标题： 数字$n-$流形 有边界或无边界 显示英文标题

标题： Digital $n-$Manifolds With Or Without Boundaries

摘要： 本工作旨在将流形的概念在数字图像上进行定义，该概念在拓扑学中占有非常重要的地位。 因此，为数字曲线和数字表面的二维和三维成像研究提供了总体视角。 在整个研究过程中，特别强调了在拓扑流形中存在的特征，但在离散版本中不满足的特征。 此外，还讨论了与流形密切相关的其他概念，如子流形、定向和单位分解。 显示英文摘要

摘要： This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital surfaces. Throughout the study, the features present in topological manifolds but that are not satisfied in the discrete version are specifically underlined. In addition, other concepts closely related to manifolds such as submanifold, orientation, and partition of unity are also discussed in digital images.