Publication

Innovation modelling and wavelet analysis of fractal processes in bio-imaging

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti
2008
Conference Papers

Abstract

Growth and form in biology are often associated with some level of fractality. Fractal characteristics have also been noted in a number of imaging modalities. These observations make fractal modelling relevant in the context of bio-imaging.

Official source

https://infoscience.epfl.ch/entities/publication/e2a16a31-5898-4508-8085-ad1c8cff12fa

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Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti
2008
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/e2a16a31-5898-4508-8085-ad1c8cff12fa

About this result

Related concepts (15)

Fractal

In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar.

Fractal dimension

In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension. The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.

Fractal expressionism

Fractal expressionism is used to distinguish fractal art generated directly by artists from fractal art generated using mathematics and/or computers. Fractals are patterns that repeat at increasingly fine scales and are prevalent in natural scenery (examples include clouds, rivers, and mountains). Fractal expressionism implies a direct expression of nature's patterns in an art work. The initial studies of fractal expressionism focused on the poured paintings by Jackson Pollock (1912-1956), whose work has traditionally been associated with the abstract expressionist movement.

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