juul
Henriksen, South Denmark University, March 28, 2007
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Raju, S. Sabari; Pati, P. B.; Ramakrishnan, A. G. (2005). "Text
Localization and Extraction from Complex Color Images".
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197:
61:
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3597:"A time-causal and time-recursive scale-covariant scale-space representation of temporal signals and past time"
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S Sabari Raju, P B Pati and A G Ramakrishnan, âText
Localization and Extraction from Complex Color Images,â
4441:
3537:"An evaluation of the two-dimensional gabor filter model of simple receptive fields in cat striate cortex"
1453:{\displaystyle G_{s}=Ce^{-{\frac {(i^{2}+j^{2})}{2\sigma ^{2}}}}\sin(2\pi f(i\cos \theta +j\sin \theta ))}
1290:{\displaystyle G_{c}=Be^{-{\frac {(i^{2}+j^{2})}{2\sigma ^{2}}}}\cos(2\pi f(i\cos \theta +j\sin \theta ))}
4151:
3914:
Lyons, M.; Akamatsu, S.; Kamachi, M.; Gyoba, J. (1998). "Coding facial expressions with Gabor wavelets".
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Haghighat, M.; Zonouz, S.; Abdel-Mottaleb, M. (2013). "Identification Using
Encrypted Biometrics".
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Fischer, Sylvain; Ć roubek, Filip; Perrinet, Laurent; Redondo, Rafael; CristĂłbal, Gabriel (2007).
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is the spatial aspect ratio, and specifies the ellipticity of the support of the Gabor function.
4242:
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4152:"Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression"
989:
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Pati, Peeta Basa; Ramakrishnan, A.G. (July 2008). "Word level multi-script identification".
2887:
4307:
3974:
3780:"Gabor filter based block energy analysis for text extraction from digital document images"
3744:
3360:
3317:
3308:
MarÄelja, S. (1980). "Mathematical description of the responses of simple cortical cells".
3252:
1033:
8:
3917:
Proceedings Third IEEE International
Conference on Automatic Face and Gesture Recognition
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104:
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First
International Workshop on Document Image Analysis for Libraries, 2004. Proceedings
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1538:, we change the support of the basis or the size of the image region being analyzed.
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83:
3493:(1980), "Two-dimensional spectral analysis of cortical receptive field profiles",
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99:
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Proceedings of the 12th IEEE Workshop on Neural
Networks for Signal Processing
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Proc. First International Conference on Advances in Visual Computing (ISVC05)
3871:
3764:
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3451:
3390:
3229:
3208:
Granlund G. H. (1978). "In Search of a General Picture Processing Operator".
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Fogel, I.; Sagi, D. (June 1989). "Gabor filters as texture discriminator".
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2D Gabor filters have rich applications in image processing, especially in
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Lagae, Ares; Lefebvre, Sylvain; Drettakis, George; Dutré, Philip (2009).
1518:, we can look for texture oriented in a particular direction. By varying
239:
235:
140:
with Gabor filters is thought by some to be similar to perception in the
3853:
74:
3904:, Nevada, USA, LNCS 3804, Springer Verlag, Dec. 5-7, 2005, pp. 486-493.
3848:. Lecture Notes in Computer Science. Vol. 3804. pp. 486â493.
3650:. Lecture Notes in Computer Science. Vol. 8048. pp. 440â448.
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represents the orientation of the normal to the parallel stripes of a
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Gabor filter for image processing and computer vision (demonstration)
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3915:
3681:"Neural network-based segmentation of textures using Gabor features"
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defines the frequency being looked for in the texture. By varying
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4103:. Applied and Numerical Harmonic Analysis. Boston: BirkhÀuser.
3678:
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4159:
IEEE Transactions on Acoustics, Speech, and Signal Processing
4101:
Foundations of time-frequency analysis : with 15 figures
3645:
1653:"""Gabor feature extraction."""
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is the sigma/standard deviation of the Gaussian envelope and
4058:
Gabor analysis and algorithms : theory and applications
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Ramakrishnan, A.G.; Kumar Raja, S.; Raghu Ram, H.V. (2002).
1098:
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1551:
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4019:
MATLAB code for Gabor filters and Gabor feature extraction
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http://www.mathworks.com/matlabcentral/fileexchange/44630
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226:. Because of the multiplication-convolution property (
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directions. The two components may be formed into a
178:. Please help to ensure that disputed statements are
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python implementation of log-Gabors for still images
3841:
1542:
Applications of 2D Gabor filters in image processing
1006:
represents the wavelength of the sinusoidal factor,
3778:Raju S, S.; Pati, P.B.; Ramakrishnan, A.G. (2004).
34:
may be too technical for most readers to understand
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4290:
4243:"Procedural Noise using Sparse Gabor Convolution"
3690:. Martigny, Switzerland: IEEE. pp. 365â374.
2882:Code for Gabor feature extraction from images in
4423:
4291:Manduchi, R.; Perona, P.; Shy, D. (April 1998).
3734:
976:{\displaystyle y'=-x\sin \theta +y\cos \theta }
3789:. Palo Alto, CA, USA: IEEE. pp. 233â243.
3207:
918:{\displaystyle x'=x\cos \theta +y\sin \theta }
3189:Gabor, D. (1946). "Theory of communication".
3413:
3293:: CS1 maint: multiple names: authors list (
234:of a Gabor filter's impulse response is the
128:Some authors claim that simple cells in the
3534:
3353:Journal of the Optical Society of America A
2898:This is another example implementation in
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1471:are normalizing factors to be determined.
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3594:
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3372:
3310:Journal of the Optical Society of America
3188:
198:Learn how and when to remove this message
136:can be modeled by Gabor functions. Thus,
103:scientists to be similar to those of the
78:Example of a two-dimensional Gabor filter
62:Learn how and when to remove this message
46:, without removing the technical details.
4377:International Journal of Computer Vision
3648:Computer Analysis of Images and Patterns
3590:
3588:
3307:
1119:Time-causal analogue of the Gabor filter
1097:
174:Relevant discussion may be found on the
73:
4370:"Self-Invertible 2D Log-Gabor Wavelets"
4149:
3489:
3350:
1478:for texture analysis and segmentation.
16:Linear filter used for texture analysis
4424:
4300:IEEE Transactions on Signal Processing
4024:3D Gabor demonstrated with Mathematica
3210:Computer Graphics and Image Processing
1107:Gabor filters are directly related to
222:for 2D Gabor filters) multiplied by a
3585:
2335:This is an example implementation in
2324:For an implementation on images, see
1593:This is an example implementation in
44:make it understandable to non-experts
4214:
1701:# Number of standard deviation sigma
1558:. The Gabor space is very useful in
151:
18:
4293:"Efficient deformable filter banks"
13:
4046:
3535:Jones, J.P.; Palmer, L.A. (1987).
1128:Extraction of features from images
14:
4453:
4056:; Strohmer, Thomas, eds. (1998).
4012:
3595:Lindeberg, T. (23 January 2023).
2360:sigma, theta, lambda, psi, gamma
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23:
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1:
4099:Gröchenig, Karlheinz (2001).
3176:
1564:optical character recognition
147:
4247:ACM Transactions on Graphics
3987:10.1088/0967-3334/35/12/2415
3845:Advances in Visual Computing
3757:10.1016/j.patrec.2008.01.027
3656:10.1007/978-3-642-40246-3_55
3507:10.1016/0042-6989(80)90065-6
3222:10.1016/0146-664X(78)90047-3
7:
4217:"Tutorial on Gabor Filters"
3737:Pattern Recognition Letters
3149:
10:
4458:
4284:Eero Simoncelli's page on
4197:"Online Gabor filter demo"
3614:10.1007/s00422-022-00953-6
2893:
1576:
4399:10.1007/s11263-006-0026-8
4109:10.1007/978-1-4612-0003-1
3967:Physiological Measurement
3795:10.1109/DIAL.2004.1263252
3696:10.1109/NNSP.2002.1030048
3556:10.1152/jn.1987.58.6.1233
2330:
1588:
3926:10.1109/AFGR.1998.670949
2904:
2345:
1599:
999:{\displaystyle \lambda }
4269:10.1145/1531326.1531360
1584:Example implementations
1572:fingerprint recognition
1531:{\displaystyle \sigma }
1511:{\displaystyle \theta }
1083:{\displaystyle \gamma }
1063:{\displaystyle \sigma }
1019:{\displaystyle \theta }
246:component representing
4150:Daugman, J.G. (1988).
4060:. Boston: BirkhÀuser.
3601:Biological Cybernetics
3422:Biological Cybernetics
3383:10.1364/JOSAA.2.001160
3330:10.1364/JOSA.70.001297
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254:or used individually.
79:
1562:applications such as
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1050:is the phase offset,
1045:
1043:{\displaystyle \psi }
1021:
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978:
920:
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4281:Steerable Pyramids:
4215:Movellan, Javier R.
4054:Feichtinger, Hans G.
3920:. pp. 200â205.
3191:J. Inst. Electr. Eng
1522:
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1034:
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167:factual accuracy is
4442:Pattern recognition
4312:1998ITSP...46.1168M
3979:2014PhyM...35.2415G
3854:10.1007/11595755_59
3749:2008PaReL..29.1218P
3365:1985JOSAA...2.1160D
3322:1980JOSA...70.1297M
3257:1996Natur.381..607O
228:Convolution theorem
142:human visual system
105:human visual system
4358:2010-06-13 at the
4347:2021-11-12 at the
4286:Steerable Pyramids
4039:2018-05-29 at the
3444:10.1007/BF00204594
1528:
1508:
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1476:feature extraction
1450:
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986:In this equation,
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4320:10.1109/78.668570
3973:(12): 2415â2428.
3863:978-3-540-30750-1
3804:978-0-7695-2088-9
3705:978-0-7803-7616-8
3665:978-3-642-40245-6
3316:(11): 1297â1300.
3251:(6583): 607â609.
1491:{\displaystyle f}
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232:Fourier transform
224:Gaussian function
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4437:Image processing
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4306:(4): 1168â1173.
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4222:. Archived from
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1568:iris recognition
1560:image processing
1537:
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349:
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333:
214:is defined by a
212:impulse response
203:
196:
192:
189:
183:
180:reliably sourced
160:
159:
152:
134:mammalian brains
84:image processing
67:
60:
56:
53:
47:
27:
26:
19:
4457:
4456:
4452:
4451:
4450:
4448:
4447:
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4422:
4421:
4390:10.1.1.329.6283
4372:
4360:Wayback Machine
4349:Wayback Machine
4295:
4273:
4271:
4260:10.1.1.232.5566
4232:
4230:
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4219:
4206:
4204:
4195:
4181:10.1109/29.1644
4172:10.1.1.371.5847
4154:
4119:
4068:
4049:
4047:Further reading
4041:Wayback Machine
4015:
4010:
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3959:
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3593:
3586:
3578:
3544:J. Neurophysiol
3539:
3533:
3529:
3488:
3484:
3479:
3475:
3435:10.1.1.367.2700
3418:
3414:
3374:10.1.1.465.8506
3349:
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3306:
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3156:Gabor transform
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204:
193:
187:
184:
173:
165:This section's
161:
157:
150:
123:Gabor transform
114:modulated by a
112:kernel function
68:
57:
51:
48:
40:help improve it
37:
28:
24:
17:
12:
11:
5:
4455:
4445:
4444:
4439:
4434:
4432:Linear filters
4420:
4419:
4383:(2): 231â246.
4365:
4364:
4363:
4288:
4279:
4238:
4212:
4193:
4147:
4117:
4096:
4066:
4048:
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4044:
4043:
4031:
4026:
4021:
4014:
4013:External links
4011:
4009:
4008:
3957:
3934:
3906:
3893:
3862:
3834:
3803:
3770:
3727:
3704:
3671:
3664:
3638:
3607:(1â2): 21â59.
3584:
3581:on 2020-02-28.
3527:
3501:(10): 847â56,
3482:
3473:
3428:(2): 103â113.
3412:
3343:
3300:
3235:
3216:(2): 155â173.
3200:
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3178:
3175:
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3168:
3163:
3158:
3151:
3148:
2905:
2895:
2892:
2395:% Bounding box
2346:
2332:
2329:
1689:# Bounding box
1600:
1590:
1587:
1585:
1582:
1579:Morlet wavelet
1543:
1540:
1527:
1507:
1487:
1461:
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1160:
1157:
1154:
1149:
1145:
1129:
1126:
1120:
1117:
1109:Gabor wavelets
1095:
1092:
1079:
1059:
1039:
1028:Gabor function
1015:
995:
972:
969:
966:
963:
960:
957:
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951:
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938:
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278:
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269:
252:complex number
206:
205:
164:
162:
155:
149:
146:
138:image analysis
90:, named after
70:
69:
31:
29:
22:
15:
9:
6:
4:
3:
2:
4454:
4443:
4440:
4438:
4435:
4433:
4430:
4429:
4427:
4416:
4412:
4408:
4404:
4400:
4396:
4391:
4386:
4382:
4378:
4371:
4366:
4361:
4357:
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4350:
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4325:
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4317:
4313:
4309:
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4294:
4289:
4287:
4283:
4282:
4280:
4270:
4266:
4261:
4256:
4252:
4248:
4244:
4239:
4229:on 2009-04-19
4225:
4218:
4213:
4203:on 2009-06-15
4202:
4198:
4194:
4190:
4186:
4182:
4178:
4173:
4168:
4164:
4160:
4153:
4148:
4144:
4140:
4136:
4132:
4128:
4124:
4120:
4118:0-8176-4022-3
4114:
4110:
4106:
4102:
4097:
4093:
4089:
4085:
4081:
4077:
4073:
4069:
4067:0-8176-3959-4
4063:
4059:
4055:
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4042:
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4025:
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3953:
3949:
3945:
3941:
3937:
3935:0-8186-8344-9
3931:
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188:February 2013
181:
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130:visual cortex
126:
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96:linear filter
93:
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52:February 2017
45:
41:
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32:This article
30:
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4272:. Retrieved
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92:Dennis Gabor
88:Gabor filter
87:
81:
58:
49:
33:
3495:Vision Res.
2677:% Rotation
236:convolution
4426:Categories
4274:2009-09-12
4233:2008-05-14
4207:2009-05-25
3880:2005936803
3813:2003116308
3177:References
3166:Gabor atom
2064:# Rotation
1577:See also:
1549:trabecular
670:Imaginary
248:orthogonal
220:plane wave
216:sinusoidal
148:Definition
119:plane wave
116:sinusoidal
4407:0920-5691
4385:CiteSeerX
4336:926890247
4328:1053-587X
4255:CiteSeerX
4189:0096-3518
4167:CiteSeerX
4003:206078730
3944:11390549M
3872:0302-9743
3765:0167-8655
3714:812617471
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3452:0340-1200
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176:talk page
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3253:Bibcode
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2894:Haskell
2868:x_theta
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2127:=
2121:)
2115:(
2109:.
2103:*
2100:y
2097:+
2094:)
2088:(
2082:.
2076:*
2073:x
2070:=
2058:1
2055:+
2049:,
2043:(
2037:.
2028:1
2025:+
2019:,
2013:(
2007:.
2001:(
1995:.
1989:=
1986:)
1983:x
1980:,
1977:y
1974:(
1968:-
1965:=
1956:-
1953:=
1941:,
1938:1
1935:(
1929:(
1923:.
1917:=
1911:)
1902:(
1896:.
1890:*
1884:*
1878:(
1866:(
1860:.
1854:*
1848:*
1842:(
1836:(
1830:=
1818:,
1815:1
1812:(
1806:(
1800:.
1794:=
1788:)
1779:(
1773:.
1767:*
1761:*
1755:(
1743:(
1737:.
1731:*
1725:*
1719:(
1713:(
1707:=
1698:3
1695:=
1683:/
1680:)
1674:(
1668:=
1659:=
1644:,
1638:,
1632:,
1626:,
1620:(
1486:f
1469:C
1465:B
1448:)
1445:)
1433:j
1430:+
1418:i
1415:(
1412:f
1406:2
1403:(
1387:2
1379:2
1374:)
1369:2
1365:j
1361:+
1356:2
1352:i
1348:(
1338:e
1334:C
1331:=
1328:]
1325:j
1322:,
1319:i
1316:[
1311:s
1307:G
1285:)
1282:)
1270:j
1267:+
1255:i
1252:(
1249:f
1243:2
1240:(
1224:2
1216:2
1211:)
1206:2
1202:j
1198:+
1193:2
1189:i
1185:(
1175:e
1171:B
1168:=
1165:]
1162:j
1159:,
1156:i
1153:[
1148:c
1144:G
962:y
959:+
947:x
941:=
934:y
904:y
901:+
889:x
886:=
879:x
854:)
847:+
835:x
826:2
822:(
811:)
802:2
794:2
786:2
778:y
772:2
764:+
758:2
750:x
739:(
729:=
726:)
720:,
714:,
708:,
702:,
696:;
693:y
690:,
687:x
684:(
681:g
654:)
647:+
635:x
626:2
622:(
611:)
602:2
594:2
586:2
578:y
572:2
564:+
558:2
550:x
539:(
529:=
526:)
520:,
514:,
508:,
502:,
496:;
493:y
490:,
487:x
484:(
481:g
454:)
449:)
442:+
430:x
421:2
417:(
413:i
409:(
398:)
389:2
381:2
373:2
365:y
359:2
351:+
345:2
337:x
326:(
316:=
313:)
307:,
301:,
295:,
289:,
283:;
280:y
277:,
274:x
271:(
268:g
201:)
195:(
190:)
186:(
182:.
172:.
65:)
59:(
54:)
50:(
36:.
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