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Efficient computation of objects' spatial relations in digital images
Abstract
Both quantitative and qualitative measures of directional spatial relationships (e.g., left, right, above) between two raster objects in a digital image are important for high-level computer vision tasks such as scene analysis and robot navigation. The histogram of forces can provide such measures, but cannot be computed in real-time. A new approach for real-time computation, based on a vector representation of raster objects, is presented. The performance of the proposed approach is examined in an extensive experiment. Considering processing time and accuracy, optimal assessments of directional spatial relationships for use in real-time applications can be obtained.
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This chapter discusses an integrated work in the definition and implementation of sets of fuzzy spatial relationships concerning topology and direction. We present our basic approach to defining these relationships as an extension to previous work in temporal relations. We also discuss several extensions to this approach that include refinements and alternate definitions. Two implementations are also described, one in a C++, Oracle database environment and another utilizing the expert system shell Fuzzy Clips. Finally we discuss the integration of this querying approach in an agent-based framework. Agent technology has become a leading implementation paradigm for distributed and complex systems, and has recently garnered much interest from researchers in the area of spatial databases. Agents offer many advantages with respect to intelligence abilities and mobility that can provide solutions for issues related to uncertainty in spatial data, such as those of spatial relationships.
Information describing the layout of objects in space is commonly conveyed through the use of linguistic terms denoting spatial relations that hold between the objects. Though progress has been made in the understanding and modelling of many individual relations, a better understanding of how human subjects use spatial relations together in natural language to is required. This paper outlines the design and completion of an experiment resulting in the collection of 1920 spoken descriptions from 32 human subjects; they describe the relative positions of a variety of objects within an image space. We investigate the spatial relations that the subjects express in their descriptions, and the terms through which they do so, in an effort to determine variations and commonalities. Analysis of the descriptions determines that common elements of spatial perception do indeed exist between subjects, and that the subjects are quite consistent with each other in the use of spatial relations.
The histogram of forces is a generic relative position descriptor with remarkable properties, and it has found many applications, in various domains. So far, however, the applications involve objects in raster form. The fact is that several general algorithms for the computation of force histograms when dealing with such objects have been developed; on the other hand, there is no general algorithm available for objects in vector form, and the algorithms for raster objects cannot be adapted to vector objects. Here, the first general algorithm for calculating force histograms using vector data is presented.
The purpose of this paper is twofold. Firstly, we would like to comment on the study of similarity measures carried out by Pappis and Karacapilidis (1993). Their definition of ‘approximate equality’ of fuzzy sets is modified and relevant properties related to this correlated definition are listed. Secondly, a new class of similarity measures, extracted from the work of Bandler and Kohout (1980) on fuzzy power sets, is presented. The properties of the concept of approximate equality corresponding to these similarity measures are discussed, and involve a study of implication operators.
How to satisfactorily model spatial relationships between 2D or 3D objects? If the objects are far enough from each other,
they can be approximated by their centers. If they are not too far, not too close, they can be approximated by their minimum
bounding rectangles or boxes. If they are close, no such simplifying approximation should be made. Two concepts are at the
core of the approach described in this paper: the concept of the F\mathcal{F}-histogram and that of the F\mathcal{F}-template. The basis of the former was laid a decade ago; since then, it has naturally evolved and matured. The latter is
much newer, and has dual characteristics. Our aim here is to present a snapshot of these concepts and of their applications.
It is to highlight (and reflect on) their duality–a duality that calls for a clear distinction between the terms spatial relationship,
relationship to a reference object, and relative position. Finally, it is to identify directions for future research.
The relative position between two 2-D spatial regions is often represented quantitatively by a force histogram. In the case of raster data, force histograms are usually computed in O(KN√N) time, where N is the number of pixels in the image and K is the number of directions in which forces are considered. When the regions are defined as fuzzy sets instead of crisp sets, the complexity also depends on the number M of possible membership degrees. In this paper, we show that the force histogram can be defined in a completely different but equivalent way, one which leads to an O(NlogN) algorithm, with complexity independent of K and M. Moreover, the equivalent definition is better adapted to the solving of theoretical issues. We use it here to determine the behavior of the force histogram towards any invertible affine transformation.
In 3D image data sets generated by voxel-based classification, each voxel is marked with a specific class label. Voxels of the same class label can form 3D objects of extremely complex shape. Interactively drawn regions are usually represented by their 2D region borders. In order to combine automatically classified with interactively drawn regions, a contour tracing and coding algorithm for generating optimized 2D contours from 3D classified objects is presented. A special conversion algorithm allows a chain or a crack code representation. An application to medical images shows the method's necessity and usefulness in dealing with highly complex regions.
Fuzzy set methods have been used to model and manage uncertainty in various aspects of image processing, pattern recognition, and computer vision. High-level computer vision applications hold a great potential for fuzzy set theory because of its links to natural language. Linguistic scene description, a language-based interpretation of regions and their relationships, is one such application that is starting to bear the fruits of fuzzy set theoretic involvement. In this paper, we are expanding on two earlier endeavors. We introduce new families of fuzzy directional relations that rely on the computation of histograms of forces. These families preserve important relative position properties. They provide inputs to a fuzzy rule base that produces logical linguistic descriptions along with assessments as to the validity of the descriptions. Each linguistic output uses hedges from a dictionary of about 30 adverbs and other terms that can be tailored to individual users. Excellent results from several synthetic and real image examples show the applicability of this approach.
The fuzzy qualitative evaluation of directional spatial
relationships (such as “to the right of”, “to the
south of...”) between areal objects often relies on the
computation of a histogram of angles, which is considered to provide a
good representation of the relative position of an object with regard to
another. In this paper, the notion of the histogram of forces is
introduced. It generalizes and may supersede the histogram of angles.
The objects (2D entities) are handled as longitudinal sections (1D
entities), not as points (OD entities). It is thus possible to fully
benefit from the power of integral calculus and, so, ensure rapid
processing of raster data, as well as of vector data, explicitly
considering both angular and metric information