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Considering the distance to target object
The fuzzy landscape defined by Equation 2.10 is adequate when the size of the target object is comparable to the size of the concavity. However, when this is not the case, the obtained fuzzy landscape is not appropriate. For instance, if B is the reference object in Figure 2.6(a), A1 should have a high satisfaction degree for the relation surrounded, since there is a portion of the boundary of ∂B\∂CH(B) which goes around the object and which is close to it. On the contrary, intuitively, the object A2 should not have a high satisfaction degree of the relation surround. Even if there is a portion of the boundary of ∂B\∂CH(B) which goes around the object, some of the points belonging to this portion of boundary are so “far” from A2, that they are not considered visible from A2. The interpretation of “far” and “near” according to an object can depend on its intrinsic characteristic, for instance on its size [Hernandez et al., 1995].
The second and third columns of Table 2.1 show the results of evaluating the relation “surround by” using Equation 2.10. Both the [N,] and the M measures give similar results for A2 and A1, although, intuitively, A1 should better satisfy the relation since it is more inside the concavity of B (hence more surrounded).
Considerations for modeling alignment
Alignment can be defined as the spatial property possessed by a group of objects arranged in a straight line2. As it was highlighted by the Gestalt theory, alignment should be seen as a whole [Desolneux et al., 2008]: if we observe each element of the group individually, then the alignment property is lost. Having to look at it as a whole makes alignment detection a difficult task, since in order to detect an aligned group of objects we have to identify its members, but to know if an object belongs to an aligned group the alignment has to be already identified. In the following we study the different approaches to model alignment, and introduce the notions of local and global alignment.
Stability with respect to segmentation errors
One interesting feature of our approach is that it is robust to the quality of the segmentation of the objects. This property is particularly important in real applications where it is difficult to guarantee that all objects have been segmented and that the segmentation is accurate. Figure 2.22 shows two examples of the stability of the algorithm with respect to segmentation errors such as the absence of an object, or the merging of an undesired region to one of the objects. Figure 2.22(b) shows a segmentation of the houses of Figure 2.22(a), which is almost correct, except for some false detections and a missing house. Two of the aligned groups of objects extracted from this segmentation are shown in Figure2.22(c). Actually more groups are extracted by the algorithm but for the sake of clarity only a few groups are shown. Figure 2.22(d) shows another segmentation which was manually modified to introduce errors: two missing houses, and one of the houses is merged with other regions. Figure 2.22(e) shows two of the retrieved aligned groups, which correspond to the groups found in Figure2.22(c). We can see that the blue group in Figure 2.22(e) is retrieved even with the absence of two objects, and that the orange group is retrieved although the center of mass of one of its members has been displaced.
For this example we used a Voronoi neighborhood constrained by a distance d, where d was larger than the separation between the objects. However, if we had used a smaller distance, then the algorithm would not have retrieved the blue group, since there would have been a disconnection between the upper and the lower part of the blue group of Figure 2.22(e), and therefore only the lower part of the group would have been retrieved. This is an expected behavior.
Parallelism with a globally aligned group of objects
When considering parallelism with a globally aligned group of objects, the group has a similar role as the linear object in the definitions introduced in the previous section. When defining the relation with a group there is a modification, with respect to the case of a linear object, in the way the visibility constraint is computed, this modification will be discussed in the following.
Table of contents :
Résumé des travaux
Introduction
I Spatial representations and reasoning
1 Spatial relations for satellite image interpretation: state of the art
1.1 Cognitive aspects of spatial representations
1.2 Classification of spatial relations
1.3 The set of relations
1.3.1 Topological relations
1.3.2 Metric relations
1.3.3 Structural relations
1.4 Conclusion
2 New spatial relations
2.1 Surround
2.1.1 Related work
2.1.2 Definition of surroundedness as a fuzzy landscape
2.1.3 Properties
2.1.4 Computational complexity
2.1.5 Illustrative example
2.1.6 Discussion
2.2 Alignment
2.2.1 Related work
2.2.2 Considerations for modeling alignment
2.2.3 Definition and identification of aligned groups of objects
2.2.4 Stability with respect to segmentation errors
2.2.5 Complexity analysis
2.2.6 Discussion
2.3 Parallelism
2.3.1 Considerations
2.3.2 Related work
2.3.3 Parallelism with (fuzzy) linear objects
2.3.4 Properties
2.3.5 Parallelism with a globally aligned group of objects
2.3.6 Discussion
2.4 Line-region relations
2.4.1 Set of line-region relations
2.4.2 Go Across
2.4.3 “Enter”
2.4.4 Illustrative example
2.4.5 Comments about “along” and “go around”
2.4.6 Discussion
2.5 Conclusion
3 Spatial reasoning
3.1 Qualitative spatial reasoning (QSR)
3.2 Reasoning with fuzzy spatial relations based on fusion operators
3.3 Illustrative examples: Spatial reasoning for object recognition
3.4 Conclusion
II Satellite image interpretation
4 Knowledge based image interpretation: an overview
4.1 Introduction
4.2 Knowledge based systems (KBS)
4.2.1 Knowledge representation schemes
4.2.2 Sources and types of information imperfections
4.2.3 Reasoning under imperfections
4.3 Discussion
4.4 Conclusion
5 A new mapping approach for satellite image interpretation using a structural model
5.1 Structural model representation
5.1.1 Choice of the representation framework: conceptual graphs vs. description logics
5.1.2 Nested conceptual graphs
5.1.3 Vocabulary
5.2 Mapping a conceptual graph to an image: general principle
5.3 Simple case
5.3.1 Constraint Satisfaction Problems (CSP)
5.3.2 Illustration
5.3.3 Discussion
5.4 Including fuzzy spatial relations
5.4.1 Fuzzy constraint satisfaction problems (FCSP)
5.4.2 Dealing with alignments
5.4.3 Dealing with groups (not necessarily aligned)
5.4.4 Proposed algorithm
5.4.5 Complexity and improvements
5.4.6 Finding a solution
5.4.7 Discussion
5.5 Interpreting an unlabeled image
5.5.1 Image partition
5.5.2 Region labeling
5.5.3 Spatial reasoning over the tree of regions
5.5.4 Finding a solution
5.5.5 Results
5.6 Towards the introduction of priorities and uncertainties
5.7 Conclusion
6 Conclusion
6.1 Main contributions
6.1.1 Novel definitions of spatial relations
6.1.2 Spatial reasoning and image interpretation guided by a model
6.2 Perspectives
6.2.1 Short-term perspectives
6.2.2 Long-term perspectives
Notations
A List of publications
Bibliography
