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 The retina (from la, rete "net") is the innermost, light-sensitive layer of tissue of the eye of most vertebrates and some molluscs. The optics of the eye create a focused two-dimensional image of the visual world on the retina, which then ...

. Mach reported the effect in 1865, conjecturing that filtering is performed in the retina itself, by

lateral inhibition In neurobiology, lateral inhibition is the capacity of an excited neuron to reduce the activity of its neighbors. Lateral inhibition disables the spreading of action potentials from excited neurons to neighboring neurons in the lateral direction ...

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 In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is ...

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 In digital photography, computer-generated imagery, and colorimetry, a grayscale image is one in which the value of each pixel is a single sample representing only an ''amount'' of light; that is, it carries only intensity information. Graysca ...

images of teeth and bone are analyzed for abnormal variances of density. A

false-positive A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition (such as a disease when the disease is not present), while a false negative is the opposite error, where the test result ...

radiological diagnosis of

dental caries Tooth decay, also known as cavities or caries, is the breakdown of teeth due to acids produced by bacteria. The cavities may be a number of different colors from yellow to black. Symptoms may include pain and difficulty with eating. Complicatio ...

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 A pneumothorax is an abnormal collection of air in the pleural space between the lung and the chest wall. Symptoms typically include sudden onset of sharp, one-sided chest pain and shortness of breath. In a minority of cases, a one-way valve ...

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 Gouraud shading, named after Henri Gouraud, is an interpolation method used in computer graphics to produce continuous shading of surfaces represented by polygon meshes. In practice, Gouraud shading is most often used to achieve continuous l ...

. Computer image processing systems use edge-detection in a way analogous to the brain, using

unsharp masking Unsharp masking (USM) is an image sharpening technique, first implemented in darkroom photography, but now commonly used in digital image processing software. Its name derives from the fact that the technique uses a blurred, or "unsharp", negat ...

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