Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 05 - Aufgabe 1 - Mach band

„Mach bands are an optical illusion consisting of an image of two wide bands, one light and one dark, separated by a narrow strip with a light-to-dark gradient. The human eye perceives two narrow bands of different brightnesses either side of the gradient that are not present in the original image. The illusion is named after Ernst Mach.“ [Wikipedia] Examples (try to differ as many colors as possible) White to black in 10 Steps

White to grey (255,255,255 -> 200,200,200) in 20 Steps

White to a lighter grey(220) in 20 steps (you can see the difference? – probably)

Same as above but with seperators (Can you see a difference in the middle part?)

This effect is supposed to be caused by lateral inhibition. Imagine three neighbouring retina cells - each one of them is stimulated at a different label. The level of the stimulation is transformed into action potentials and later on forwarded to its neighbours. Inhibitory interneurons weaken these signals and transfer them to so called secondary neurons. The attenuation is proportional to the excitation of the interneurons. By the summation of exciting and alleviative factors to the second neuron a contrast enhancement is archieved. We have to examine the edge which is represented schematically between an homogenous bright area (between receptor 1 and 5) and an homogenous dark area (between receptor 6 and 10). Without interaction every receptor of 1 to 5 would represent the same high and every receptor from 6-10 the same low signal. But because of the connection by an horizontal cell the signal of for example receptor 3 is attenuated because his neighbours impact on it inhibitorily. Only 5 and 6 are not affected because the have the same amount of inhibitory and excitatory neighbours.

Machband and Rendering Due to the linear intensity interpolation the Mach bands can cause trouble when using Gouroud Shading for rendering. Here the Machband effect can be visible at the edges of polygons. A rendering method which can work around the mach-band is Phong Shading.

Quellen: http://www.uni-koblenz.de/~lb/lehre/ws2006/bv/bvbuch.pdf , Fragmente eines Skripts zur Bildverarbeitung Wikipedia http://www.biokurs.de/skripten/12/bs12-38b.htm http://perceptualstuff.org/machbandsbasic.html http://www.yorku.ca/eye/machband.htm