Double-nail illusion
The double-nail illusion is a [|multi-modal illusion] in which two similar physical objects, which are located one behind the other in depth, appear visually to be next to each other instead of one being directly behind the other.
This observation cannot be explained on the basis of classical theories of binocular depth perception, but it can be explained by binocular [|ghosts in a neural network].
The basic setup was mentioned in 1950 by Rønne and rediscovered and systematically investigated in 1978 by Krol, see [|Research history].
The conditions for the illusion and the main observations are described under [|Basic double-nail illusion], under [|Measurements of ghost images] and under [|Variations]. Related observations are listed under [|Edges and surfaces].
Basic double-nail illusion
Identical images. In the basic illusion, the two objects are upright in the visual field at the same height and with the same length and colour, and are behind each other, in line with the nose.Area for fine stereopsis. In order to experience the illusion, both real objects must be within the range for fine stereopsis . At a viewing distance of 30 cm, this area has a range of only 7 – 22 mm straight ahead, symmetrically around the fixation point; further to the side, the range increases rapidly. This means that the maximum distance between the two objects may be between 7 and 22 mm, provided that the eyes are focused on a point in the middle between the two objects. If the eyes are focused on the front object, this object is seen as a single fused image, and the other object as a double image without depth on the viewing distance. These observations are predicted by classical findings for binocular depth perception. The binocular ghosts are not seen.
Distance. If the viewing distance to the two objects is increased, the depth range in mm increases. The distance between the two objects can then be greater. Conversely, if the viewing distance is reduced, the distance between the objects must be smaller. By varying the viewing distance, it is possible to switch between seeing the illusion and seeing the double images.
Nose support to fix the head.
Convergence. If an observer with normal vision focuses his attention on both objects, both eyes automatically cohere and accommodate at a point between the two objects. This is increasingly the case as the distance between the two objects becomes smaller. At the moment this happens, a stable state is created in which it is more difficult to converge at a different distance. This means that once the illusion is seen, it is easy to continue seeing it.
Nose rest. The illusion is very sensitive to disturbances, and can be evoked most quickly with a viewing arrangement that is precisely aligned and in which the position of the head is stabilized, for example with a nose rest. But it can also be done with the following simple demonstration.
Ghosts in a neural network
The lower part of the figure contains a simplified representation of the neuromodel that initiated the investigation of the double-nail illusion. This model is based on the existence in the visual cortex of nerve cells with input from both eyes, which are tuned to a particular binocular disparity.In the double-nail illusion, four binocular cells A', B', C' and D' are stimulated, which signal the location and depth of A, B, C and D. If there were no interaction between the cells, the model predicts that four objects should be perceived.
To explain the observation in the double-nail illusion, it is assumed that the binocular cells, when activated, influence each other as follows:
- Cells tuned to the same depth amplify each other's activity ;
- Cells tuned to different depths attenuate each other's activity.
The above explanation applies to the situation where the two actual stimuli are within the range of stereopsis. If A and B are further apart and fall outside this area, then according to the model, A and B are not seen because there are no binocular cells that can signal the presence of an object. In other words, there cannot and need not be any interaction between binocular neurones to explain the perception, as in the [|Wheatstone stereogram] below.
The model described above is part of a model that, in addition to fine stereopsis, also includes single vision and double vision.
Measurements of ghost images
Krol investigated the exact position at which ghost images are observed when the double-nail arrangement is rotated out of the mid-sagittal plane : see the figure. If the two real objects A and B are rotated around a point midway between A and B, the geometric ghost images C and D slowly shift apart in depth: see the two left pictures. In the third picture, Panum's limiting case, AB and CD coincide. With even greater rotation, C and D move apart very quickly.Observers in the experiments had to fix a fixed point and indicate with a pointer where the observed left and right images were located.
Figure Depth measurements shows a typical measurement. The figure shows the actual depth positions of A, B, C and D relative to the fixation distance. The symbols show the perceived depth. At small inclinations the perceived images are seen at the positions of the ghost images C, D. From Panum's limiting case the images are seen at the positions of the real images A, B. The latter can be explained by the fact that C, D are then outside the area for stereopsis.
Conclusion: at small inclinations the binocular ghost images are indeed seen. At inclinations greater than Panum's limiting case the real objects are seen.
Variants
The hypothesis that binocular ghost images are seen in the basic double-nail illusion leads to the prediction of different appearances when the fixation point and the distance, shape or orientation of the two "nails" are varied. These variations have been demonstrated :- Thickness difference: If the front and back objects are unequally thick, two rotated surfaces are seen, the amount of rotation being predicted by the thickness difference, see figure.
- Length difference: If the front and back objects are unequally long, the illusion only occurs for the part where both objects are the same height. The part that protrudes above this is seen at its actual position and appears to float. If the shortest object has a ball, this ball is seen at its actual position and appears to float, see figure.
- Vergence: The illusion occurs when the eyes converge between the front and back objects and the distance between the objects is small enough. If the vergence is shifted from a point midway between both objects to the front or back object, the fixed object is seen single and the other object double; the illusion does not occur.
- Distance: At a viewing distance of an arm's length, the illusion only occurs at a small distance between the two objects, in the order of millimeters. If the distance between the two objects is increased or the viewing distance is decreased, the front or back object is automatically converged and the other object is seen double; the illusion does not occur.
- Inclination with double image: If the front object has a small ball and the distance between the objects is increased and the setup is rotated a few degrees, the following can be seen: the front ball appears as a double image at the fixation distance, the ghost images appear slightly behind it and shifted in depth, see figure inclination with double image.
- Tilt: If the front and back objects tilt relative to each other in a left-right direction, the perceived objects tilt in depth, see figure tilt.
- Contrast difference: if the front and back objects are both lighter or darker than the background, the depth illusion is unchanged and independent of the contrast between the two. If one object is lighter and the other darker than the background, no fusion is possible and double images are seen of either the front or the back object, near the distance of the horopter.
- Color difference: if the front and back objects have a red and a green ball respectively at the same height, the depth illusion is unchanged. The balls are seen next to each other, with the left one being green at different times and the right one being red and vice versa, or both having the same color. No color mixing is seen.
Edges and surfaces