Genericity of dimension drop on self-affine sets
نویسندگان
چکیده
منابع مشابه
Genericity of Dimension Drop on Self-affine Sets
We prove that generically, for a self-affine set in R, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.
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Self-affine maps were successfully used for edge detection, image segmentation, and contour extraction. They belong to the general category of patch-based methods. Particularly, each self-affine map is defined by one pair of patches in the image domain. By minimizing the difference between these patches, the optimal translation vector of the self-affine map is obtained. Almost all image process...
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ژورنال
عنوان ژورنال: Statistics & Probability Letters
سال: 2017
ISSN: 0167-7152
DOI: 10.1016/j.spl.2017.02.028