In the visual world, objects are partially occluded by nearer objects, separating them into image fragments. However, the image fragments of the object can easily be grouped and organized together by the visual system. Psychophysical data and theoretical analysis indicate that such perceptual grouping might be mediated in the early stages of visual processing. Here I show that some orientation-selective cells in the primary visual cortex (V1) have response properties that can mediate the grouping of image fragments. These cells stopped responding to a stimulus bar when it was partly occluded by a small patch. The cells also did not respond when the patch had uncrossed disparity so that it appeared to be behind the bar. However, the cells began responding again when the patch had crossed disparity so that it appeared to be in front of the bar. These results indicate that cells as early as V1 have the computational power to make inferences about the nature of partially invisible forms seen behind occluding structures.