A General Approach to the Fuzzy Modeling of Spatial Relationships

Efficient computation of objects' spatial relations in digital images

“…Also note that different types of forces can actually be considered. The force histograms calculated in Section 4 are constant force histograms [3] [4].…”

Learning of fuzzy spatial relations between handwritten patterns

“…For instance, an F-template can describe the relation to be in direction α from R, where R is a reference object. A F-template is a type of model that can be used for localization of objects, since it is directly defined in the image space [MWN10] and only requires a reference object. The duality of Fhistograms and F-templates concepts has not been fully investigated yet, and no direct transformation is possible from one to the other, but these works constitute an interesting step toward unified models for evaluation and localization tasks.…”

“…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]. Spatial templates effectively handle the localization task, since they are defined directly in the image space and only require the definition of one reference object.…”

“…This concept matches the notion of spatial template referred to by Matsakis et. al [MWN10]. Intuitively, a fuzzy landscape can be seen as a map (think of a distance map, or a direction map) which associates to every point of the plane a degree of truth with respect to the relation described, and the chosen reference object.…”

“…In previous work, we highlighted the benefits of considering shape variations when describing relative positioning, in the context of handwritten recognition [BMA06]. The main contribution of this work is to introduce trainable models of spatial relations that can address the two important tasks related to spatial analysis of structured expressions, namely the evaluation task and the localization task [MWN10]:…”