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. 2021 May 12;11:10074. doi: 10.1038/s41598-021-89277-2

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Boundaries without luminance step edges. (a) A luminance step boundary (LSB) and a simple detection model in which a linear Gabor filter measures the regional luminance difference. (b) Model similar to that in (a) where the LSB is analyzed by multiple Gabor filters at varying spatial scales. (c) Example of luminance texture boundary (LTB). The luminance difference is defined by differing proportions of black and white micropatterns on each side of the boundary, with no sharp luminance change at the boundary. (d) Two juxtaposed textures from the Brodatz database. Although there is clearly a regional difference in luminance, there is no sharp luminance change at the boundary.