Relationship Between Phase and Energy Methods for Disparity Computation

2000 ◽  
Vol 12 (2) ◽  
pp. 279-292 ◽  
Author(s):  
Ning Qian ◽  
Samuel Mikaelian

The phase and energy methods for computing binocular disparity maps from stereograms are motivated differently, have different physiological relevances, and involve different computational steps. Nevertheless, we demonstrate that at the final stages where disparity values are made explicit, the simplest versions of the two methods are exactly equivalent. The equivalence also holds when the quadrature-pair construction in the energy method is replaced with a more physiologically plausible phase-averaging step. The equivalence fails, however, when the phase-difference receptive field model is replaced by the position-shift model. Additionally, intermediate results from the two methods are always quite distinct. In particular, the energy method generates a distributed disparity representation similar to that found in the visual cortex, while the phase method does not. Finally, more elaborate versions of the two methods are in general not equivalent. We also briefly compare these two methods with some other stereo models in the literature.

1994 ◽  
Vol 6 (3) ◽  
pp. 390-404 ◽  
Author(s):  
Ning Qian

Many models for stereo disparity computation have been proposed, but few can be said to be truly biological. There is also a rich literature devoted to physiological studies of stereopsis. Cells sensitive to binocular disparity have been found in the visual cortex, but it is not clear whether these cells could be used to compute disparity maps from stereograms. Here we propose a model for biological stereo vision based on known receptive field profiles of binocular cells in the visual cortex and provide the first demonstration that these cells could effectively solve random dot stereograms. Our model also allows a natural integration of stereo vision and motion detection. This may help explain the existence of units tuned to both disparity and motion in the visual cortex.


Neuron ◽  
2001 ◽  
Vol 30 (1) ◽  
pp. 263-274 ◽  
Author(s):  
Ilan Lampl ◽  
Jeffrey S. Anderson ◽  
Deda C. Gillespie ◽  
David Ferster

NeuroImage ◽  
2021 ◽  
Vol 244 ◽  
pp. 118554
Author(s):  
Eline R. Kupers ◽  
Akhil Edadan ◽  
Noah C. Benson ◽  
Wietske Zuiderbaan ◽  
Maartje C. de Jong ◽  
...  
Keyword(s):  

Of the many possible functions of the macaque monkey primary visual cortex (striate cortex, area 17) two are now fairly well understood. First, the incoming information from the lateral geniculate bodies is rearranged so that most cells in the striate cortex respond to specifically oriented line segments, and, second, information originating from the two eyes converges upon single cells. The rearrangement and convergence do not take place immediately, however: in layer IVc, where the bulk of the afferents terminate, virtually all cells have fields with circular symmetry and are strictly monocular, driven from the left eye or from the right, but not both; at subsequent stages, in layers above and below IVc, most cells show orientation specificity, and about half are binocular. In a binocular cell the receptive fields in the two eyes are on corresponding regions in the two retinas and are identical in structure, but one eye is usually more effective than the other in influencing the cell; all shades of ocular dominance are seen. These two functions are strongly reflected in the architecture of the cortex, in that cells with common physiological properties are grouped together in vertically organized systems of columns. In an ocular dominance column all cells respond preferentially to the same eye. By four independent anatomical methods it has been shown that these columns have the form of vertically disposed alternating left-eye and right-eye slabs, which in horizontal section form alternating stripes about 400 μm thick, with occasional bifurcations and blind endings. Cells of like orientation specificity are known from physiological recordings to be similarly grouped in much narrower vertical sheeet-like aggregations, stacked in orderly sequences so that on traversing the cortex tangentially one normally encounters a succession of small shifts in orientation, clockwise or counterclockwise; a 1 mm traverse is usually accompanied by one or several full rotations through 180°, broken at times by reversals in direction of rotation and occasionally by large abrupt shifts. A full complement of columns, of either type, left-plus-right eye or a complete 180° sequence, is termed a hypercolumn. Columns (and hence hypercolumns) have roughly the same width throughout the binocular part of the cortex. The two independent systems of hypercolumns are engrafted upon the well known topographic representation of the visual field. The receptive fields mapped in a vertical penetration through cortex show a scatter in position roughly equal to the average size of the fields themselves, and the area thus covered, the aggregate receptive field, increases with distance from the fovea. A parallel increase is seen in reciprocal magnification (the number of degrees of visual field corresponding to 1 mm of cortex). Over most or all of the striate cortex a movement of 1-2 mm, traversing several hypercolumns, is accompanied by a movement through the visual field about equal in size to the local aggregate receptive field. Thus any 1-2 mm block of cortex contains roughly the machinery needed to subserve an aggregate receptive field. In the cortex the fall-off in detail with which the visual field is analysed, as one moves out from the foveal area, is accompanied not by a reduction in thickness of layers, as is found in the retina, but by a reduction in the area of cortex (and hence the number of columnar units) devoted to a given amount of visual field: unlike the retina, the striate cortex is virtually uniform morphologically but varies in magnification. In most respects the above description fits the newborn monkey just as well as the adult, suggesting that area 17 is largely genetically programmed. The ocular dominance columns, however, are not fully developed at birth, since the geniculate terminals belonging to one eye occupy layer IVc throughout its length, segregating out into separate columns only after about the first 6 weeks, whether or not the animal has visual experience. If one eye is sutured closed during this early period the columns belonging to that eye become shrunken and their companions correspondingly expanded. This would seem to be at least in part the result of interference with normal maturation, though sprouting and retraction of axon terminals are not excluded.


1997 ◽  
Vol 77 (6) ◽  
pp. 2879-2909 ◽  
Author(s):  
Izumi Ohzawa ◽  
Gregory C. Deangelis ◽  
Ralph D. Freeman

Ohzawa, Izumi, Gregory C. DeAngelis, and Ralph D. Freeman. Encoding of binocular disparity by complex cells in the cat's visual cortex. J. Neurophysiol. 77: 2879–2909, 1997. To examine the roles that complex cells play in stereopsis, we have recorded extracellularly from isolated single neurons in the striate cortex of anesthetized paralyzed cats. We measured binocular responses of complex cells using a comprehensive stimulus set that encompasses all possible combinations of positions over the receptive fields for the two eyes. For a given position combination, stimulus contrast could be the same for the two eyes (2 bright or 2 dark bars) or opposite (1 bright and 1 dark). These measurements provide a binocular receptive field (RF) profile that completely characterizes complex cell responses in a joint domain of left and right stimulus positions. Complex cells typically exhibit a strong selectivity for binocular disparity, but are only broadly selective for stimulus position. For most cells, selectivity for disparity is more than twice as narrow as that for position. These characteristics are highly desirable if we assume that a disparity sensor should exhibit position invariance while encoding small changes in stimulus depth. Complex cells have nearly identical binocular RFs for bright and dark stimuli as long as the sign of stimulus contrast is the same for the two eyes. When stimulus contrast is opposite, the binocular RF also is inverted such that excitatory subregions become suppressive. We have developed a disparity energy model that accounts for the behavior of disparity-sensitive complex cells. This is a hierarchical model that incorporates specific constraints on the selection of simple cells from which a complex cell receives input. Experimental data are used to examine quantitatively predictions of the model. Responses of complex cells generally agree well with predictions of the disparity energy model. However, various types of deviations from the predictions also are found, including a highly elongated excitatory region beyond that supported by a single energy mechanism. Complex cells in the visual cortex appear to provide a next level of abstraction in encoding information for stereopsis based on the activity of a group of simple-type subunits. In addition to exhibiting narrow disparity tuning and position invariance, these cells seem to provide a partial solution to the stereo correspondence problem that arises in complex natural scenes. Based on their binocular response properties, these cells provide a substantial reduction in the complexity of the correspondence problem.


Sign in / Sign up

Export Citation Format

Share Document