Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects

Abstract

The analysis of spatial relations between objects in digital images plays a crucial role in various application domains related to pattern recognition and computer vision. Classical models for the evaluation of such relations are usually sufficient for the handling of simple objects, but can lead to ambiguous results in more complex situations. In this article, we investigate the modeling of spatial configurations where the objects can be imbricated in each other. We formalize this notion with the term enlacement, from which we also derive the term interlacement, denoting a mutual enlacement of two objects. Our main contribution is the proposition of new relative position descriptors designed to capture the enlacement and interlacement between two-dimensional objects. These descriptors take the form of circular histograms allowing to characterize spatial configurations with directional granularity, and they highlight useful invariance properties for typical image understanding applications. We also show how these descriptors can be used to evaluate different complex spatial relations, such as the surrounding of objects. Experimental results obtained in the different application domains of medical imaging, document image analysis and remote sensing, confirm the genericity of this approach.

Learning Fuzzy Relations and Properties for Explainable Artificial Intelligence

“…Vanegas Orozco [7] worked on geometrical relations such as the parallelism and the alignment between fuzzy regions. Clément et al [16] proposed new fuzzy spatial relations representing objects imbricated in each other. Colliot et al [8] studied the symmetry of fuzzy objects and proposed a measure that defines the degree of symmetry of an object with respect to a given plane.…”

Local Enlacement Histograms for Historical Drop Caps Style Recognition

“…These works illustrated the interest of considering spatial relations descriptors into the bags-of-features framework. A new relative position descriptor was recently proposed in [13], and illustrated notably the interest of considering enlacement and interlacement configurations to classify the style of drop caps images. However, the descriptors were applied globally on the whole images, which does not allow to capture distinctive patterns depicted in drop caps at a more local scale.…”

“…We briefly present the model used to describe the relative enlacement of objects, which was initially introduced in [13].…”

“…) represents to which degree A is enlaced by B along the oriented line ∆ (θ,ρ) . For crisp objects (i.e., each point is either 0 or 1), this corresponds to the total number of ordered triplets of points (b i , a k , b j ), i < k < j, which can be seen as arguments to put in favor of the proposition "A is enlaced by B" in direction θ. Algorithmically, this value can be derived by an appropriate distribution of segments lengths along the longitudinal cuts of both objects (see [13] for more details).…”

Fuzzy directional enlacement landscapes for the evaluation of complex spatial relations

“…To better formalize these complex spatial configurations, a new spatial relation called "enlacement" was recently introduced in [3]. In this work, the latter is defined as a generalization of spatial configurations where an arbitrary, potentially complex object surrounds or squeezes another object.…”