T. D. Sanger. Stereo disparity computation using gabor filters. Biol. Cybern., 59:405--418, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a peu pres constante sur le support du filtre. Ces deux propri et es sont antinomiques, comme le montre le theoreme d incertitude [BRACEWELL, 1965] Le mieux que l on puisse faire est donc de choisir un filtre qui minimise le produit de la largeur spatiale par la largeur de bande. A la suite de Sanger [SANGER, 1988], de Langley et al. LANGLEY et al. 1991] et de Fleet [FLEET, 1992] notre choix s est port e sur le filtre de Gabor pour deux raisons: il minimise le produit de la largeur spatiale par la largeur de bande; l etude comparative de Fleet [FLEET, 1992] montre sa superiorite pour l estimation de ....

T. D. SANGER. Stereo disparity computation using gabor filters. Biological Cybernetics, (59):405--418, 1988.

....components that can be combined, at a higher level, to yield a specific motion in depth selectivity. The rationale of this statement relies upon analytical considerations on phase based dynamic stereopsis, as a time ex tension of the well known phase based techniques for disparity estimation [6] [7] The resulting model is based on the computation of the total temporal derivative of the disparity through the combination of the outputs of binocular disparity energy units [4] 5] characterized by different ocular dominance indices. Since each energy unit is just a binocular Addson and ....

....of the binocular disparity and that held by the interocular velocity differences. 2 Phase based dynamic stereopsis In the last decades, a computational approach for stereopsis, that rely on the phase information contained in the spectral components of the stereo image pair, has been proposed [6] [7] Spatially localized phase measures on the left and right images can be obtained by filtering operations with a complex valued quadrature pair of Gabor : e x a e x, where c0 lS the peak frequency of the filter and rr filters h(x, lo) 2 2 . relates to its spatial extension. The ....

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T.D. Sanger. Stereo disparity computation using Gabor filters. Biol. Cybern., 59:405-418, 1988.

....framework considering a phase based disparity encoding scheme. 2 Phase based measurements of local disparity According to the Fourier Shift Theorem, the spatial shift 5 in an image domain effects a phase shift k8 in the Fourier domain. On the basis of this property, several researchers (e.g. [4]) proposed phase based techniques in which dis parity is estimated in terms of phase differences in the spectral components of the stereo image pair. Spatially localized phase measures can be obtained by filtering operations with complex valued quadrature pair of Gabor filters x2 r 2 ikox ....

....and conclusions There are at least two binocular cues that can be used to determine the motion of an object toward or away from an observer [1] binocular combination of monocular velocity signals or the rate of change of retinal disparity. Assuming a phase based disparity encoding scheme [4], we demonstrated that informa tion hold in the interocular velocity difference is the same of that derived by the evaluation of the total derivative of the binocular disparity. The resulting computation relies upon spatiotemporal differentials of the left and right retinal phases that can be ....

T.D. Sanger. Stereo disparity computation using Gabor filters. Biol. Cybern., 59:405-418, 1988.

....and contrast conditions in both cameras, correlation is sensitive to noise. An algorithm based on bandpass filters could give more stable results under real world conditions. Gabor filters [9] with limited spatial width and finite bandwidth are suitable filters for computing stereo disparity [18] in such an approach. We use a phase based approach with spatial Gabor filters to compute multi resolution disparity maps in real time. The disparity in the center of the map is used to control the vergence movement. A coarse to fine strategy helps us deal with large disparity values unmeasurable ....

....as a phase shift in the Fourier spectrum. To recover the local disparity as a spatial shift the local phase differences have to be computed. Extracting the local phase in both images of a stereo pair with complex filters like Gabor filters leads to a direct computation of local disparity. Sanger [18], Langley et al. 11] and Fleet et al. 8] have employed phase based approaches in one or two dimensions to recover disparity information with complex Gabor filters (2) on different scales. 2) The response in the frequency domain is: g(f x ; oe; 2oe 2 (fx Gamma ) e ....

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T.D. Sanger. Stereo Disparity Computation Using Gabor Filters. Biol.Cybernetics. 59, 1988, 405-418.

....need for stereoscopic depth perception. Such a joint representation can be related to the spatial properties of binocular filters tuned to specific disparity values. This problem has an elegant formulation in the frequency domain, in relation to the so called phase based matching methods [16]. Basically, disparity estimation is computed as the shift necessary to align the phase values of the band pass filtered version of the binocular stereo signals. One can assume that the disparity between the stereo image pair occurs only along the direction of the epipolar lines. In the simplest ....

....lines. In the simplest configuration, in which optical axes are parallel, epipolar lines are parallel to the line joining the optical centers of the cameras. In such conditions, stereo phase based matching can be casted as a 1D problem. The local phase is computed following Sanger s algorithm [16], from the output of a pair of Gabor filters in quadrature (see Fig. 6) The differential measure of the local phase, obtained by the left and right retinas, is validated by a confidence measure, thus deriving a reliable Analog Early Processing Vision Microsystem Perceptual analog control ....

T.D. Sanger. Stereo disparity computation using Gabor filters. Biol. Cybern., 59:405--418, 1988.

....Gabor filter which optimally processes Planar stimuli. The right panel contains the 50 level sets of the optimal Gabor filter. The method for finding this filter is given in Appendix D. On the right is an image of the optimal Gabor filter intersecting the Planar filter, to illustrate the fit. [13, 14, 21, 38, 27, 53] and their simple parametrization. The 50 level sets of a resulting filter is shown in fig. 11 in the first panel. The filter is unique except that it may be rotated within the Planar filter spectrum. We created a set of control stimuli by passing white noise through the optimal Gabor filter ....

T. D. Sanger. Stereo disparity computation using gabor filters. Biol. Cybern., 59:405--418, 1988.

....the description in [6] Instead of directly evaluating the raw intensities of stereo images, further transformation into low level feature maps may facilitate the search for corresponding points because they yield a better discrimination and noise robustness than simple pixel intensities. Sanger [13] proposed to use Gabor wavelets [9] g(x) 1 p 2 oe e Gammax 2 =2 oe 2 e k0 x (1) with filter width oe and filter frequency k 0 for solving the correspondence problem. This product of a complex harmonic and a Gaussian envelope yields a joint spatial and frequency representation of ....

....a spatial shift d in the image domain effects a phase shift k d in Fourier domain. Since Gabor filters produce a localized frequency description, the normal ized phase difference 1 d(x) OE R (x) Gamma OE L (x) k 0 (5) is supposed to be a suitable approximation for the local image shift [13]. Additionally, this estimation can be improved by using local frequencies dOE L =dx; dOE R=dx instead of the filter mid frequency k 0 [8, 11] 2 Position and Disparity of Edges In spite of its sound theoretical foundation, phase based techniques alone proved to be reliable only for certain ....

T. Sanger. Stereo disparity computation using gabor filters. Biological Cybernetics, 59:405--418, 1988.

....in both techniques that a search process is required to find the best match between the areas or features. As a third approach, a new technique has been proposed in which disparity is expressed in terms of phase differences in the output of local, bandpass filters applied to the stereo views [10, 23, 29]. The main advantages of such local, phase based approaches include computational simplicity, stability against varying lighting condition and especially direct localization of the estimated disparities. Also, there is biological evidence supporting different aspects of this method including [23] ....

....29] The main advantages of such local, phase based approaches include computational simplicity, stability against varying lighting condition and especially direct localization of the estimated disparities. Also, there is biological evidence supporting different aspects of this method including [23], e.g. bandpass spatial frequency filters are thought to be plausible models of the way in which the primary visual cortex processes a visual image [7] We consider the characteristics of this search free and thus fast approach as suitable to provide stereoscopic disparity as a basic feature in ....

T. D. Sanger. Stereo disparity computation using Gabor filters. Biological Cybernetics, 59:405--418, 1988.

....4912 To whom correspondence should be addressed. 1 Abstract In a stereoscopic system both eyes or cameras have a slightly different view. As a consequence small variations between the projected images exist ( disparities ) which are spatially evaluated in order to retrieve depth information [Sanger, 1988, Fleet et al. 1991] A strong similarity exists between the analysis of visual disparities and the determination of the azimuth of a sound source [Wagner and Frost, 1993] The direction of the sound is thereby determined from the temporal delay between the left and right ear signals [Konishi and ....

....to analyze corresponding cross sections of both images line by line because the epipolar lines are now horizontal. Thus, stereoscopic depth estimation is reduced to a 1 dimensional spatial problem and common methods use acausal spatial filters to retrieve the disparity as a convolution result [Sanger, 1988, Fleet et al. 1991] The inherently present restriction to one dimension, however, makes it also possible to interpret each line from the left and right image as a temporal signal , which could for example be imagined as scan line from a CCD camera arriving pixel after pixel. With the ....

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Sanger, T. D. (1988). Stereo disparity computation using gabor filters. Biol. Cybern., (59):405--418.

....properties from image data often suffer from computational complexity as well as from sensitivity to image noise. As an example, estimation of depth from stereo is often implemented as a correlation between the left and right images in order to determine disparity from which depth can be computed [24] [13] Though simple in its nature, this correlation process is computationally tough. Furthermore, in presence of image noise we would either expect the accuracy of the estimate to decrease more or less gracefully or we would have to employ more complex correlation methods. The same argument ....

T. D. Sanger. Stereo disparity computation using gabor filters. Biological cybernetics, 59:405--418, 1988. 25

....dynamic vergence using binocular disparities [4, 17] has significantly improved the performance of stereo active vision systems. We describe in this section a method based on the Fourier shift theorem to recover spatial displacements from phase difference which is well adapted to our application [20]. To cope with the local characteristics of disparity in stereo images, the algorithm uses local phase information from the output of complex band pass filters instead of the global phase with Fourier transformations [27] The method is robust, produces dense maps and is very well suited for ....

....been suggested [26] but the computational complexity becomes important and the precision decreases drastically with the size of the local window. A more interesting approach is to recover the local phase and frequency components in the signal using the output of complex valued bandpass filters [20]. Fig. 9 shows a binocular disparity map obtained from the phase information after convolution with a complex valued Gaussian di#erence filter [27] Figure 9: Disparity estimation. The original stereo pair (left) and the phase based disparity map (right) The horopter. By definition, any point ....

T. D. Sanger. Stereo disparity computation using gabor filters. Biol. Cybern., 59:405--418, 1988.

....phase by90 ffi (i.e. are Hilbert transforms of each other [17] Such pairs allow for analyzing spectral strength independent of phase, and allow for synthesizing filters of a given frequency response with arbitrary phase. They have application in motion, texture, shape, and orientation analysis [4, 7, 16, 30, 37, 36, 35, 45, 47, 57, 77, 94]. Gaussian derivatives are useful functions for image analysis [61, 62, 63, 116] and a steerable quadrature pair of them would be useful for many vision tasks. First, we design a steerable basis set for the second derivative of a Gaussian, f(x# y) G 0 ffi 2 = 4x 2 ; 2)e ; x 2 y 2 ) ....

T. Sanger. Stereo disparity computation using Gabor filters. Biol. Cybern., 59:405--418, 1988.

....which makes use of the fact that the disparity from bandpass signals is equivalent to the local phase difference between them. This approach has generated some interest mainly because of its parallel efficiency and because of its applicability to theories of stereopsis in the human visual cortex. Sanger (1988) implemented a basic algorithm using simple disparity estimates from phase differences, and analyzed the errors which accrue when using such a method. Jenkin and Jepson (1994) used a cross correlation method on band pass filtered images to find the phase differences, and compared such a method to ....

.... is the average local spatial frequency. In most cases in the literature, the band pass filter frequencies are the same for left and right images ( l = r ) an assumption which is supported by the available physiological data and which is further discussed in section 4. It is then possible (Sanger, 1988) to use the average of the filter center pass frequencies from left and right images = 1 2 ( l r ) However, this is only an approximation since the spatial frequency of the filters and hence of the band pass filtered signals is not exactly l and r , but is localized in a region of ....

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Sanger, T. (1988). Stereo disparity computation using gabor filters. Biological Cybernetics, 59:405--418.

....mechanics involved in obtaining raw disparity measurements. The mechanism utilizes local phase differences as the underlying measurement primitive. The relationship between local phase differences in band pass channels and interocular disparity has been established previously byanumber of authors [7, 11,14,8,3,6]. We begin by considering the input to be one dimensional and then extend the measurement algorithm to two dimensions in the following section. Left (I l (x) and right(I r (x) signals are convolved with a complex Gabor (Gabor( # oe) kernel with frequency and standard deviation oe obtaining ....

T. D. Sanger. Stereo disparity computation using gabor filters. Biol. Cybern., 59:405--418, 1988.

....in layer k is shown. The procedure in the dashed box corresponds to equation (2) and (5) Down at the original scale (k = 1) the disparity and the certainty maps are taken as the outputs of the algorithm. 1 algorithm using output phase of Gabor filters was introduced as a disparity estimator [9, 11, 4], several works based on the technique have reported on its efficiency both by extensive analysis and applications [5, 10, 2, 8] While the advantages of the phase based method include computational simplicity, stability against varying lighting condition and especially direct localization of the ....

T. D. Sanger. Stereo disparity computation using Gabor filters. Biological Cybernetics, 59:405--418, 1988.

....Poggio s paradigm [03,04] correspondences between patterns in fine resolution are determined in parallel, and disparity is determined from that. Perhaps one of the first advances towards explaining the computational approach used by byological systems to estimate disparity is the work of Sanger [24]. He uses Gabor filters, that are local approximations of Fourier transforms, to calculate the disparity (see Freeman and Adelson [25] for more details on steerable filters) The model uses the fact that the displacement of a function generates a proportional phase shift in its Fourier transform. ....

T. D. SANGER. Stereo Disparity Computation using Gabor Filters.Biol. Cybernetics, 59: 405418. 1988.

....on Computer Analysis of Images and Patterns (pp. 868 873) Address: NADA, KTH, S 100 44, Stockholm, Sweden Email: maki bion.kth.se (http: www.bion.kth.se) 1 1 Introduction Since the stereopsis algorithm using output phase of Gabor filters was introduced as a disparity estimator [3, 8, 10], several works based on the technique have reported on its efficiency through extensive analysis and applications [1, 4, 6, 9] such as usage of multiple Gabor filters with different frequencies, coarse to fine strategy, attempts with alternative quadrature filters as substitutes, and singularity ....

....a complex filter, such as a Gabor filter. As the local shift between stereo images is approximately proportional to the local phase difference, a disparity estimate at each point in the image is derived accordingly. While extensive work have been carried out in phase based disparity estimation [1, 3, 4, 6, 8, 9, 10], a brief overview of the approach is provided in this section. 2.1 The framework We describe the framework for 1 dimensional images 2 where a constant image shift, disparity Deltax, is observed across some part of the scene. Let l(x) and r(x) 2 We keep the model simple for the conceptual ....

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T. D. Sanger. Stereo disparity computation using gabor filters. Biol. Cybern., 59:405--418, 1988.

.... Classical approaches to stereo analysis try to deal with the correspondence problem with two basic algorithms; area based [20, 16] and feature based approaches [21, 16] Several approaches take into consideration available biological and neurophysiological data about the human visual system [21, 24, 19]. There is biological evidence that the pattern of light projected on the human retina is sampled and spatially filtered. Early in cortical visual processing, receptive fields become oriented and are well approximated by linear spatial filters, with impulse response functions that are similar to ....

T. Sanger. Stereo disparity computation using gabor filters. Biological Cybernetics, 59:405 -- 418, 1988.

....techniques using only the responses of appropriate filters. It was shown that the local disparity variation can be computed from the intensity derivatives [5, 6] However, a more general filter based approach exhibited the most robust performance until now: the phase based approach introduced in [11, 12] and further developed and studied in [3, 8, 13, 14, 10] The phase based disparity computation may be apparently justified by the shift theorem for the Fourier transform of an image. However, the shift theorem is exact only for a globally 1 constant disparity. To capture varying disparity, all ....

....approaches apply the local spectral representation of the complex valued Gabor filter responses. As we will describe later, the shift theorem for the phase difference of the Gabor responses is not valid even in the case of simple sinusoidal input. A more plausible formulation of the shift theorem [12, 3] assumes the preservation of the local phase in the left and the right image. Application of the Taylor expansion to the local phase yields the disparity as the ratio of phase difference and the first spatial derivative of the phase if the higher order disparity terms and derivatives are ....

T.D. Sanger. Stereo disparity computation using gabor filters. Biol.Cybernetics, 59:405--418, 1988.

....which decomposes the signal as a polynomial of the disparity variables, the Fourier based expansion separates the disparity variables from the signal as a multi1 plication of a complex exponential phase term by using the time shifting property of the Fourier transform. The phase approaches such as [15, 5, 10] use this expansion model to compute the disparity values. One fundamental drawback of the Fourierbased expansion is that it is unstable for low frequency information. For any finite width band pass filter, its frequency resolution is limited by the uncertainty principle [6] The exact frequency ....

T. D. Sanger. Stereo disparity computation using Gabor filters. Biological Cybernetics, 59:405--418, 1988.

....correlation measure provide information about any distortion that may exist between the two signals at the matching points. As an alternative to spatial correlation phase based methods of disparity measurement have been proposed by a number of researchers including Jenkin and Jepson [5] Sanger [10], Langley et al. 8] and Fleet et al. 4] This approach is based around using Gabor filters in quadrature pairs to obtain local phase information and instantaneous frequency. The disparity is estimated from the local phase difference divided by the instantaneous frequency, where the ....

T. Sanger. Stereo disparity computation using Gabor filters. Biological Cybernetics, (59):405-- 418, 1988.

....depth estimation is mainly based on disparity measurement. Disparity is a local property that can be associated to a stereo pair (left and right) of images or image sequences. The problem has an elegant formulation in the frequency domain, in relation to the so called phase based matching methods [20]. Basically, disparity estimation is computed as the shift necessary to align the phase values of the band pass filtered version of the binocular stereo signals. One can assume that the disparity between the stereo image pair occurs only along the direction of the epipolar lines [ ....

....architecture of the module for stereo depth perception. The convolution with Gabor like functions of any phase can be obtained through the weighted sum of the output of three neighboring nodes in the perceptual array. phase and thence the local disparity are computed following Sanger s algorithm [20], whose response can be obtained through the computational scheme evidenced in Fig. 6. Motion analysis Several approaches to motion analysis rely upon correspondence measures in the spatio temporal domain of a visual scene [15] i.e. upon space time linear filtering of the visual input. It is ....

T.D. Sanger. Stereo disparity computation using Gabor filters. Biol. Cybern., 59:405--418, 1988.

....need for stereoscopic depth perception. Such a joint representation can be related to the spatial properties of binocular filters tuned to specific disparity values. This problem has an elegant formulation in the frequency domain, in relation to the so called phase based matching methods [16]. Basically, disparity estimation is computed as the shift necessary to align the phase values of the band pass filtered version of the binocular stereo signals. One can assume that the disparity between the stereo image pair occurs only along the direction of the epipolar lines. In the simplest ....

....lines. In the simplest configuration, in which optical axes are parallel, epipolar lines are parallel to the line joining the optical centers of the cameras. In such conditions, stereo phase based matching can be casted as a 1D problem. The local phase is computed following Sanger s algorithm [16], from the output of a pair of Gabor filters in quadrature (see Fig. 6) The differential measure of the local phase, obtained by the left and right retinas, is validated by a confidence measure, thus deriving a reliable Analog Early Processing Vision Microsystem Perceptual analog control ....

T.D. Sanger. Stereo disparity computation using Gabor filters. Biol. Cybern., 59:405--418, 1988.

....right) of images or image sequences. Hence, a joint representation of the information flows coming from the two eyes is a definitive need for stereoscopic depth perception. Such a joint representation can be related to the spatial properties of binocular filters tuned to specific disparity values [Sanger1988] This problem has an elegant formulation in the frequency domain, in relation to the so called phase based matching methods [Sanger1988] Basically, disparity estimation is computed as the shift necessary to align the phase values of the band pass filtered version of the binocular stereo ....

....for stereoscopic depth perception. Such a joint representation can be related to the spatial properties of binocular filters tuned to specific disparity values [Sanger1988] This problem has an elegant formulation in the frequency domain, in relation to the so called phase based matching methods [Sanger1988] Basically, disparity estimation is computed as the shift necessary to align the phase values of the band pass filtered version of the binocular stereo signals. Exploiting the properties of the perceptual engine one can change the phase of the resulting Gabor filter in order to find the local ....

T.D. Sanger. Stereo disparity computation using Gabor filters. Biol. Cybern., 59:405--418, 1988.

....depth estimation is mainly based on disparity measurement. Disparity is a local property that can be associated to a stereo pair (left and right) of images or image sequences. This problem has an elegant formulation in the frequency domain, in relation to the so called phase based matching methods [12]. Basically, disparity estimation is computed as the shift necessary to align the phase values of the band pass filtered version of the binocular stereo signals. One can assume that the disparity between the stereo image pair occurs only along the direction of the epipolar lines [13] In the ....

....to the line joining the optical centers of the cameras. In such conditions, stereo phase based matching can be cast as a 1D problem. Hence, we can use a rank of 1D Perceptual Engines acting separately on different rows of the input image. The local phase is computed following Sanger s algorithm [12], from the output of a pair of Gabor filters in quadrature (see Fig. 3) The functional organization of the stereoscopic perception system is sketched in Fig. 4: the differential measure of the local phase, obtained by the left and right retinas, is validated by a confidence measure, thus ....

T.D. Sanger. Stereo disparity computation using Gabor filters. Biol. Cybern., 59:405--418, 1988.

....they achieve throughput up to five frames per second. Neuro physiological studies (Julesz Saarinen 1991) show evidence that in some tasks biological systems achieve up to dozen times that throughput. To achieve better throughput one could use the biologically based approach offered by Sanger (Sanger 1988). This approach employs Gabor filters (Freeman Adelson 1991) local approximations of Fourier transformations, as the basis for disparity computation. This model uses the fact that the displacement of a function generates a proportional phase shift in its Fourier transform. The binocular ....

Sanger, T. D. 1988. Stereo disparity computation using gabor filters. Biological Cybernetics 59:405--418.

....shifted regions on the same vertical position and then to find the shift that gave maximum correlation. This is, however, a computationally very expensive method. Later approaches have been more focused on using the phase information given by for example Gabor filters or quadrature filters [9, 11, 7, 10]. An advantage of phase based methods is that phase is a continuous variable that allows for sub pixel accuracy. In phase based methods, the disparity can be estimated as a ratio between the phase difference between corresponding vertical line edge filter outputs from the two images and the ....

T. D. Sanger. Stereo disparity computation using gabor filters. Biological Cybernetics, 59:405--418, 1988.

....method. Details can be found in [TM93] A global spatial shift d can be detected as a phase shift k d in the Fourier spectrum. Convolving the left and right image with complex Gabor filters yields local phase shifts between the images containing the information about varying spatial shifts [San88]. The Gabor profile at a certain position is called receptive field (RF) A set of complex Gabor functions g ij (x) with different mean frequencies k fij = k f i cos # fj ; k f i sin # fj ) differing in magnitude k f i = k f0 ( 1 t 1 Gammat ) i and orientation # fj = j J (i = 0 : ....

T. Sanger. Stereo Disparity Computation Using Gabor Filters. Biological Cybernetics, 59:405 -- 418, 1988.

....to have different sizes, but is intended to function as a high precision refinement technique: without proper guidance from other sources it tends to get stuck in local minima and flatten out sloped surfaces. Several phase based stereo methods have been described in the literature [FJJ91] [San88] [Wen90] and a review of the more popular variations can be found in [JJ94] Although some of these mention foreshortening as an issue, none has explicitly modeled it or corrected for it. 3 Background 3.1 Stereo Matching Stereo matching is a useful tool in a variety of applications: robot ....

....In feature based stereo (e.g. Mat89] the dense image is converted into a spatially sparse set of features (e.g. corners, edges) which are matched. This results in a sparse disparity map which must be interpolated to yield disparities at every pixel. Finally, in frequency based stereo (e.g. [San88]) the original signal is transformed to Fourier space, and the phase of the transformed signal is used to compute the disparity, in any of several possible ways [JJ94] 3.3 The Scalogram: A Unified View of Scale Space The scalogram is one of several representations that makes use of the local ....

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Terence D Sanger. Stereo disparity computation using gabor filters. Biological Cybernetics, 59:405--418, 1988.

....a peu pres constante sur le support du filtre. Ces deux propri et es sont antinomiques, comme le montre le theoreme d incertitude [BRACEWELL, 1965] Le mieux que l on puisse faire est donc de choisir un filtre qui minimise le produit de la largeur spatiale par la largeur de bande. A la suite de Sanger [SANGER, 1988], de Langley et al. LANGLEY et al. 1991] et de Fleet [FLEET, 1992] notre choix s est port e sur le filtre de Gabor pour deux raisons: il minimise le produit de la largeur spatiale par la largeur de bande; l etude comparative de Fleet [FLEET, 1992] montre sa superiorite pour l estimation de ....

T. D. SANGER. Stereo disparity computation using gabor filters. Biological Cybernetics, (59):405--418, 1988.

.... Theta R 2 : 20) Therefore, the complex cell essentially sums up two related cross products between the bandpassed filtered left and right retinal images, resembling cross correlation type of operation. In this sense, our model is related to a class of stereo algorithms using complex image phases (Sanger, 1988; Fleet, Jepson and Jenkin, 1991) since those algorithms are also in some ways related to cross correlation. However, we would like to emphasize that although the complex cells are doing something similar to cross correlation, they are quite different from the standard cross correlators. The ....

.... frequency channels interact with each other (Wilson, Blake and Halpern, 1991; Rohaly and Wilson, 1993; Rohaly and Wilson, 1994; Smallman, 1995; Mallot, Gillner and Arndt, 1996) Computational studies have also suggested possible ways of pooling across different scales (Marr and Poggio, 1979; Sanger, 1988; Grzywacz and Yuille, 1990; Fleet et al. 1996) The exact mechanism used by the brain for combining scales, however, remains unknown. The simplest method is to average across the disparity maps computed by different scales (Sanger, 1988) Such an average for Figs. 11a, b and c is shown in Fig. ....

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Sanger, T. D. (1988). Stereo disparity computation using gabor filters, Biol. Cybern. 59: 405-- 418.

....directions and Ballard [Bal 93] uses steerable filters which are steered in the direction of the gradient. It is also possible to characterize a signal locally in the frequency space. Gabor filters are often used for stereo correspondence or for verging an active stereo head [Wes 92, Fle 91, San 88] These filters allow to obtain local phase information. This information is then used to estimate the disparity between two images. However, this measure is local in frequency and directional in space. It, therefore, only resists to small image rotations and small scale changes. In order to ....

T. Sanger. Stereo disparity computation using gabor filters. Biological Cybernetics, 2(59): 405--418, 1988.

....at each pixel can be thought of as the Fourier component at frequency of a window centred around that pixel. The size of the window is controlled by the standard deviation of the Gaussian function. These properties have motivated Gabor phasebased approaches to disparity analysis in stereo images[6] and vergence control[7] where the phase shift between two stereo images is measured at each pixel to measure disparity or to generate a vergence control signal. By analyzing the change of phase over time, one can also determine image motion[8] In this work, we assume that the fixation point in ....

T. Sanger, "Stereo disparity computation using Gabor filters,", Biol. Cybern., vol. 59, no. 6, pp. 40518, 1988.

....local phase difference observed in the Fourier domain. The local phase is extracted in the left and the right stereo images by taking the argument of the convolution product with a complex filter, such as a Gabor filter [1] Since the stereopsis algorithm was introduced as a disparity estimator [3, 8, 10], several works based on the technique have reported on its efficiency through extensive analysis and applications [2, 4, 5, 9] While the advantageous properties in the phase based method include computational simplicity, stability against varying lighting condition and especially direct ....

T. D. Sanger. Stereo disparity computation using gabor filters. Biol. Cybern., 59:405--418, 1988.

....the same qualities as those present in actual discrete imagery. Indeed, using continuous functions as input can often simplify the presentation by allowing the solution to be expressed analytically (in closed form) rather than operationally (e.g. the result after 10 iterations ) as in [5] [6]. This level of description is also useful for discerning and describing any theoretical limitations of the method, e.g. the points at which its assumptions break down. 2.1 Example 1: Phase difference as disparity The use of phase difference as disparity lies at the heart of many phase based ....

....description is also useful for discerning and describing any theoretical limitations of the method, e.g. the points at which its assumptions break down. 2. 1 Example 1: Phase difference as disparity The use of phase difference as disparity lies at the heart of many phase based stereo algorithms [6] [7] 5] 8] But unless one is already quite familiar with the frequency domain, the name itself inspires fear. Suppose one remained uncertain of the underlying principles; how could you convince yourself that the technique really works By considering the simplest possible examples according to ....

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T. D. Sanger, "Stereo disparity computation using gabor filters," Biological Cybernetics, vol. 59, pp. 405--418, 1988.

....The basic idea of the filter is to use a phase difference estimation in the Fourier domain in conjunction with a correlation measurement in the spatial domain to extract features with small horizontal disparity. While extensive work has been carried out on phase based disparity estimation [20, 23, 15], a brief overview of the theory is presented here for a better understanding of the mechanism of our filter. Convolving the left (l x;y ) and right (r x;y ) images using a complex filter produces two signals L x;y and R x;y which can be related to each other by: L x;y e j x;y Dx;y R x;y (5) ....

T. D. Sanger. Stereo disparity computation using gabor filters. Biol. Cybern., 59:405--418, 1998.

....performance, but in normal situations and for normal velocities we need faster algorithms for the tracking and pursuit tasks. Neuro physiological studies [30] show evidence that in some tasks biological systems achieve up to a dozen times that throughput. To achieve better throughput, Sanger [24] offers an approach based on biological models of the disparity computation. This Proceedings of XI SIBGRAPI (1998) 1 11 MULTI MODAL SENSORY INTEGRATION CONTROL 2 approach employs Gabor filters, local approximations of Fourier transformations, as the basis for disparity computation (see Freeman ....

T. D. SANGER. Stereo Disparity Computation using Gabor Filters. Biological Cybernetics, 59:405418. 1988.

....and contrast conditions in both cameras, correlation is sensitive to noise. An algorithm based on bandpass filters could give more stable results under real world conditions. Gabor filters [1] with limited spatial width and finite bandwidth are suitable filters for computing stereo disparity [5] in such an approach. We use a phase based approach with spatial Gabor filters to compute multi resolution disparity maps in real time. The disparity in the center of the map is used to control the vergence movement. A coarse to fine strategy helps us to deal with large disparity values ....

....as a phase shift in the Fourier spectrum. To recover the local disparity as a spatial shift the local phase differences have to be computed. Extracting the local phase in both images of a stereo pair with complex filters like Gabor filters leads to a direct computation of local disparity. Sanger [5], Langley et al. 8] and Fleet et al. 9] have employed phase based approaches in one or two dimensions to recover disparity information with complex Gabor filters (2) on different scales. G(x; oe; 1 p 2 oe e Gammax 2 =2oe 2 e Gammai x (2) We denote the Gabor filter responses f g ....

[Article contains additional citation context not shown here]

Sanger T.D.: Stereo disparity computation using Gabor filters.Biol.Cybernetics. 59,1988, 405-418.

.... motion processing (Reichardt, 1961; Hildreth, 1984; Watson and Ahumada, 1985; van Santen and Sperling, 1985; Adelson and Bergen, 1985; Heeger, 1987; Grzywacz and Yuille, 1990) and stereo vision (Marr and Poggio, 1976; Marr and Poggio, 1979; Prazdny, 1985; Pollard, Mayhew and Frisby, 1985; Sanger, 1988; Qian and Sejnowski, 1989; Yeshurun and Schwartz, 1989) have been proposed, but few dealt with these two visual functions at the same time. Although it is clear that at an abstract level both motion and stereo vision can be formulated as solving a correspondence problem (see Marr (1982) for ....

....on the other hand, cannot be said to be truly biological. Some (Marr and Poggio, 1976; Marr and Poggio, 1979; Prazdny, 1985; Pollard et al. 1985; Qian and Sejnowski, 1989) require very sharply disparitytuned units and use explicit matching of fine image features (see the Discussion) Others (Sanger, 1988; Yeshurun and Schwartz, 1989) contain certain mathematical operations (such as the explicit extraction of complex phases of stimuli) that are unlikely to be physiological. We have recently proposed a physiologically realistic model for stereo vision (Qian, 1994) We briefly review the model in ....

Sanger, T. D. (1988). Stereo disparity computation using gabor filters, Biol. Cybern. 59: 405-- 418.

.... past through the convolution of the image with gaussian like and mexican hat functionalities[1] 2] However, in some important applications, like stereo depth estimation and motion detection we need oscillatory kernels (Gabor like functions) to extract precise phase and local frequency information [3]. In [4] it has been demonstrated that the response to a constant stimulus of a network in which only first and second neighbors interact with the site (i.e. order two network) is a function in the form: h(n) Ce Gammajnj ( 1 e Gamma2 ) sin( 0 ) cos( 0 n) 1 Gamma e Gamma2 ) ....

T.D. Sanger. Stereo disparity computation using Gabor filters. Biol. Cybern., 59:405--418, 1988.

....to be demonstrated if these cells can be used to compute disparity maps from stereograms. Many models for disparity computation have been proposed over the years (Marr and Poggio, 1976; Marr and Poggio, 1979; Quam, 1984; Prazdny, 1985; Pollard, Mayhew and Frisby, 1985; Qian and Sejnowski, 1988; Sanger, 1988; Yeshurun and Schwartz, 1989) Unfortunately, most of them are non biological, either because they require sharply disparitytuned units with preferred disparities covering a wide range of values, or because of certain mathematical operations involved that are unlikely to be physiological or at ....

....disparitytuned units with preferred disparities covering a wide range of values, or because of certain mathematical operations involved that are unlikely to be physiological or at least have not been demonstrated physiologically. Some models are biologically inspired (Marr and Poggio, 1979; Sanger, 1988), but they are not solely based on the properties of binocular cells in the brain. Among the existing algorithms, the one that comes closest to physiology is perhaps the model proposed by Sanger (1988) who used Gabor filters for disparity computation. The model uses the fact that displacement of ....

[Article contains additional citation context not shown here]

Sanger, T. D. (1988). Stereo disparity computation using gabor filters, Biol. Cybern. 59: 405-- 418.

....at the coarse scales is valid. The disparity estimate might be wrong, might have a different value than at finer scales, or might not be present at all. Thus hierarchical approaches will fail under various circumstances. A third way for calculating disparities is known as phase based methods [4, 5]. These approaches derive Fourier phase images from the raw intensity data. Extraction of the Fourier phase can be considered as a local contrast equalization reducing the effects of many intensity variations between the two stereo views. Algorithmically, these approaches are in fact ....

T.D. Sanger, Stereo Disparity Computations Using Gabor Filter, Biol. Cybern. 59, 405--418, 1988.

No context found.

T. D. Sanger. Stereo disparity computation using gabor filters. Biol. Cybern., 59:405--418, 1988.

No context found.

T. D. SANGER. Stereo disparity computation using gabor filters. Biology and Cybernetics, 59:405--418, 1988.

No context found.

T.D. Sanger. Stereo disparity computation using Gabor filters. Biological Cybernetics, 59:405--418, 1988.

No context found.

T. D. Sanger. Stereo disparity computation using gabor filters. Biological Cybernetics, 59:405--418, 1988.

No context found.

T. D. Sanger, "Stereo disparity computation using gabor filters," Biological Cybernetics, vol. 59, pp. 405--418, 1988.

No context found.

T. Sanger. Stereo disparity computation using gabor filters. Biological Cybernetics, 59:405--418, 1988.

No context found.

Sanger, T. (1988) Stereo disparity computation using Gabor filters. Biological Cybernetics 59, pp. 405-418

No context found.

T.D. Sanger, "Stereo Disparity Computation Using Gabor Filters", Biological Cybernetics, vol. 59, pp. 405-418, 1988.

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