Directional relationships to a reference object: A quantitative approach based on force fields

Abstract

A directional map (or spatial template, fuzzy landscape) is an image where the value of each pixel represents the degree to which the pixel satisfies some directional relationship (e.g., right, left, above, below) to some reference object (i.e., a given set of pixels). There exists a simple quantitative model of such relationships, and the computation of directional maps is usually based on algorithmic implementations of this model. We show here that the model has important flaws, and we respond to the issue with a new, promising approach: all directional maps induced by the reference object are generated from a force field that the object (which is seen as a physical entity) creates around itself. Preliminary experiments illustrate and show the interest of the approach.

SIMD-based Exact Parallel Fuzzy Dilation Operator for Fast Computing of Fuzzy Spatial Relations

“…However, the standard fuzzy morphological dilation is computationally expensive and thus only approximate methods have been proposed [3,23] to compute it efficiently. Besides, force-fields methods have been proposed for directional relations [16,12] but they do not have the same properties and are not as generic as fuzzy-dilation-based methods.…”

“…multi-core and SIMD properties of modern processors. The fuzzy dilation generates a fuzzy landscape [3] (also known as directional map [16] or spatial template [23]). In a fuzzy landscape, the value of each pixel represents to what extent it verifies the relation under study, as shown in Fig.…”