Neurons in the visual cortex typically respond selectively to the orientation, and velocity and direction of movement, of moving-bar stimuli. These responses are generally thought to provide information about the orientation and position of lines and edges in the visual field. Some cells are also endstopped, that is selective for bars of specific lengths. Hubel and Wiesel first observed that endstopped hypercomplex cells could respond to curved stimuli and suggested they might be involved in detection of curvature, but the exact relationship between endstopping and curvature has never been determined. We present here a mathematical model relating endstopping to curvature in which the difference in response of two simple cells gives rise to endstopping and varies in proportion to curvature. We also provide physiological evidence that endstopped cells in area 17 of the cat visual cortex are selective for curvature, whereas non-endstopped cells are not, and that some are selective for the sign of curvature. The prevailing view of edge and curve determination is that orientations are selected locally by the class of simple cortical cells and then integrated to form global curves. We have developed a computational theory of orientation selection which shows that measurements of orientation obtained by simple cells are not sufficient because there will be strong, incorrect responses from cells whose receptive fields (RFs) span distinct curves (Fig. 1). If estimates of curvature are available, however, these inappropriate responses can be eliminated. Curvature provides the key to structuring the network that underlies our theory and distinguishes it from previous lateral inhibition schemes.

Humans use distance information to scale the size of objects. Earlier studies demonstrated changes in neural response as a function of gaze direction and gaze distance in the dorsal visual cortical pathway to parietal cortex. These findings have been interpreted as evidence of the parietal pathway's role in spatial representation. Here, distance-dependent changes in neural response were also found to be common in neurons in the ventral pathway leading to inferotemporal cortex of monkeys. This result implies that the information necessary for object and spatial scaling is common to all visual cortical areas.

The problem of detecting curves in visual images arises in both computer vision and biological visual systems. Our approach integrates constraints from these two sources and suggests that there are two different stages to curve detection, the first resulting in a local description, and the second in a global one. Each stage involves a different style of computation: in the first stage, hypotheses are represented explicitly and coarsely in a fixed, preconfigured architecture; in the second stage, hypotheses are represented implicitly and more finely in a dynamically constructed architecture. We also show how these stages could be related to physiology, specifying the earlier parts in a relatively fine-grained fashion and the later ones more coarsely.

Hypercomplex or endstopped visual cortical neurons are usually supposed to be concerned with length or end point analysis. However. recent evidence demonstrates that endstopped neurons are curvature-selective. a connection that we explore here in sorne detail. A model of endstopped simple cells is developed and a variety of computational simulations examine the connection of the model to the reported length and orientation responses of endstopped neurons. Even and odd versions of the model are described.bath of which are shown to be curvature-selective. Even-symmetric instances of the model respond weil to thm curves over a range of curve orientation and curvature. independent of sign of curvature. In contrast. odd-symmetric instances respond to both thin and thlck curves whlle exhlblting a more complex curvature-sign dependence -respondmg m a slgnselective fashion to curved Ilnes but not to curved edges Finally. the response of the endstopped model to curve singularlties is explored. and the possible role of nonendstopped and endstopped cells in building curve descriptions is discussed. (1985) have proposed that shapes be decomposed into parts at the minima of negative curvature. Asada and Brady (1986) attempt to Infer the shape of an object from the sequence of curvature extrema and Inflectlons on its boundmg contour. It has also been argued that curv~ture is essentlal to reliably find the contours in images (Parent & Zucker. 1985). It is in the latter context that the present work has developed.Curve inference in visual images differs from curve-fitting (approximating or interpolating a curve to given points) in important respects. First. image contours differ ..

Different parts of the DMN exhibit divergent relationships to alpha power. Our results highlight the relationship between DMN activity and alpha power, indicating that networks, such as the DMN, may have subcomponents that exhibit different behaviors.