Editing Mach bands (section)

==Explanation==
The Mach bands effect is due to the [[Unsharp masking|spatial high-boost filtering]] performed by the human visual system on the [[luminance]] channel of the image captured by the [[retina]]. Mach reported the effect in 1865, conjecturing that filtering is performed in the retina itself, by [[lateral inhibition]] among its neurons.<ref>{{Cite book|url=https://books.google.com/books?id=iwwpAQAAMAAJ|title=Mach bands: quantitative studies on neural networks in the retina|last=Ratliff|first=Floyd|date=1965|publisher=Holden-Day|isbn=9780816270453|language=en}}</ref> This conjecture is supported by observations on other (non-visual) senses, as pointed out by [[Georg von Békésy]].<ref>{{Cite journal |last=von Békésy |first=Georg |date=1967-01-01 |title=Mach Band Type Lateral Inhibition in Different Sense Organs |url=https://rupress.org/jgp/article/50/3/519/30908/Mach-Band-Type-Lateral-Inhibition-in-Different |journal=The Journal of General Physiology |language=en |volume=50 |issue=3 |pages=519–532 |doi=10.1085/jgp.50.3.519 |issn=1540-7748 |pmc=2225686 |pmid=11526844}}</ref> The visual pattern is often found on curved surfaces subject to a particular, naturally-occurring illumination, so the occurrence of filtering can be explained as the result of learnt image statistics. The effect of filtering can be modeled as a [[convolution]] between a trapezoidal function that describes the illumination and one or more [[Band-pass filter|bandpass filters]]. A tight approximation is obtained by a model employing 9 [[Even and odd functions|even-symmetric]] filters scaled at octave intervals.<ref>{{cite journal |author=Frederick A. A. Kingdom |date=4 November 2014 |title=Mach bands explained by response normalization |journal=Frontiers in Human Neuroscience |volume=8 |issn=1662-5161 |pages=843 |doi=10.3389/fnhum.2014.00843 |pmid=25408643 |pmc=4219435 |doi-access=free }}</ref>

The effect is independent of the orientation of the boundary.