​The Kanizsa triangle illusion makes us realise the way our visual systems work—which we do not notice in our everyday experience. Looking at the figure, most people will have the visual experience of an apparent brightness contour defining an upright triangle which is occluding three black discs and a second, inverted triangle outlined in black. Of course, these triangles do not in fact exist, and we are not perceiving occluded discs but rather ‘Pac-Man’-like fragments of discs. (‘Pacmen’ is now the standard nomenclature for such inducing elements). A similar illusory ‘filling-in’ of colour that we experience in the  upright triangle, such that the figure appears filled with a solid white that is brighter than the rest of the figure, is also highly evident in the Kanizsa square (Fig. 1). Note that both the Kanizsa triangle and the Kanizsa square create an illusion of depth – the central figure appears to sit in a higher plane than the inducing pacmen (or the occluded downward pointing triangle).
​ Kanizsa (1955) makes a distinction between modal and amodal completion of contours. In modal completion one has a visual experience as of an object in virtue of experiencing edges that appear to be created by a luminance, colour or texture boundary. On reflection, one can tell that there is no such boundary and there is not a difference in luminance, colour or texture where there appears to be one; but, nonetheless, that is what we experience. In the Kaniza triangle the triangle that one seems to see pointing upwards, in virtue of a difference in luminance between it and the background, is a classic example of modal completion. The apparent discs in the Ehrenstein figure are also an example of modal completion, as they are experienced in virtue of experiencing an apparent lightness boundary where none is present.

In contrast to this, the triangle that one seems to see pointing downwards in the Kanizsa traingle image, that appears to be partly behind the upwards pointing triangle that we previously mentioned, provides an example of amodal completion. The experience that one has of the downward pointing triangle does not consist in experienced boundaries consisting of colour, lightness or texture corresponding the occluded portion of the triangle. Yet, nonetheless, it does seem as if a triangle is present. This is a case of amodal completion, and it contrasts with modal completion in that it occurs when part of an object is experienced as occluded and is reported as having a particular shape, yet the occluded portion of the object is not experienced as being defined by colour, lightness or texture boundaries. The horizontal and vertical lines in the Ehrenstein figure are usually perceived as amodally completed – they appear to continue behind the disc - but they are not experienced in virtue of an experience of an apparent luminance or colour boundary. A good discussion of these phenomena from a psychological perspective is given in Gerbino, W., and R. van Lier (2015). Philosophical accounts of modal and amodal perception can be found in Nanay (2010), Briscoe (2011), and Macpherson (2015).

The mechanisms underlying contour completion and filling-in are not entirely understood. It is generally accepted that contour completion is an example of the perceptual system rejecting ‘coincidence’, in the sense that a symmetrical arrangement of fragments and line elements as seen in the Kanizsa triangle is unlikely in the natural environment. A similar retinal stimulation is more often caused by one continuous surface occluding another, and so this is how the Kanizsa stimulus is represented by our perceptual system (Rock and Anson 1979). As far as physiology goes, Peterhans et al. (1986) suggest that the illusory completed contour can be explained by the action of end-stopped neurons in the visual cortex. These cells correspond to elongated receptive fields on the retina and can fire selectively for both length and orientation of stimulus. Activity in spatially separated, end-stopped cells may trigger a gating mechanism, allowing for communication between neurons at previously inactive synapses.

The concept of 'filling-in' are explored in the article on the Troxler Effect.