Marr, D. and Ullman, S. (1981). Directional selectivity and its use in early visual processing. Proceedings of the Royal Society London Set., B-211:151-180.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....further aggravated if the measurement of visual motion is carried out by a mechanism which examines only a limited area of the image. The ability of a limited area motion detection mechanism to extract only partial information about the real 2D velocity field, called the aperture problem ( 161] [98], 64] may be illustrated by the following example. Consider an extended oriented pattern in the image, such as an intensity edge, moving behind a relatively small aperture, representing the limited area of the image analyzed by a motion detection mechanism. Because of the aperture, it is only ....

....to recover a better approximation to the true velocity field. According to Matt s approach, this can be done by constraining the solution to the recovery problem to comply with prior assumptions that reflect the physical nature of the problem. The assumption that the velocity field must be smooth ([98], 64] proved to be a good compromise between physical reality and computational convenience. Hildreth [53] incorporated this assumption into the measurement of motion by formulating the computational problem as constrained minimization. The true velocity V was estimated by minimizing an error ....

D. Mart and S. Ullman. Directional selectivity and its use in early visual processing. Proceedings of the Rolal Societ.l of London B, 211:151-180, 1981.

.... methods Matching methods estimate image translations by attempting to match local image regions or characteristic image features at subsequent instants of time [33, 39, 14, 8, 9, 28, 29] Gradient methods Gradient methods use derivatives of image intensity over space and time to form estimates [20, 25, 16, 46]. Frequency based or Filter based methods Frequency based methods is an umbrella term for a collection of methods developed by considering the problem in the spatio temporal frequency domain. These methods fall into two di#erent categories amplitude based [17, 15, 37] and phase based [13] ....

D. Marr and S. Ullman. Directional selectivity and its use in early visual processing. Proc. R. Soc. Lond. B, 211:151--180, 1981.

....Signals that are termed as degenerate have a spatially constant intensity gradient or, in other words, a unique texture orientation. This phenomenon is generally referred to as the aperture problem which arises when the Fourier spectrum of I i (x) is concentrated on a line rather than on a plane [18, 33]. Spatiotemporally, this depicts the situation in which I i (x; t) exhibits a single orientation. In this case, one only obtains the speed and direction of motion normal to the orientation, noted as v i (x; t) If many normal velocities are found in a single neighborhood, their respective spectra ....

D. Marr and S. Ullman. Directional selectivity and its use in early visual processing. Proceedings of Royal Society London, B 211:151-180, 1981. On the Fourier Properties of Discontinuous Visual Motion 19

....analysis procedes by rst computing local 2d velocities, and then by combining these local estimates to compute the global motion of an object. A well known problem with this approach is that local motion information is often ambiguous, a situation often referred to as the aperture problem [13, 6, 2, 8]. Consider the scene depicted in Figure 1. A local analyzer that sees only the vertical edge of a square can only determine the horizontal component of the motion. Whether the square translates horizontally to the right, diagonally up and to the right, or diagonally down and to the right, the ....

D. Marr and S. Ullman. Directional selectivity and its use in early visual processing. Proceedings of the Royal Society of London B, 211:151-180, 1981.

....Treisman and Gelade [37] identified a preattentive stage wherein certain features, primitives, are detected in parallel across the visual field. Possible primitives include colour, line ends (terminators) spatial frequency, motion, line orientation, binocular disparity, and texture (see [5, 8, 21, 18, 26, 37, 40]) These features could then be combined to produce a saliency map by forming a weighted combination of the feature values. Depending on the precise weights, the point of maximum saliency will appear at different points. Changing these weights corresponds to shifting the point of maximum saliency, ....

David Marr and Shimon Ullman. Directional selectivity and its use in early visual processing. Proc. R. Soc. Lond. B, 211:151--180, 1981.

....vector falling on the constraint line [Wallach, 1935] Only the velocity component perpendicular to the feature in the direction of the motion is well defined. In the computational literature this component is 2 referred to as normal flow and the ambiguity is referred to as the aperture problem [Marr and Ullman, 1981]. a) b) Fig. 2. Aperture problem: a) Line feature observed through a small aperture at time t. b) At time t ffit the feature has moved to a new position. It is not possible to determine exactly where each point has moved to. From local measurements only the flow component perpendicular to ....

D. Marr and S Ullman. Directional selectivity and its use in early visual processing. Proc. Royal Society, London B, 211:151--180, 1981.

....to the detection of local motion that invariably result in inaccurate and non unique motion measurements. In general, motion computation falls into the category of problems which are ill posed (Poggio Koch 1985) A key problem for local motion estimation is what is known as the aperture problem (Marr Ullman 1981), which states that any localized motion sensor can only detect motion orthogonal to a local contour. Such motion measurements are ambiguous, in the sense that any direction within a 180 range is equally compatible with the local motion measurement (Figure 1) A local motion detector, therefore, ....

....direction. Since the details of the initial motion extraction mechanism are of little importance in this context, a simple correlation scheme (e.g. Reichardt, 1961; Van Santen Sperling, 1984, 1985) was chosen for it computational simplicity. More complex energy models (Fennema Thompson, 1979; Marr Ullman, 1981; Adelson Bergen, 8 1985; Grossberg Rudd, 1989, 1992) could also serve as a front end to the current model. For the simulations described below, two successive image frames were used to compute correlation. For each position in space, a small window of pixels was chosen from the first frame. ....

Marr, D. & Ullman, S. (1981). Directional selectivity and its use in early visual processing ". Proceeding of the Royal Society of London: B, 211, 151-180.

....not really be called illusions they are interpretations that are fully consistent with the retinal input. Since the ellipse is bounded by a smooth contour, there exist an infinite number of velocity fields that would generate the same retinal sequence. Due to the well known aperture problem (Marr and Ullman, 1981; Hildreth, 1983; Wallach, 1935) at any point along the contour the local motion information is consistent with an infinite number of possible motions (figure 1a) Graphically, this ambiguity corresponds to a constraint line in velocity space (Adelson and Movshon, 1982; Nakayama and Silverman, ....

Marr, D. and Ullman, S. (1981). Directional selectivity and its use in early visual processing.

....locations.b. When the constraints are plotted together they intersect at a single point yielding the physically correct velocity of the square. This is an example of how integrating multiple constraints can resolve the local ambiguity of motion measurements. 1981; Adelson and Movshon, 1982; Marr and Ullman, 1981; Fennema and Thompson, 1979) refers to the impossibility of determining the two dimensional motion when a signal only contains a single orientation. For example, a local analyzer that sees only the vertical edge of a square can only determine the horizontal component of the motion. Whether the ....

....a single object, estimating that motion is nontrivial. This difficulty arises from the ambiguity of individual velocity measurements which may give only a partial constraint on the unknown motion (Wallach, 1935) i.e. the aperture problem , Horn and Schunck, 1981; Adelson and Movshon, 1982; Marr and Ullman, 1981). To solve this problem, most models assume a two stage scheme whereby local readings are first computed, and then integrated in a second stage to produce velocity estimates. Psychophysical (Adelson and Movshon, 1982; Movshon et al. 1986; Welch, 1989) and neurophysiological (Movshon et al. 1986; ....

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Marr, D. and Ullman, S. (1981). Directional selectivity and its use in early visual processing. Proceedings of the Royal Society of London B, 211:151--180.

....displacements along epipolar lines whose magnitude are small in regions where the object lies close to the virtual quadric. The residual displacements are later refined by use of local spatio temporal detectors that implement the constant brightness equation, or any correlation scheme (cf. [14, 22, 1]) along the epipolar lines. In the implementation section we have shown that two views of a face with typical displacements of around 20 pixels are brought closer to displacements of around 1 2 pixels by the transformation. Most optical flow methods can deal with such small displacements quite ....

D. Marr and S. Ullman. Directional selectivity and its use in early visual processing. Proceedings of the Royal Society of London B, 211:151--180, 1981.

....that can be represented using symbols but do not correspond to real objects (because they have no corresponding stimulus in the real world) A tutorial on visual cognition with an emphasis on shape recognition was written by Pinker [61] 2. 2 Modern Theories of Visual Perception Marr et al. [62, 63, 43, 64, 65, 66] made significant contributions to the study of the human visual perception system. In Marr s paradigm [67] the focus of research is shifted from applications to topics corresponding to modules of the human visual system. An illustration of this point is the so called shape from x research which ....

D. Marr and S. Ullman. Directional selectivity and its use in early visual processing. Proceedings of the Royal Society of London, B211:151--180, 1981.

....in sequences of images [59] Receptive elds built using the weighted sum of separable spatial and temporal lters can be used to model directional response characteristics of neurons. This idea was originally suggested by Marr and Ullman using the product of separable lters in space and time [45]. Biological support for such an approach was found experimentally in the cat visual cortex [7,8] As was pointed out by Grossberg and Rudd [17] the separable lter approach su ers from two limitations: sensitivity to direction of contrast and lack of temporal decay mechanisms. We have ....

Marr, D. and S. Ullman (1981). Directional selectivity and its use in early visual processing. Proc. of the Royal Society of London (B) 211, 151-180.

....termed as degenerate have a spatially constant intensity gradient or, in other words, a unique texture orientation. This phenomenon is generally referred to as the aperture problem which arises when the Fourier spectrum of an intensity image I i (x) is concentrated on a line rather than on a plane [17, 31]. Spatiotemporally, this depicts the situation in which I i (x; t) exhibits a single orientation. In this case, one only obtains the speed and direction of motion normal to the orientation, noted as v i (x; t) If many normal velocities are found in a single neighbourhood, their respective ....

D. Marr and S. Ullman. Directional selectivity and its use in early visual processing. Proceedings of Royal Society London, B 211:151--180, 1981.

....displacements along epipolar lines whose magnitude are small in regions where the object lies close to the virtual quadric. The residual displacements are later refined by use of local spatio temporal detectors that implement the constant brightness equation, or any correlation scheme (cf. [17], 25] 1] along the epipolar lines. In the implementation section 14 we have shown that two views of a face with typical displacements of around 20 pixels are brought closer to displacements of around 1 2 pixels by the transformation. Most optical flow methods can deal with such small ....

D. Marr and S. Ullman. Directional selectivity and its use in early visual processing. Proceedings of the Royal Society of London B, 211:151--180, 1981.

....y (5) Normal flow fields can be computed in real time. Many approaches have been undertaken in order to compute the optical flow field based on the normal flow adding constraints such as smoothness [13] or second derivatives [14, 15, 16] of the flow field. The reconstructionist school (started by [17]) followed the ambitious goal of deriving closed form solutions for egomotion parameters and scene layout based on optical flow fields. Practical applications however showed: ffl There are cases where the optical flow field is not equivalent to the motion field [18] ffl The parameter recovery ....

D. Marr and S. Ullman, ""Directional selectivity and its use in early visual processing "", Proc. R. Soc. Lond., vol. B 211, pp. 151--180, Mar. 1981.

....t) 3 c(u; v; w r x u r y v) where 3 indicates the 3D Fourier transform. The psychophysical work includes that of Watson, Barlow, VanSanten, Fleet and Heeger [Heeg87, Wats85, Barl65, VanS85, Adel85, Flee84a, Flee84b] Computational models include those developed by Marr, Buxton, and Liou [Marr81, Buxt83, Buxt84, Liou89]. According to Liou and Jain [Liou89] filter models suffer from several fundamental problems. First, most filter models assume constant velocity. Second, filter models suffer from the scale problem, i.e. they have problems separating events at different scales. Third, filter models are suitable ....

D. Marr and S. Ullman. Directional selectivity and its use in early visual processing. Proc. Roy. Soc London B, 211:151--180, 1981.

.... (1989ab, 1990abef, 1991, 1992b) has used EXIN networks to model several aspects of visual perception, including the development of disambiguation mechanisms for pattern motion (Movshon, Adelson, Gizzi, Newsome, 1985) in the aperture problem (Adelson Movshon, 1982; Hildreth, 1983; Marr, 1982; Marr Ullman, 1981), the development of end stopping and length sensitivity (Hubel Wiesel, 1977; Kato, Bishop, Orban, 1978; Orban, Kato, Bishop, 1979) and the development of orientation sensitivity (Hubel Wiesel, 1962) in neurons capable of representing edge intersections (Walters, 1987) Preliminary ....

Marr, D. & Ullman, S. (1981). Directional selectivity and its use in early visual processing.

.... general research that has investigated the use of spatiotemporal gradients in support of motion analysis (see, e.g. 9, 10, 18] or for general review [3] Of particular relevance is previous research that has dealt with the interpretation of such information in terms of directional selectivity [1, 19, 20]. The current work contributes to previous research mainly as follows. A novel method is proposed for recovering a measure of motion salience with reference to surveillance applications. This method is based on simple early vision operations and therefore can be used to help in the earliest stages ....

D. Marr & S. Ullman, "Directional selectivity and its use in early visual processing," Proc. of the Roy. Soc. of Lond. B 211, 151--180, 1981.

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Marr, D. 8z Ullman, S. "Directional selectivity and its use in early visual processing". Proc. to Soc. Lond. B, 211, 151-180, 1981.

....series of two dimensional pictures, taken over short temporal and spatial intervals [10, 12] This is performed by tracking a set of features in each of the frames. The major problem in computing optical flow fields is that only motion perpendicular to these features can be accurately established [17]. The other components of motion must be inferred. This is commonly known as the aperture problem (see figure 5) Because contour matching is ambiguous, attempts to resolve the problem within the optical flow domain have been based on general constraints such as smoothness or assumptions of local ....

D.Marr and S.Ullman. Directional selectivity and its use in early visual processing. Proc. R. Soc. London Ser., B211:151-180.

....a series of two dimensional pictures, taken over short temporal and spatial intervals [9, 11] This is performed by tracking a set of features in each of the frames. The major problem in computing optical flow fields is that only motion perpendicular to these features can be accurately established [15]. This is commonly known as the aperture problem (see figure 5) Because contour matching is ambiguous, attempts to resolve the problem within the optical flow domain have been based on general constraints such as smoothness or assumptions of local affine motion fields [1, 10] One could utilize ....

D.Marr and S.Ullman. Directional selectivity and its use in early visual processing. Proc. R. Soc. London Ser., B211:151-180.

....A few contours that could be used as features are highlighted. contour 1 contour 2 Figure 4: The aperture problem Looking through a local aperture a point on contour 1 may match with any of an infinite number of points on contour 2. Only the perpendicular component of the match can be recovered [18] still ambiguous as to the exact matches between individual points on the two contours. This problem is similar to the aperture problem in motion correspondence (see figure 4) In motion computation, the ambiguity problem is usually approached by using general constraints such as smoothness or ....

D.Marr and S.Ullman. Directional selectivity and its use in early visual processing. Proc. R. Soc. London Ser., B211:151-180.

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Marr, D. and Ullman, S. (1981). Directional selectivity and its use in early visual processing. Proceedings of the Royal Society London Set., B-211:151-180.

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Marr, D. and Ullman, S., "Directional selectivity and its use in early visual processing", Proc.R Soc Lond B , vol. 211 pp. 150-180, 1981.

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Marr D. and Ullman S. 1981, Directional selectivity and its use in early visual processing. Proc. R. Soc. Lond. B 211, 151- 180.

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