Exaggerated contrast between edges of the slightly differing shades of gray appears as soon as they touchAlong 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 anoptical illusion named after the physicistErnst Mach. It exaggerates thecontrast 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 theChevreul illusion.[1]
The Mach bands effect is due to thespatial high-boost filtering performed by the human visual system on theluminance channel of the image captured by theretina. Mach reported the effect in 1865, conjecturing that filtering is performed in the retina itself, bylateral inhibition among its neurons.[2] This conjecture is supported by observations on other (non-visual) senses, as pointed out byGeorg von Békésy.[3] 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 aconvolution between a trapezoidal function that describes the illumination and one or morebandpass filters. A tight approximation is obtained by a model employing 9even-symmetric filters scaled at octave intervals.[4]
The effect is independent of the orientation of the boundary.
An illusory cross (×) appears in the large image due to gradient discontinuity[5]
This visual phenomenon is important to keep in mind when evaluatingdental radiographs for evidence of decay, in whichgrayscale images of teeth and bone are analyzed for abnormal variances of density. Afalse-positive radiological diagnosis ofdental 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] and the boundary betweenenamel anddentin.[6] Mach bands may also result in the misdiagnosis of horizontal root fractures because of the differing radiographic intensities of tooth and bone.[7]
Mach effect can also lead to an erroneous diagnosis ofpneumothorax by creating a dark line at the lung periphery (whereas a true pneumothorax will have a white pleural line).[8]
Example of Mach bands at the ends of gradients where the derivative of the luminance is discontinuous
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 inGouraud shading.
Computer image processing systems use edge-detection in a way analogous to the brain, usingunsharp masking to clarify edges in photos for example.
^Devlin, Hugh (2006).Operative dentistry: a practical guide to recent innovations; with ... 5 tables. Berlin Heidelberg: Springer. p. 11.ISBN978-3-540-29616-4.
^Parker, M. S.; Chasen, M. H.; Paul, N. (2009). "Radiologic Signs in Thoracic Imaging: Case-Based Review and Self-Assessment Module".American Journal of Roentgenology.192 (3_Supplement): S34-48.doi:10.2214/AJR.07.7081.PMID19234288.S2CID34785665.
