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The principles of similarity and proximity often work together to form a Visual Hierarchy. Either principle can dominate the other, depending on the application and combination of the two. For example, in the grid to the left, the similarity principle dominates the proximity principle; the rows are probably seen before the columns.
From a spatial point of view, nearness (a.k.a. proximity) is considered a generalization of set intersection.For disjoint sets, a form of nearness set intersection is defined in terms of a set of objects (extracted from disjoint sets) that have similar features within some tolerance (see, e.g., §3 in).
Contour completion occurs in accordance with the Gestalt laws of grouping: similarity, closure, figure-ground, continuity and proximity. The automatic utilisation of Gestalt laws allows us to perceive these objects as separate, but does not provide a fully completed image of the occluded stimulus.
The Law of Similarity is employed by selecting similar map symbols for similar kinds of features or features with similar properties; the Law of Proximity is crucial to identifying geographic patterns and regions; and the Laws of Closure and Continuity allow users to recognize features that may be obscured by other features (such as when a road ...
Closeness is a basic concept in topology and related areas in mathematics.Intuitively, we say two sets are close if they are arbitrarily near to each other. The concept can be defined naturally in a metric space where a notion of distance between elements of the space is defined, but it can be generalized to topological spaces where we have no concrete way to measure distances.
For example, spaces are symmetric. The distance between two points is the same regardless of which point you start from. However, psychological similarity is not symmetric. For example, we often prefer to state similarity in one direction. For example, it feels more natural to say that 101 is like 100 than to say that 100 is like 101.
Triadic closure is a concept in social network theory, first suggested by German sociologist Georg Simmel in his 1908 book Soziologie [Sociology: Investigations on the Forms of Sociation]. [1] Triadic closure is the property among three nodes A, B, and C (representing people, for instance), that if the connections A-B and A-C exist, there is a ...
Abstract closure or interior operators can be used to define a generalized topology on the lattice. Since neither unions nor the empty set appear in the requirement for a Moore closure operator, the definition may be adapted to define an abstract unary operator : on an arbitrary poset.