This paper reviews some of the recent neurophysiological studies that explore the variety of visual computations in the early visual cortex in relation to geometric inference, i.e. the inference of contours, surfaces and shapes. It attempts to draw connections between ideas from computational vision and findings from awake primate electrophysiology. In the classical feed-forward, modular view of visual processing, the early visual areas (LGN, V1 and V2) are modules that serve to extract local features, while higher extrastriate areas are responsible for shape inference and invariant object recognition. However, recent findings in primate early visual systems reveal that the computations in the early visual cortex are rather complex and dynamic, as well as interactive and plastic, subject to influence from global context, higher order perceptual inference, task requirement and behavioral experience. The evidence argues that the early visual cortex does not merely participate in the first stage of visual processing, but is involved in many levels of visual computation.