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Relative Position Descriptors - A Review
Abstract
A relative position descriptor is a quantitative representation of the relative position of two spatial objects. It is a low-level image descriptor, like colour, texture, and shape descriptors. A good amount of work has been carried out on relative position description. Application areas include content-based image retrieval, remote sensing, medical imaging, robot navigation, and geographic information systems. This paper reviews the existing work. It identifies the approaches that have been used as well as the properties that can be expected from relative position descriptors. It compares and provides a brief overview of various descriptors, including their main properties, strengths and limitations, and it suggests areas for future work.
In the paper, a method for image search is proposed. It allows for finding images starting from a text query that contains names of object classes and their expected spatial relations. The input query containing the description of desired objects and their spatial relations is used to select and score relevant images. Next, the score is used to sort the output images putting more relevant ones on the top of the list. The proposed approach is based on object detection methods and a fuzzy approach describing the position of detected objects in relation to other ones. The method may be used to retrieve images from databases containing images with metadata produced by object detectors.
A major challenge in scene understanding is the handling of spatial relations between objects or object parts. Several descriptors dedicated to this task already exist, such as the force histogram which is a typical example of relative position descriptor. By computing the interaction between two objects for a given force in all the directions, it gives a good overview of the configuration, and it has useful properties that can make it invariant to the 2D viewpoint. Considering that using complementary forces (negative for repulsion, positive for attraction) should improve the description of complex spatial configurations, we propose to extend the force histogram to a panel of forces so as to make it a more complete descriptor. This gives a 2D descriptor that we called “(discrete) Force Banner” and which can be used as input of a classical Convolutional Neural Network (CNN), benefiting from their powerful performances, and reduced into more compact spatial features to use them in another system. As an illustration of its ability to describe spatial configurations, we used it to solve a classification problem aiming to discriminate simple spatial relations, but with variable configuration complexities. Experimental results obtained on datasets of synthetic and natural images with various shapes highlight the interest of this approach, in particular for complex spatial configurations.
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.
Fuzziness is found everywhere, in modeling spatial relations, fuzziness is found at object level as well as in relation semantics. Commonly, fuzzy topological relations are computed between fuzzy objects. Fuzziness in relation semantics is represented by fuzzy topological relations between crisp objects and these types of fuzzy topological relations are much less developed. In this paper, we propose a method for combining fuzzy topological and directional relations. We also propose an algorithm for defuzzification of relations which provides us a binary topological and directional relation between a 2D object pair. These relations are represented in a neighborhood graph. For validation and assessment, a number of experiments have been performed on artificial data.
A novel shape descriptor, named as ratio histograms (R-histogram), is proposed to represent the relative attitude relationship between two independent shapes. For a pair of two shapes, the shapes are treated as the longitudinal segments parallel to the line connecting centroids of the two shapes, and the R-histogram is composed of the length ratios of collinear longitudinal segments. R-histogram is theoretically affine invariant due to collinear distance invariance of the affine transformation. In addition, as the computation of the length ratio weakens the noise contribution, R-histogram is robust to noise. Based on the R-histogram, the shape-matching algorithm includes two major phases: preprocessing and matching. The first phase, which can be processed off-line, is trying to obtain the R-histograms of all original shape pairs. In the second phase, for each transformed shape pair, its R-histogram is computed and the candidate matched shape pair with minimal R-histogram matching error is found. Subsequently, a voting strategy, which further improves the accuracy of shape matching, is adopted for the candidate corresponding shape pairs. Experimental results demonstrate that the proposed R-histogram is robust and efficient.
In conversation, people often use spatial relationships to describe their environment, e.g., "There is a desk in front of me and a doorway behind it," and to issue directives, e.g., "go around the desk and through the doorway." In our research, we have been investigating the use of spatial relationships to establish a natural communication mechanism between people and robots, in particular, for novice users. In this paper, the work on robot spatial relationships is combined with a multimodal robot interface. We show how linguistic spatial descriptions and other spatial information can be extracted from an evidence grid map and how this information can be used in a natural, human-robot dialog. Examples using spatial language are included for both robot-to-human feedback and also human-to-robot commands. We also discuss some linguistic consequences in the semantic representations of spatial and locative information based on this work.
Searching for relevant knowledge across heterogeneous geospatial databases requires an extensive knowledge of the semantic meaning of images, a keen eye for visual patterns, and efficient strategies for collecting and analyzing data with minimal human intervention. In this paper, we present our recently developed content-based multimodal Geospatial Information Retrieval and Indexing System (GeoIRIS) which includes automatic feature extraction, visual content mining from large-scale image databases, and high-dimensional database indexing for fast retrieval. Using these underpinnings, we have developed techniques for complex queries that merge information from heterogeneous geospatial databases, retrievals of objects based on shape and visual characteristics, analysis of multiobject relationships for the retrieval of objects in specific spatial configurations, and semantic models to link low-level image features with high-level visual descriptors. GeoIRIS brings this diverse set of technologies together into a coherent system with an aim of allowing image analysts to more rapidly identify relevant imagery. GeoIRIS is able to answer analysts' questions in seconds, such as "given a query image, show me database satellite images that have similar objects and spatial relationship that are within a certain radius of a landmark."
. This paper surveys the work of the qualitative spatial reasoning group at the University of Leeds. The group has developed a number of logical calculi for representing and reasoning with qualitative spatial relations over regions. We motivate the use of regions as the primary spatial entity and show how a rich language can be built up from surprisingly few primitives. This language can distinguish between convex and a variety of concave shapes and there is also an extension which handles regions with uncertain boundaries. We also present a variety of reasoning techniques, both for static and dynamic situations. A number of possible application areas are briefly mentioned. Keywords: qualitative spatial reasoning, spatial logics, topology, shape, vague boundaries 1. Introduction Qualitative Reasoning (QR) has now become a mature subfield of AI as its tenth annual international workshop, several books (e.g. (Weld and De Kleer 1990, Faltings and Struss 1992)) and a wealth of conference...
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.
In this paper, we present an approach for modeling and comparing small sets of 2-D objects based on their spatial relationships. This situation can arise in the conflation of a hand- or machine-drafted map to a satellite image, or in the correspondence problem of matching two images taken under different viewing conditions. We focus on the specific problem of matching a sketched map containing several 2-D objects to hand-segmented satellite imagery. We define a similarity measure between the spatial configurations of two object sets, which uses attributed relational graphs to represent scene information. Objects are represented as graph nodes and edges are defined by the histograms of forces between object pairs. We develop a memetic algorithm based on a (μ+λ) evolution strategy to solve this scene-matching problem with three domain-specific local search operators that are compared experimentally.
The importance of topological and directional relationships between spatial objects has been stressed in different fields, notably in Geographic Information Systems (GIS). In an earlier work, we introduced the notion of the F-histogram, a generic quantitative representation of the relative position between two 2D objects, and showed that it can be of great use in understanding the spatial organization of regions in images. Here, we illustrate that the F-histogram constitutes a valuable tool for extracting directional and topological relationship information. The considered objects are not necessarily convex and their geometry is not approximated through, e.g., Minimum Bounding Rectangles (MBRs). The F-histograms introduced in this chapter are coupled with Allen’s temporal relationships based on fuzzy set theory. Allen’s relationships are commonly extended into the spatial domain for GIS purposes, and fuzzy set theoretic approaches are widely used to handle imprecision and achieve robustness in spatial analysis. For any direction in the plane, the F-histograms define a fuzzy 13-partition of the set of all object pairs, and each class of the partition corresponds to an Allen relation. Lots of directional and topological relationship information as well as different levels of refinements can be easily obtained from this approach, in a computationally tractable way. Keywords. F-histograms, Allen relations, spatial relations, spatial analysis, Geographic
In this paper, we introduce a system able to generate an intuitive, human-like linguistic description of the topological relationships between two objects. The description includes approximate terms commonly found in daily communications. It attempts to capture the essential characteristics of the relationships, while leaving out superfluous and possibly overwhelming detail. The objects are 2-D image objects. They need not be convex, nor connected, and they may have holes in them. Each description is built around Allen relations, based on information extracted from F-histograms. It consists of a topological component that indicates the primary topological relationships, directional estimates of where these relationships are most prominent, and a self-assessment component which reflects the complexity of the situation. Experiments on synthetic and real data validate the approach.
Object recognition and scene analysis tasks can be greatly enhanced when information about spatial organization in an image is available. Moreover, for recognition of complex objects a suitable representation of spatial relations between objects' components taking into account shape, size, orientation, etc., is required. This cannot be accomplished by reducing a region to one or a few representative points; instead the region as a whole must be treated.This paper presents a fuzzy logic approach to the representation and recognition of spatial relations between regions in a 2D image. The main source of information on spatial relations is the geometry of the regions in question and we argue that this is complex enough to cause ambiguity in spatial relations, and hence to warrant a fuzzy logic approach. The basic idea is to calculate the angles between the line connecting two points (one in each region) and the horizontal line, to construct a histogram of these angles, and then upon an interpretation of the histogram as a fuzzy set to match it with the fuzzy sets representing a vocabulary of spatial relations. Other expressions of the spatial information which may be context dependent can be easily obtained by adding context knowledge. Several examples are used to illustrate our approach.
A general approach to the evaluation of parameters from fuzzy regions is outlined. The main idea is to consider a fuzzy subset of an images as the nested family of its level-cuts, interpret this family as a body of evidence in the sense of Shafer. Any intrinsic parameter can then be calculated as a mathematical expectation based on a probability density function. Fuzzy-valued parameters can also be derived. The approach encompasses recent proposals by Rosenfeld for specific parameters such as perimeter, diameter, etc., as well as the cardinality of a fuzzy set. It is also extended to relational parameters between fuzzy regions in the image.
In spatial reasoning, relationships between spatial entities play a major role. In image interpretation, computer vision and structural recognition, the management of imperfect information and of imprecision constitutes a key point. This calls for the framework of fuzzy sets, which exhibits nice features to represent spatial imprecision at different levels, imprecision in knowledge and knowledge representation, and which provides powerful tools for fusion, decision-making and reasoning. In this paper, we review the main fuzzy approaches for defining spatial relationships including topological (set relationships, adjacency) and metrical relations (distances, directional relative position).
Representation of relative spatial relations between objects is often required in many multimedia database applications because spatial relations between objects in an image convey important information about the image. Quantitative representation of spatial relations taking into account shape, size, orientation and distance is often required. The R-Histogram is such a quantitative representation of spatial relations between two objects. However, this method only considers pixels on the object boundary, assuming that the objects are homeomorphic to a 2-ball. For objects with more complicated topology, we propose in this paper the R*-Histogram, a new extension to the R-Histogram. The R*-Histogram generalizes the R-Histogram by taking into account all the pixels in the objects. We also introduce an efficient O(kN log N) time algorithm to compute the R*-Histogram, which is asymptotically faster than the original O(N2) time algorithm for the R-Histogram even when k=O(n). Here, N=n2 denotes the number of pixels in the processed n x n image and k is the number of different directions considered. The effectiveness of the R*-Histogram is evaluated empirically with a Query By Example (QBE) system on a database of 2000 synthetic images containing objects with complicated shape and topology. Experiments have shown that the similarly search results match human intuition very well.
Representation of relative spatial relations between objects is required in many multimedia database applications. Quantitative representation of spatial relations taking into account shape, size, orientation and distance is often required. This cannot be accomplished by assimilating an object to elementary entities such as the centroid or the minimum bounding rectangle. Thus many authors have proposed numerous representations based on the notion of histograms of angles. However, they can only represent directional relations, but not the topological spatial relations "inside" and "overlap." Moreover, distance information is not explicitly taken into account. To address these issues, we propose in this paper a new histogram representation called R-Histogram that extends the histogram of angles by incorporating both angles and labeled distances. Dissimilarity between images is then defined by the distance between corresponding R-Histograms. A prototype Query By Example (QBE) system using the R-Histogram has been implemented. The effectiveness of our algorithm is demonstrated with experiments on two databases of 2000 synthetic images.
Concept of combined extraction of topological and directional relations information developed by Zahzah et al. [1] by employing the Allen's temporal relations in 1D spatial domain was improved by Matsakis and Nikitenko [2]. This latter algorithm has high computational complexity due to its limitations of object approximation and segment fuzzification.In this paper, fuzzy Allen relations are used to define the fuzzy topological and directional relations information between different objects. Some extended results of Salamat and Zahzah [3] are discussed. Polygonal object approximation allows us to use fuzzy operators and this approach reduces computational complexity of the method for computing the combined topological and directional relations. To validate the method, some experiments are tested giving satisfactory and promising results. Affine transformation are depicted, these properties will be helpful for using the method in other areas of image analysis such as object tracking.
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