Thus in our previously cited example, the nasal vowel is more complex acoustically than its oral counterpart in that it involves nasal resonances in addition to the oral resonances of oral vowels.” (Joseph Greenberg, 1980 ). The marked member is relatively complex in relation to the unmarked. “The term ‘mark’ derives from its earliest use in phonology. Complexity is hard to define or to measure but there is surely some sense in which elephants and oak trees are more complex than bacteria, and bacteria than the first replicating molecules.” (John Maynard Smith and Eörs Szathmáry, 1995 ).
The most that we can say is that some lineages have become more complex in the course of time. “Bacteria, for example, are probably no more complex than their ancestors 2000 million years ago. Thus, the quantification of structural richness can be adapted to time signals and distributions of various kinds. Although, for the sake of concreteness, our complexity measure is introduced for B/W images, the definition can be straightforwardly extended to any object that admits a mathematical representation as a function of one or more variables. Results show that the complexity index is able to clearly reveal regions with intricate topographical features such as river drainage networks and fjord-like coasts. As an application of the complexity index, we build a “complexity map” for South-American topography, by analyzing a large B/W image that represents terrain elevation data in the continent. Since the index provides an objective quantification of image complexity, it could be used as the counterpart of subjective visual complexity in experimental perception research. We introduce a complexity index which captures the structural richness of images with a wide range of typical scales, and compare several images with each other on the basis of this index.
In this sense, the proposed measure penalizes images where typical scales are limited to small lengths, of a few pixels –as in an image where gray levels are distributed at random– or to lengths similar to the image size –as when gray levels are ordered into a simple, broad pattern. Complexity is associated with diversity in those length scales.
We propose a complexity measure for black-and-white (B/W) digital images, based on the detection of typical length scales in the depicted motifs.
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