A new model of contour extraction and perceptual grouping in the primary visual cortex is presented and discussed. It differs from previous models since it incorporates four main mechanisms, according to recent physiological data: a feed-forward input from the lateral geniculate nucleus, characterized by Gabor elongated receptive fields; an inhibitory feed-forward input, maximally oriented in the orthogonal direction of the target cell, which suppresses non-optimal stimuli and warrants contrast invariance; an excitatory cortical feedback, which respects co-axial and co-modularity criteria; and a long-range isotropic feedback inhibition. Model behavior has been tested on artificial images with contours of different curvatures, in the presence of considerable noise or in the presence of broken contours, and on a few real images. A sensitivity analysis has also been performed on the role of intracortical synapses. Results show that the model can extract correct contours within acceptable time from image presentation (30-40 ms). The feed-forward input plays a major role to set an initial correct bias for the subsequent feedback and to ensure contrast-invariance. Long-range inhibition is essential to suppress noise, but it may suppress small contours due to excessive competition with greater contours. Cortical excitation sharpens the initial bias and improves saliency of the contours. Model results support the idea that contour extraction is one the primary steps in the visual processing stream, and that local processing in V1 is able to solve this task even in difficult conditions, without the participation of higher visual centers.