Qualitative similarity measures—The case of two-dimensional outlines
Introduction
In computer vision, similarity matching is frequently viewed as a matter of taking a number of measurements using quantitative reference systems: given two vectors (each one describing an image or a single object); we suppose that each vector consists of n attributes. Then, the question is how large their difference is. Similarity measures which are based on real valued attributes reflect how similar objects are along n quantitatively partitioned spectra, each of which comprises a metric on some particular granularity level. The similarity between objects, then, can be determined with corresponding precision. From what follows, we are concerned with the usual n-dimensional feature space.
One might ask whether precision is always that important; indeed, whether quantitative reference systems are to be taken at all; or, is there an alternative approach for the purpose of determining similarities in computer vision? The class of methods we advocate in this article, do in fact also pertain to methods at the feature space level—though, what distinguishes them is that they rely on differences in kind, rather than of measurement. According to Freksa [5], this means taking into account qualitative distinctions obtained by comparing features within the object domain rather than by measuring them in terms of some artificial external scale. In this sense, qualitative features are of a relative kind where the reference entity is a single value rather than a whole set of categories. For instance, in a scene we distinguish whether two points lie on the same side with respect to a line (the reference entity) or whether they lie on different sides: we focus on how features are altogether arranged, and we determine their ordering in the two-dimensional plane but omit any quantitative distinctions. As a consequence, a new category of appropriate similarity measures is required. From now on, we shall speak of measures only in the sense of those qualitative distinctions.
It is not our purpose to propose just any alternative class of similarity measures. Our concept of qualitative similarity measures distinguishes itself to be robust and efficient. However, we have to pay for it with imprecision. Interestingly, imprecise descriptions are frequently sufficient, and in particular, frequently related to the human’s visual system, who can comprehend such qualitative, imprecise features better than precise quantitative measurements (we are able to state whether two points lie on the same side of a line or not, but we are not able to state how far they are apart). This is where our method will be useful: either coarse descriptions are sufficient for our purposes, or features have to be provided which can be comprehended by the user.
In order to relate our method to the state of the art we shall finally compare it with a number of quantitative approaches. Since many methods have been devised in computer vision we have to select some of them; we do this by focusing on those methods which fall into the same complexity class (concerning the costs for the comparison of two-dimensional outlines). Also, there exist some qualitative methods which have been proposed over the last decade. These include Cohn [1], who describes a region-orientated technique that distinguishes different concave shapes by considering the notion of the connection of regions and their convex hulls; Schlieder [21], who introduced a point-oriented approach by describing how triples of vertices of a polygon are related relative to each other; Galton and Meathrel [6] proposed a representation of outlines by means of strings over an alphabet of seven qualitative curvature types. Eventually, the slope projection approach of Jungert [17] maps the vertices of polygons onto both the x-axis and the y-axis; depending on the ordering of vertices on these axes several features can be derived, for instance, whether a vertex forms a convex or concave part of a closed polygon. All these approaches characterise outlines qualitatively, as we will do below. They are detailed and discussed in the context of our method in [15]. It shows that opposed to quantitative approaches qualitative approaches can be easily compared on a conceptual level. This allows their representational expressiveness easily to be determined, and as a consequence, what features they are able to distinguish.
In Section 2 we shall motivate the employment of qualitative features by showing shape properties we are going to look at. Section 3 introduces our qualitative feature scheme. Sections 4.1 Scenario I, 4.2 Scenario II provide example applications which show the usefulness of qualitative similarity measures in different domains; Section 4.3 shows how the qualitative representation performs quite well in comparison to other well-known approaches. Section 5 analyses how stable the approach is, in particular when being faced with different degrees of precision, distortions, changes in viewpoint, and segmentation errors. Then, Section 6 defines the concept of qualitative similarity measures. We conclude with a discussion about granularity and complexity issues in Section 7.
Section snippets
Accessing qualitative features
The motivation for describing qualitative features of objects is as follows. Collections of objects d’art, historical tools, or natural objects such as in the geographic domain are some examples of collections to which experts want to access efficiently. Most notably, such collections show a number of objects from the same category, each exemplar showing specific details being typical for that exemplar. Frequently, the expert has the visual appearance of those specifics in mind. Therefore, a
A qualitative feature scheme
In this section we will summarise previous work on a qualitative feature scheme. It serves as an example approach to which we shall apply the more general notion of qualitative similarity measures. For the purpose of providing a manageable overview on how qualitative representations are defined and on how they are employed, we focus on the description of linear objects (open as well as closed objects) which can be approximated by polygons. Accordingly, our feature scheme consists of a number of
Applications
The following applications demonstrate:
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How to use the qualitative representation in a query-by-sketch system (using the basis relations and scopes and their extent, i.e. relations).
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How it shows to be useful in the geographic domain (employing the circulation direction and reversals, i.e. Gestalt features).
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How it performs regarding a well known test data set (applying scope histograms, i.e. frequency distributions).
All example applications especially show how well the qualitative description
Robustness
Having shown the application of the qualitative approach, the question arises as to how stable it is. This is important inasmuch deviations between polygons might exist although these polygons approximate the same object. This is due to noisy data or differently approximated outlines. In order to analyse how qualitative shape concepts behave under such circumstances we have to address a number of issues:
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The shapes are to be approximated with different degrees of precision for the purpose of
Qualitative similarity measures
What is the distinction between our concept of qualitative similarity measures (as applied in the previous sections) and the classical approach? Many methods have been devised most of which rely on similarity measures which are defined in some quantity space, as on the Cartesian coordinate system. Such metric-driven approaches use external reference systems which define an artificial scale relative to which objects are described [5]. By contrast, a qualitative approach allows objects to get
Discussion
In the first scenario it was sufficient and not difficult to find a number of appropriate properties to make the distinctions required, but this may well be more difficult in other domains. On the other hand, having modelled a domain by a number of such qualitative properties, according to our results, they form a robust set of features appropriate in a query-by-sketch system. This is similar in the geographic domain. However, the MPEG-test additionally shows that even the renunciation of
Acknowledgments
I thank Arne Schuldt for his contributions to the qualitative shape framework and for carrying out the MPEG-test. I should also like to thank the Bamberger Naturkundemuseum for making available the historical fruit collection and Mona Hess, Bamberg University, for taking the pictures of the fruits. Prof. Otthein Herzog gave me the opportunity to carry out the research. Eventually, I am grateful to the anonymous referees for a number of useful suggestions for improving this article.
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2013, Journal of Visual Communication and Image RepresentationCitation Excerpt :Approaches that calculate a similarity measure between quantitative shape descriptions are classified as using: (i) points of high curvature [15] or landmark points [16] in the shape contour; (ii) the matching of total or partial contours [17]; (iii) shape feature descriptor vectors [18]; (iv) shock graphs/trees [19,20], etc. Other approaches for qualitative shape comparison can be classified as calculating a similarity measure: (i) between qualitative descriptions based on bipartite arrangements for matching partial or total contours [21]; (ii) based on conceptual neighbourhood diagrams for comparing qualitative shape descriptions [22]; (iii) based on matrices of qualitative concepts for comparing polygons [23]; (iv) based on scope histograms for comparing polygons described qualitatively [24]. Moreover, in literature, colour similarity measures were defined mainly on numerical colour spaces, such as: (i) Euclidean distance for cubic spaces as RGB or CIE Lab and for cylindric spaces as L∗C∗H [25]; (ii) a cylindric distance for cylindric and conic spaces like HSL, HSV and L∗C∗H [26]; (iii) the Fuzzy C-Means for defining similarity measures for comparing fuzzy colour categories based on Musell colour space [27].
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2013, Knowledge Engineering ReviewStudy on Spatial Geometric Similarity Based on Conformal Geometric Algebra
2022, International Journal of Environmental Research and Public HealthA multilevel road alignment model for spatial-query-by-sketch
2020, Applied Sciences (Switzerland)Probabilistic reference and grounding with PRAGR for dialogues with robots
2016, Journal of Experimental and Theoretical Artificial Intelligence