Editing Mach bands

{{Short description|Optical illusion}}
{{For|the shock-wave pattern|Mach diamond}}
[[File:Mach bands - animation.gif|thumb|196px|right|Exaggerated contrast between edges of the slightly differing shades of gray appears as soon as they touch]]
[[File:Bandes de mach.PNG|thumb|Along the boundary between adjacent shades of grey in the Mach bands illusion, [[lateral inhibition]] makes the darker area falsely appear even darker and the lighter area falsely appear even lighter.]]

'''Mach bands''' is an [[optical illusion]] named after the physicist [[Ernst Mach]]. It exaggerates the [[contrast (vision)|contrast]] between edges of the slightly differing shades of gray, as soon as they contact one another, by triggering edge-detection in the human visual system. The Mach band illusion is sometimes called the '''Chevreul''' illusion.<ref>{{Cite journal |last=Geier |first=János |last2=Hudák |first2=Mariann |date=2011-10-13 |title=Changing the Chevreul Illusion by a Background Luminance Ramp: Lateral Inhibition Fails at Its Traditional Stronghold - A Psychophysical Refutation |url=https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0026062 |journal=PLoS One |language=en |volume=6 |issue=10 |pages=e26062 |doi=10.1371/journal.pone.0026062 |issn=1932-6203 |pmc=3192777 |pmid=22022508 |doi-access=free}}</ref>

==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.

==In radiology==
[[File:Mach_band_cross.svg|thumb|An illusory cross (×) appears in the large image due to gradient discontinuity<ref>{{Cite report |chapter-url=https://ieeexplore.ieee.org/document/8946114 |chapter=Radiography Contrast Enhancement: Smoothed LHE Filter a Practical Solution for Digital X-Rays with Mach Band |last1=Ambalathankandy |first1=Prasoon |last2=Ou |first2=Yafei |date=December 2019 |publisher=IEEE |doi=10.1109/DICTA47822.2019.8946114 |pages=1–8 |last3=Kochiyil |first3=Jyotsna |last4=Takamaeda |first4=Shinya |last5=Motomura |first5=Masato |last6=Asai |first6=Tetsuya |last7=Ikebe |first7=Masayuki|title=2019 Digital Image Computing: Techniques and Applications (DICTA) |isbn=978-1-7281-3857-2 }}</ref>]]
This visual phenomenon is important to keep in mind when evaluating [[dental radiography|dental radiographs]] for evidence of decay, in which [[grayscale]] images of teeth and bone are analyzed for abnormal variances of density. A [[false-positive]] radiological diagnosis of [[dental caries]] can easily arise if the practitioner does not take into account the likelihood of this illusion. Mach bands manifest adjacent to metal restorations or appliances{{Citation needed|date=June 2013}} and the boundary between [[Tooth enamel|enamel]] and [[dentin]].<ref>{{Cite book |last=Devlin |first=Hugh |title=Operative dentistry: a practical guide to recent innovations; with ... 5 tables |date=2006 |publisher=Springer |isbn=978-3-540-29616-4 |location=Berlin Heidelberg |pages=11}}</ref> Mach bands may also result in the misdiagnosis of horizontal root fractures because of the differing radiographic intensities of tooth and bone.<ref>{{Cite journal |last=Nielsen |first=C |date=November 2001 |title=Effect of Scenario and Experience on Interpretation of Mach Bands |url=http://linkinghub.elsevier.com/retrieve/pii/S0099239905604852 |journal=Journal of Endodontics |language=en |volume=27 |issue=11 |pages=687–691 |doi=10.1097/00004770-200111000-00009|pmid=11716082 |url-access=subscription }}</ref>

Mach effect can also lead to an erroneous diagnosis of [[pneumothorax]] by creating a dark line at the lung periphery (whereas a true pneumothorax will have a white pleural line).<ref>{{Cite journal | last1 = Parker | first1 = M. S. | last2 = Chasen | first2 = M. H. | last3 = Paul | first3 = N. | doi = 10.2214/AJR.07.7081 | title = Radiologic Signs in Thoracic Imaging: Case-Based Review and Self-Assessment Module | journal = American Journal of Roentgenology | volume = 192 | issue = 3_Supplement | pages = S34-48 | year = 2009 | pmid =  19234288| s2cid = 34785665 }}</ref>

==In computer graphics==
[[File:Mach bands gradient overshoot.svg|thumb|Example of Mach bands at the ends of gradients where the derivative of the luminance is discontinuous {{olist
    |Actual luminance profile
    |Perceived luminance profile
    |Smooth luminance profile for comparison
}}]]
Mach bands can also appear when there is a discontinuity in the derivative of a gradient, a visual effect common when intensities are linearly interpolated such as in [[Gouraud shading]].

Computer image processing systems use edge-detection in a way analogous to the brain, using [[unsharp masking]] to clarify edges in photos for example.

==See also==
*[[Acutance]]
*[[Cornsweet illusion]]
*[[Hermann grid illusion]]
*[[Lateral inhibition]]
*[[Optical illusions]]
*[[Watercolour illusion]]
*[[Gibbs phenomenon]]

==References==
{{Reflist}}

==Further reading==
*{{cite journal |vauthors=Lotto RB, Williams SM, Purves D |title=Mach bands as empirically derived associations |journal=[[Proceedings of the National Academy of Sciences]] |volume=96 |issue=9 |year=1999 |pages=5245–50 |pmid=10220451 |doi=10.1073/pnas.96.9.5245 |pmc=21849 |bibcode=1999PNAS...96.5245L|doi-access=free }}
*Eagleman, DM (2001) "Visual Illusions and Neurobiology." ''[[Nature Reviews Neuroscience]]''. 2(12): 920–6.

==External links==
{{Commons category|Mach bands}}
*[https://web.archive.org/web/20160719014926/http://www.nist.gov/lispix/imlab/illusions/machband.html Demonstration of the Mach band] was at [[NIST]] until July 2016
*[http://purveslab.net/mach-bands-2/ Mach Band figure and explanatory hypothesis, Laboratory of Dale Purves]

{{Optical illusions}}

[[Category:Optical illusions]]
[[Category:Ernst Mach]]