Directional relative position between objects in image processing: a comparison between fuzzy approaches

Learning of fuzzy spatial relations between handwritten patterns

“…Objects shapes are even explicitly considered in the morphological method, and Bloch has shown that the resulting description better fit the intuition in comparison to other positioning descriptions based on histograms [BR03]. F-templates and morphological approach provide two different ways to build spatial templates, and Matsakis pointed out the equivalence of the two definitions under some conditions [MWN10].…”

Fuzzy and Bipolar Mathematical Morphology, Applications in Spatial Reasoning

“…As for the second type, the adequation between B and the fuzzy dilated region can be evaluated. Other fuzzy approaches to this type of relation are reviewed in [39]. This example also highlights another important issue, which concerns the representation, for which several forms can be interesting, depending on the raised question.…”

Using anatomical knowledge expressed as fuzzy constraints to segment the heart in CT images

“…In 3D (using spherical coordinates) the direction is represented by two angles, that are denoted by α 1 and α 2 (with α 1 ∈ [0, 2π[ and α 2 ∈ [−π/2, π/2], the 2D case corresponding to α 2 = 0) [29]. Given an axis of reference, say the x axis denoted by u x , for each pair of points (p 1 , p 2 ) with p 1 ∈ A 1 and p 2 ∈ A 2 , the angles between the axis and the segment joining these two points, − − → p 1 p 2 , are computed: α 2 is the angle between − − → p 1 p 2 and its projection on the x-y plane and α 1 is the angle between this projection and u x .…”