Mach bands is an

optical illusion Within visual perception, an optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by a visual perception, percept that arguably appears to differ from reality. Illusions come in a wide v ...

named after the physicist

Ernst Mach Ernst Waldfried Josef Wenzel Mach ( , ; 18 February 1838 – 19 February 1916) was a Moravian-born Austrian physicist and philosopher, who contributed to the physics of shock waves. The ratio of one's speed to that of sound is named the 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.

Explanation

The Mach bands effect is due to the spatial high-boost filtering performed by the human visual system on the

luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls withi ...

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. This conjecture is supported by observations on other (non-visual) senses, as pointed out by von Békésy. 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. The effect is independent of the orientation of the boundary.

In radiology

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 and the boundary between enamel and

dentin Dentin () (American English) or dentine ( or ) (British English) ( la, substantia eburnea) is a calcified tissue of the body and, along with enamel, cementum, and pulp, is one of the four major components of teeth. It is usually covered by ena ...

. Mach bands may also result in the misdiagnosis of horizontal root fractures because of the differing radiographic intensities of tooth and bone. 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).

In computer graphics

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

Demonstration of the Mach band
was at

NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...

until July 2016
Mach Band figure and explanatory hypothesis, Laboratory of Dale Purves
{{Optical illusions Optical illusions

Explanation

In radiology

In computer graphics

See also

References

Further reading

External links