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首页> 外文期刊>Knowledge-Based Systems >Topological invariants can be used to quantify complexity in abstract paintings
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Topological invariants can be used to quantify complexity in abstract paintings

机译：拓扑不变性可用于量化抽象绘画中的复杂性

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The Abstract art screams of complexity: its visual language purposely creates complex images that are a distorted artist-driven vision of the real world. Complexity can be recognized from either the composition, form, color, brightness, among other aspects. In this paper we show that it is possible to objectively assess the complexity of abstract paintings by determining the values of the Betti numbers associated with the image. These quantities, which are topological invariants, capture the amount of connectivity and spatial distribution of the paint traces. We apply this analysis to a series of abstract paintings, demonstrating that the complexity of Jackson Pollock paintings produced by his famous dripping technique, is superior compared with many other abstract paintings by different authors. Opposed to what was previously discussed considering only fractal properties, the complexity does not simply increase with time; instead, it displays a local maximum at a certain year which coincides with the time when Pollock perfected his technique. This tool has been used before to measure complexity in other scientific areas, but not for art assessment. (C) 2017 Elsevier B.V. All rights reserved.
机译：抽象艺术惊叹于复杂性：它的视觉语言故意创建复杂的图像，这些图像是艺术家驱动的真实世界的扭曲视觉。可以从组成，形式，颜色，亮度以及其他方面来识别复杂性。在本文中，我们表明可以通过确定与图像相关的贝蒂数的值来客观地评估抽象绘画的复杂性。这些数量是拓扑不变量，它们捕获了油漆迹线的连通性和空间分布。我们将此分析应用于一系列抽象画中，证明了杰克逊·波洛克的著名滴灌技术所产生的复杂性要比不同作者的许多其他抽象画要优越。与先前讨论的仅考虑分形特性相反，复杂度并不会随时间增加。相反，它会显示某年的局部最大值，该最大值与Pollock完善其技术的时间相吻合。该工具以前曾用于测量其他科学领域的复杂性，但尚未用于艺术评估。 （C）2017 Elsevier B.V.保留所有权利。

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