Space decomposition based on visible objects in an indoor environment

When a person moves, the set of objects in their visual range changes. Hence, the set of objects perceived from a specific range of locations may be considered as a signature (possibly non-unique) of this region and be used for the localization of this person. In the case of fixed objects, the number of regions with a set of specific visible objects is limited. A verbal description containing references to elements of this set of visible objects could then be used to localize a person in the space. This paper proposes an approach for decomposing a space into regions that are characterized by such sets of visible objects. In our approach, at least a portion of partial surfaces of an object must be visible (beyond single points) to make part of the signature. Our method calculates two-dimensional visibility polygons for a portion of an object’s surface. Overlaying these polygons, we partition the space in regions of visibility signatures. The approach has been implemented, and we demonstrate how to represent space by qualitative locations using these visibility signatures. We further show how this representation can be used to locate a person within a space by a set of visible objects.

Dynamic Algorithms for Visibility Polygons in Simple Polygons

We devise the following dynamic algorithms for both maintaining as well as querying for the visibility and weak visibility polygons amid vertex insertions and deletions to the simple polygon. A fully-dynamic algorithm for maintaining the visibility polygon of a fixed point located interior to the simple polygon amid vertex insertions and deletions to the simple polygon. The time complexity to update the visibility polygon of a point [Formula: see text] due to the insertion (resp. deletion) of vertex [Formula: see text] to (resp. from) the current simple polygon is expressed in terms of the number of combinatorial changes needed to the visibility polygon of [Formula: see text] due to the insertion (resp. deletion) of [Formula: see text]. An output-sensitive query algorithm to answer the visibility polygon query corresponding to any point [Formula: see text] in [Formula: see text] amid vertex insertions and deletions to the simple polygon. If [Formula: see text] is not exterior to the current simple polygon, then the visibility polygon of [Formula: see text] is computed. Otherwise, our algorithm outputs the visibility polygon corresponding to the exterior visibility of [Formula: see text]. An incremental algorithm to maintain the weak visibility polygon of a fixed-line segment located interior to the simple polygon amid vertex insertions to the simple polygon. The time complexity to update the weak visibility polygon of a line segment [Formula: see text] due to the insertion of vertex [Formula: see text] to the current simple polygon is expressed in terms of the sum of the number of combinatorial updates needed to the geodesic shortest path trees rooted at [Formula: see text] and [Formula: see text] due to the insertion of [Formula: see text]. An output-sensitive algorithm to compute the weak visibility polygon corresponding to any query line segment located interior to the simple polygon amid both the vertex insertions and deletions to the simple polygon. Each of these algorithms requires preprocessing the initial simple polygon. And, the algorithms that maintain the visibility polygon (resp. weak visibility polygon) compute the visibility polygon (resp. weak visibility polygon) with respect to the initial simple polygon during the preprocessing phase.