Qian, N., & Zhu, Y. (1997). Physiological computation of binocular disparity. Vision Research, 37, 1811 -- 1827.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for the presence of phase based disparity computations in the cat visual cortex. It is very possible that both mechanisms are at work and complement each other. Implementations of such a hybrid model have shown good stereo computation properties using only physiologically plausible mechanisms (Qian and Zhu, 1997; Fleet et al. 1996) The existence of retinal receptive fields which are closely related to Gabor functions and the presence of phase based stereo computations in the visual cortex makes the approach proposed here an interesting one. Some of the constraints used in this implementation have a ....

....regularization. An extension to the algorithm to deal with boundaries could involve an iterative procedure such as that described in (Chang and Chatterjee, 1992) Physiological studies have shown that sharp boundaries may be achieved through the use of spatial pooling of complex cell responses (Qian and Zhu, 1997) or through divisive normalization of simple and complex cell responses (Fleet et al. 1997) Either of these techniques would be interesting to implement as extensions of the algorithm presented here. The phase based procedure also showed poor results across surfaces with little or no texture, a ....

Qian, N. and Zhu, Y. (1997). Physiological computation of binocular disparity. Vision Research, 37:1811--1827.

....Freeman [23] found that the left and right spatial receptive field profiles of a binocular simple cell in cat s primary visual cortex can be described by two Gabor functions with the same Gaussian envelops but having sinusoidal modulations with different phase parameters. Recently, new research [20,21,22] have proposed new approaches for the neural encoding of binocular disparity that seems to be reasonable. The neurophysiological data supports that two models for determining the disparity are used by the binocular simple and complex cells in primary visual cortex [22] These models involve ....

N. QIAN and Y. ZHU. Physiological Computation of Binocular Disparity. Vision Research, 37:18111827, 1997.

....maturation, or do they continue to evolve throughout our lifetime For some of these questions, the answers have been well established. Simple cells [10] have receptive elds that resemble two dimensional Gaussians or oriented one dimensional derivatives of Gaussians [13, 38, 15] or Gabor lters [25, 20]. The development of these receptive elds is in uenced by stimulation of the visual system. Computational models exist that explain how they may develop in response to images of natural scenes exposed to uncommitted neurons in a properly biased adaptive visual system [21, 27] Some visual ....

N. Qian and Y. Zhu. Physiological computation of binocular disparity. Vision Research, 37:1811-1827, 1997. 15

....uses the fact that the displacement of a function generates a proportional phase shift in its Fourier transform. The binocular disparity at each location is therefore proportional to the phase difference of the corresponding left and right image patches (Freeman Ohzawa 1990) Recent research (Qian 1994; 1997; Fleet, Wagner, Heeger 1997) proposes a new approach for the neural encoding of binocular disparity. The neuro physiological data supports two models for the selective disparity of simple and complex cells in the primary visual cortex (Fleet, Wagner, Heeger 1997) These involve binocular ....

Qian, N. 1997. Physiological computation of binocular disparity. Vision Research 37:1811--1827.

....Crab is described. Finally, results are presented and discussed, and performance evaluated. 2 Vision, Reaching and Grasping (Related Work) We can find a wide range of articles and text books in the literature about stereo reconstruction and its application in Computer Vision or Robotics (e.g. [1, 2, 3, 7, 8, 9, 10, 20, 21, 22, 23, 29]. A number of researchers have followed the Marr [1] and Marr Poggio [7] paradigm. They propose a model that computes depth maps using correlation measures. It is quite difficult to design algorithms for real time applications using standard (even pipeline) architectures using this paradigm. A ....

....filters) This model uses the fact that the displacement of a function generates a proportional phase shift in its Fourier transform. The binocular disparity at each location is therefore proportional to the phase difference of the corresponding left and right image patches [23] Recent research [20, 21, 22] proposes a new approach for the neural encoding of binocular disparity. The neurophysiological data supports two models for the selective disparity of simple and complex cells in the primary visual cortex [22] These involve binocular combinations of monocular receptive fields that are shifted in ....

N. QIAN and Y. ZHU. Physiological Computation of Binocular Disparity. Vision Research, 37:18111827, 1997.

....but only if they code approximately the same stimulus value [11] A valid disparity estimate would show up in such a network as a strong coherent neuronal signal. For the disparity estimators, various circuitry can be used. In the simulations reported below, units based on motion energy filtering [12, 13, 14], units based on standard optical flow estimation techniques [6] and units based on algorithms j L j R 0 far disparity planes near disparity data left data right data Figure 2: The network structure for calculating stereo by coherence detection. Simple disparity estimators are arranged in ....

N. Qian and Y. Zhu, Physiological Computation of Binocular Disparity, to appear in Vision Research '97.

.... In the past, attempts have been made to build a model of invariant recognition around Hubel and Wiesel s simple to complex hierarchy (Fukushima, 1988) Because of the recent modifications to the classical view of the complex RF (Heeger, 1992) and because of their utility in modeling stereopsis (Qian and Zhu, 1997), we decided to explore the degree of invariance which can be imparted by a complex type representation, confronted with a variety of realistically detailed shaded 3D objects. 2 A REPRESENTATION BASED ON COMPLEX CELLS 2.1 BASIC APPROACH A complex cell responds to a properly oriented line segment ....

....recently, that model has been modified to include an additional nonlinearity in the form of cross orientation inhibition (Heeger, 1992) according to which cells tuned to different orientations are made to inhibit each other. A successful application of this model to stereopsis is described in (Qian and Zhu, 1997). The main parameters of our implementation are as follows: simple cell size, 8 pixels; complex cell size, 16 pixels; overlap factor, Theta4; number of orientations, 4 (this resulted in a 3364 dimensional representation space, with 29 Theta 29 = 841 complex cells at each orientation) ....

Qian, N. and Zhu, Y. (1997). Physiological computation of binocular disparity. Vision Research, 37:--. in press.

....seem to have difficulties with the fast calculation of dense disparity maps, at least with plausible neural circuitry. In the following, a neural network implementation will be described which solves this task by using simple disparity estimators based on motion energy mechanisms (Adelson, 1985; Qian, 1997), closely resembling responses of complex cells in visual cortex (DeAngelis, 1991) Disparity units of these type belong to a class of disparity estimators which can be derived from optical flow methods (Barron, 1994) Clearly, disparity calculations and optical flow estimation share many ....

Qian, N. & Zhu, Y. (1997): Physiological Computation of Binocular Disparity, to appear in Vision Research.

....binocular disparity. 2 N. Qian and Y. D. Zhu In particular, we demonstrate that by incorporating an additional piece of physiological data into our model, we can greatly improve the quality of the computed disparity maps. The results reported here have been presented previously in abstract form (Qian and Zhu, 1995). 2 The Model We briefly review our stereo model (Qian, 1994a) in this section. Our model is based on the physiological and modeling studies of Freeman and coworkers (Freeman and Ohzawa, 1990; Ohzawa et al. 1990; DeAngelis et al. 1991) These investigators found that the left and right spatial ....

.... significantly improved by taking into account the additional physiological fact that the receptive field sizes of real complex cells are on the average larger than those of the simple cells at the same eccentricity (Hubel and Wiesel, 1962; Schiller, Finlay and Volman, 1976) We proposed recently (Qian and Zhu, 1995; Zhu and Qian, 1996) that this fact can be incorporated into the model by averaging several quadrature pairs of simple cells with nearby and overlapping receptive fields (and with otherwise identical parameters) to construct a model complex cell. Mathematically, this spatial pooling process for ....

Qian, N. and Zhu, Y. (1995). Physiological computation of binocular disparity, Soc. Neurosc.

.... With explicit assumptions about the stimulus, accurate expressions of the complex cell responses for all D values may be derived (Zhu and Qian, 1996) It can also be shown that our stereo algorithm can be extended to a more general class of receptive field profiles than the Gabor functions (Qian and Zhu, 1995). Specifically, we found that equation 3 can be derived under the general assumption that the frequency tuning of the receptive field profiles is much sharper than the frequency spectrum of the input stimulus, and that there is a phase difference DeltaOE between the left and right receptive field ....

.... of real cells, and like other energy based models (Adelson and Bergen, 1985; Watson and Ahumada, 1985; Heeger, 1987; Qian, 1994) it does not assume any explicit feature extraction or matching and the correspondence problem is solved in an implicit way through correlation like operations (Qian and Zhu, 1995). In conclusion, we have derived a unified model of motion and stereo vision using physiological mechanisms and have provided a comprehensive and quantitative explanation of a family of Pulfrich like phenomena. We also made specific predictions for further experimental tests of the model. We are ....

Qian, N. and Zhu, Y. (1995). Physiological computation of binocular disparity, Soc. Neurosc.

....phases of both left and right images, and then calculated the Fourier phase difference at each location to find disparity. The algorithm has been tested on both random dot stereograms and natural images (Sanger, 1988) The energy method for disparity computation (Qian, 1994; Zhu and Qian, 1996; Qian and Zhu, 1997; Qian and Andersen, 1997; Qian, 1997; Fleet, Wagner and Heeger, 1996) was derived from the energy model of binocular cell responses in the cat s primary visual cortex (Ohzawa, DeAngelis and Freeman, 1990; Freeman and Ohzawa, 1990; DeAngelis, Ohzawa and Freeman, 1991; Ohzawa, DeAngelis and ....

....then calculated the Fourier phase difference at each location to find disparity. The algorithm has been tested on both random dot stereograms and natural images (Sanger, 1988) The energy method for disparity computation (Qian, 1994; Zhu and Qian, 1996; Qian and Zhu, 1997; Qian and Andersen, 1997; Qian, 1997; Fleet, Wagner and Heeger, 1996) was derived from the energy model of binocular cell responses in the cat s primary visual cortex (Ohzawa, DeAngelis and Freeman, 1990; Freeman and Ohzawa, 1990; DeAngelis, Ohzawa and Freeman, 1991; Ohzawa, DeAngelis and Freeman, 1996; Ohzawa, DeAngelis and ....

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Qian, N. and Zhu, Y. (1997). Physiological computation of binocular disparity, Vision Res.

....1976) Without this pooling step, a complex cell constructed from a single quadrature pair would have the same RF size as that of the constituent simple cells. Computationally, this averaging step makes the disparity tuning of the resulting complex cells much more reliable (see the Appendix and Qian and Zhu (1995)) In our simulations, the weighting function w was chosen to be a symmetric two dimensional (2D) Gaussian. We found that the disparity tuning curves of the complex cells are not very sensitive to the width oe w of the Gaussian so long as it is larger than 1 pixel. The sampling artifacts ....

....cells compared with simple cells, and makes the disparity tuning curves of complex cells more reliable. The quality of the computed disparity maps from random dot stereograms with the pooling step added is significantly better than those without the pooling step, especially at disparity boundaries (Qian and Zhu, 1995). Our algorithm for disparity computation also works with the position shift based RF 16 Y D. Zhu and N. Qian description since Equation 11 indicates that a population of complex cells with the positionshift based RF models can also form a distributed representation of stimulus disparity. We ....

Qian, N. and Zhu, Y. (1995). Physiological computation of binocular disparity, Soc. Neurosc.

....disparity equal to its receptive field shift is not valid. Simple cells cannot have a well defined preferred disparity because their responses depend not only on the disparity but also on the detailed spatial structure of the stimulus (Ohzawa et al. 1990; Qian, 1994; Zhu and Qian, 1996; Qian and Zhu, 1997). Although one can measure a disparity tuning curve from a simple cell, the peak location of the curve (i.e. the preferred disparity) changes with some simple manipulations (such as a lateral displacement) of the stimuli. This property is formally known as Fourier phase dependence because the ....

....constructed this way are indeed independent of stimulus Fourier phases and if so, how their preferred disparities are related to their receptive field parameters. These issues have recently been investigated through mathematical analyses and computer simulations (Qian, 1994; Zhu and Qian, 1996; Qian and Zhu, 1997). The complex cell model was found to be independent of stimulus Fourier phases for some types of stimuli including the bars used in the physiological experiments of Ohzawa et al. 1990) and its preferred disparity is equal to the left right receptive field shift within the constituent simple ....

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Qian, N. and Zhu, Y. (1997). Physiological computation of binocular disparity, Vision Res.

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Qian, N., & Zhu, Y. (1997). Physiological computation of binocular disparity. Vision Research, 37, 1811 -- 1827.

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