Quantifying the complexity of black-and-white images

Area of Science:

• Image analysis
• Computational imaging
• Data science

Background:

• Quantifying image complexity is challenging, often relying on subjective visual assessment.
• Existing methods may not fully capture the structural richness or diversity of patterns within an image.

Purpose of the Study:

• To propose an objective complexity measure for black-and-white (B/W) digital images.
• To introduce a complexity index based on the diversity of typical length scales.
• To demonstrate the index's utility in analyzing complex data, such as topographical features.

Main Methods:

• Developed a complexity measure based on detecting typical length scales of motifs in B/W images.
• Introduced a complexity index that quantifies structural richness by considering a wide range of typical scales.
• Applied the complexity index to a topographical elevation dataset of South America.

Main Results:

• The proposed complexity index objectively quantifies image complexity, penalizing images with limited scale diversity.
• The index successfully identified intricate topographical features, including river drainage networks and fjord-like coastlines.
• The measure demonstrated effectiveness in revealing structural richness in complex datasets.

Conclusions:

• The developed complexity index provides an objective measure of structural richness in images.
• This objective measure can serve as a counterpart to subjective visual complexity in perception research.
• The complexity quantification method is adaptable to various data types beyond images, including time signals and distributions.