论文标题
形状的复杂性嵌入$ {\ mathbb z^n} $中，偏向正方形
Complexity of Shapes Embedded in ${\mathbb Z^n}$ with a Bias Towards Squares
论文作者
论文摘要
形状复杂性是一种难以腾出的质量，这主要是由于其相对性质。由于欧几里得思想的偏见，圆圈通常被认为是最简单的。但是，它们作为数字图像的构造只是理想形式的近似值。因此，参考圆圈计算的复杂订单是不稳定的。与在数字图像中失去循环的圈子不同，正方形保持其质量。因此，我们认为正方形（$ \ Mathbb z^n $中的超级烟）是与构造复杂性订单的最简单形状。使用$ l^\ infty $ norm和正方形之间的连接，我们有效地编码了平方适应的简化，通过这些简化，我们获得了多尺度的复杂度度量，其中规模决定了边界的兴趣水平。边界特征（附属物）消失的效果的紧急尺度与附属物接触宽度与主体的接触宽度的比率有关。我们讨论了零复杂性在信息重复和结构性方面意味着什么以及除正方形以外的形状零复杂性。
Shape complexity is a hard-to-quantify quality, mainly due to its relative nature. Biased by Euclidean thinking, circles are commonly considered as the simplest. However, their constructions as digital images are only approximations to the ideal form. Consequently, complexity orders computed in reference to circle are unstable. Unlike circles which lose their circleness in digital images, squares retain their qualities. Hence, we consider squares (hypercubes in $\mathbb Z^n$) to be the simplest shapes relative to which complexity orders are constructed. Using the connection between $L^\infty$ norm and squares we effectively encode squareness-adapted simplification through which we obtain multi-scale complexity measure, where scale determines the level of interest to the boundary. The emergent scale above which the effect of a boundary feature (appendage) disappears is related to the ratio of the contacting width of the appendage to that of the main body. We discuss what zero complexity implies in terms of information repetition and constructibility and what kind of shapes in addition to squares have zero complexity.
