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.

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

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

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

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

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

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