Thresholds of visibility for objects in images with random pixel noise are predicted in terms of the signal-to-noise ratio. From trials with volunteers marking test images, we determined visibility thresholds of objects obscured by random pixel noise. The test images had objects with a variety of simple shapes and relatively little internal structure. Aside from the noise, the background of the test images was smooth and featureless. We extend the threshold signal-to-noise ratio measurements of Rose and others to a variety of object sizes and shapes. For objects with areas less than a disc subtending 2 degrees at the eye, visibility depends on the averaged difference in intensity from background, the noise level and the number of pixels in the object. Visibility does not seem to depend on object shape.