Abstract
This paper introduces our qualitative shape representation formalism that is devised to overcome, as we have argued, the class abstraction problems created by numeric schemes. The numeric shape representation method used in conventional geometric modeling systems reveals difficulties in several aspects of architectural designing. Firstly, numeric schemes strongly require complete and detailed information for any simple task of object modeling. This requirement of information completeness makes it hard to apply numeric schemes to shapes in sketch level drawings that are characteristically ambiguous and have non-specific limitations on shape descriptions. Secondly, Cartesian coordinate-based quantitative shape representation schemes show restrictions in the task of shape comparison and classification that are inevitably involved in abstract concepts related to shape characteristics. One of the reasons why quantitative schemes are difficult to apply to the abstraction of individual shape information into its classes and categories is the uniqueness property, meaning that an individual description in a quantitative scheme should refer to only one object in the domain of representation. A class representation, however, should be able to indicate not only one but also a group of objects sharing common characteristics. Thirdly, it is difficult or inefficient to apply numeric shape representation schemes based on the Cartesian coordinate system to preliminary shape analysis and modeling tasks because of their emphasis on issues, such as detail, completeness, uniqueness and individuality, which can only be accessed in the final stages of designing. Therefore, we face the need for alternative shape representation schemes that can handle class representation of objects in order to manage the shapes in the early stages of designing. We consider shape as a boundary description consisting of a set of connected and closed lines. Moreover, we need to consider non-numeric approaches to overcome the problems caused by quantitative representation approaches.This paper introduces a qualitative approach to shape representation that is contrasted to conventional numeric techniques. This research is motivated by ideas and methodologies from related studies such as in qualitative formalism ([4], [6], [19], [13], [31]), qualitative abstraction [16], qualitative vector algebra ([7], [32]), qualitative shapes ([18], [23], [21]), and coding theory ([20], [25], [26], [1], [2], [3], [22]). We develop a qualitative shape representation scheme by adopting propitious aspects of the above techniques to suit the need for our shape comparison and analysis tasks. The qualitative shape-encoding scheme converts shapes into systematically constructed qualitative symbols called Q-codes. This paper explains how the Q-code scheme is developed and applied.
Highlights
This paper introduces our qualitative shape representation formalism that is devised to overcome, as we have argued, the class abstraction problems created by numeric schemes
When we look at a complex image, we do not see every detail of the shape in order to recognize the image, but we see and identify the characteristic features and particular configurations and register them in our memory [30]
The Q-code scheme looks at a shape and encodes only shape characteristics
Summary
When we look at a complex image, we do not see every detail of the shape in order to recognize the image, but we see and identify the characteristic features and particular configurations and register them in our memory [30]. The first principle of a Q-code scheme is the encoding of shape characteristics on particular nodes where qualitative changes occur. Each Q-code is constructed in such a way that particular shape characteristics are abstracted into a combination of symbols in order to encapsulate a geometric phenomenon in terms of attribute class and value range. The third principle of a Q-code scheme is discretisation This means that the encoding of a continuous shape contour yields a set of discrete symbols. The Q-code scheme looks at the geometric characteristics occurring between, or on, the singular nodes of a shape contour and converts them into discrete symbols. The encoding system detects the singular nodes and transforms the numeric values for particular shape attributes into discrete Q-codes that are formed in combination with a character and sign values
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