Descriptions of physical properties of visible surfaces, such as their distance and the presence of edges, must be recovered from the primary image data. Computational vision aims to understand how such descriptions can be obtained from inherently ambiguous and noisy data. A recent development in this field sees early vision as a set of ill-posed problems, which can be solved by the use of regularization methods. These lead to algorithms and parallel analog circuits that can solve 'ill-posed problems' and which are suggestive of neural equivalents in the brain.

In this article a new method for the calibration of a vision system which consists of two (or more) cameras is presented. The proposed method, which uses simple properties of vanishing points, is divided into two steps. In the first step, the intrinsic parameters of each camera, that is, the focal length and the location of the intersection between the optical axis and the image plane, are recovered from a single image of a cube. In the second step, the extrinsic parameters of a pair of cameras, that is, the rotation matrix and the translation vector which describe the rigid motion between the coordinate systems fixed in the two cameras, are estimated from an image stereo pair of a suitable planar pattern. Firstly, by matching the corresponding vanishing points in the two images the rotation matrix can be computed, then the translation vector is estimated by means of a simple triangulation. The robustness of the method against noise is discussed, and the conditions for optimal estimation of the rotation matrix are derived. Extensive experimentation shows that the precision that can be achieved with the proposed method is sufficient to efficiently perform machine vision tasks that require camera calibration, like depth from stereo and motion from image sequence.

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In a passive dendritic tree, inhibitory synaptic inputs activating ionic conductances with an equilibrium potential near the resting potential can effectively veto excitatory inputs. Analog interactions of this type can be very powerful if the inputs are appropriately timed and occur at certain locations. We examine with computer simulations the precise conditions required for strong and specific interactions in the case of a 8-like ganglion cell of the cat retina. We find some critical conditions to be that (i) the peak inhibitory conductance changes must be sufficiently large (i.e., ==50 nS or more), (ii) inhibition must be on the direct path from the location of excitation to the soma, and (iii) the time course of excitation and inhibition must substantially overlap. Analog AND-NOT operations realized by satisfying these conditions may underlie direction selectivity in ganglion cells.When two neighboring regions of a dendritic tree experience simultaneous conductance changes-induced by synaptic inputs-the resulting postsynaptic potential at the soma is usually not the sum of the potentials generated by each synapse alone. Even though the existence of such nonlinear interactions in a passive dendritic tree has been long recognized, both theoretically and experimentally (1)(2)(3)(4), it has been customary to assume linear summation of excitatory and inhibitory inputs on the dendrites and to regard the threshold associated with spike generation at the axon hillock as performing the elementary logical operations in the nervous system. It is, however, possible that synapses situated close to each other on the dendrite of a cell may interact in a highly nonlinear way. For Nonlinear synaptic interactions were found to be maximal for y and 8 cells and relatively weaker for a and ( cells. On the basis of this analysis, we conjectured that cells with a 8-like morphology are the substratum for directional selectivity in the retina. In this note, we wish to show the main properties and critical features of the interaction between transient synaptic inputs for the a cell shown in Fig. la, whose geometry was measured from histological (Golgi) material of Boycott and Wassle (11). The main result consists of a set of critical predictions about direction-selective ganglion cells and the organization and properties of their synaptic input.The branching structure, the length, and the diameters of each dendritic segment were determined as described (10, 12). The dendritic tree was approximated by short segments, each being equivalent to a cylinder. A program using Butz and Cowan's algorithm (13) was used to compute from these data (for a range of values of the membrane capacity Cm, membrane resistance Rm, and intracellular resistance R) the linear electrical properties of the cell. We assumed the dendritic membrane to be passive and the spread of current along dendrites to be adequately described by linear cable theory. In the program, the complex transfer resistances K,(w) for any two locations ij in the dendritic tr...

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