mach bands

File:Mach bands - animation.gif

File:Bandes de mach.PNG 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 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.{{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}}

Explanation

The Mach bands effect is due to the 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.{{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}} This conjecture is supported by observations on other (non-visual) senses, as pointed out by Georg von Békésy.{{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}} 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 bandpass filters. A tight approximation is obtained by a model employing 9 even-symmetric filters scaled at octave intervals.{{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 }}

The effect is independent of the orientation of the boundary.

In radiology

File:Mach_band_cross.svg

This visual phenomenon is important to keep in mind when evaluating 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 enamel and dentin.{{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}} Mach bands may also result in the misdiagnosis of horizontal root fractures because of the differing radiographic intensities of tooth and bone.{{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 }}

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).{{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 }}

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.

References

External links

[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]

Category:Optical illusions

Category:Ernst Mach