Qualitative analysis of polygon shape-change

1999

In this paper we present an approach to the qualitative representation of shape and its use. We use a qualitative coding scheme founded on landmarks in the shape. The scheme encodes a qualitative representation of angles, relative side lengths and curvatures at landmarks. We then show how such a representation can be used as a basis for reasoning about shapes using extracted shape features. We conclude with a preliminary analysis of 12 sketches of the architect Louis Kahn and show how they may be categorised based on these shape features.

1990

Model-based recognition is concerned with comparing a shape A, which is stored as a model for some particular object, with a shape B, which is found to exist in an image. If A and B ate close to being the same shape, then a vision system should report a match and return a measure of how good that match is. To be useful this measure should satisfy a number of properties, including: 1) it should be a metric, 2) it should be invariant under translation, rotation, and change-of-scale, 3) it should be reasonably easy to compute, and 4) it should match our intuition (i.e., answers should be similar to those that a person might give). We develop a method for comparing polygons that has these properties.

2009

Representing and comparing two-dimensional shapes is an important problem. Our hypothesis about human representations is that that people utilize two representations of shape: an abstract, qualitative representation of the spatial relations between the shape's parts, and a detailed, quantitative representation. The advantage of relational, qualitative representations is that they facilitate shape comparison: two shapes can be compared via structural alignment processes which have been used to model similarity and analogy more broadly. This comparison process plays an important role in determining when two objects share the same shape, or in identifying transformations (rotations and reflections) between two shapes. We demonstrate the effectiveness of our model by summarizing a series of studies which have simulated human spatial reasoning.

Pattern Recognition, 1987

The directional relationship between two polygons (e.g. left, above, beside, east, north) is an important spatial property and can also be used as a selection criterion for retrieving objects from a spatial database. If the database is large, this could help significantly in speeding search by reducing the size of the necessary search space. This paper builds upon past work to develop a model for determining the directional relationship in 2-D space between two simply-connected polygons of arbitrary shape, size and distance from each other. The model is based on visual interpretation and is data structure independent. The model is also stated in algorithmic terms, and is found to have a computational complexity of O(n), where n is the total number of vertices or cells used to represent the two polygons. Spatial relationships Direction Geometric algorithms Computer vision Geographic information systems

2005

Many shape recognition techniques have been presented in literature, most of them from a quantitative perspective. Research has shown that qualitative reasoning better reflects the way humans deal with spatial reality. The current qualitative techniques are based on break points resulting in difficulties in comparing analogous relative positions along polylines. The presented shape representation technique is a qualitative approach based on division points, resulting in shape matrices forming a shape data model and thus forming the basis for a cognitively relevant similarity measure for shape representation and shape comparison, both locally and globally.

Spatial Cognition and Computation, 2012

A computational approach for comparing qualitative shape descriptions (QSDs) of objects within digital images is presented. First, the dissimilarity of qualitative features of shape is measured: (i) intuitively using conceptual neighborhood diagrams; and (ii) mathematically using interval distances. Then, a similarity measure between QSDs is defined and tested using images of different categories of the MPEG-7-CE-Shape-1 library, images of tiles used to build mosaics, and a collection of Clipart images. The results obtained show the effectiveness of the similarity measure defined, which is invariant to translations, rotations and scaling, and which implicitly manages deformation of shape parts and incompleteness.

ACM SIGGRAPH 2012 Posters on - SIGGRAPH '12, 2012

Journal of Mathematical Psychology, 1987

ceur-ws.org

We propose a formal framework to clarify the import of and the relationship among different notions of similarity. The framework, borrowing from the general E-connections approach, allows to use multiple similarity notions in the same system by relating the domain of discourse to specialized sets of entities even across different logics. In practice, we start form the assumption that (Leibnizian) relative identity is the only local form of similarity, and show that more sophisticated notions can be conceptually understood as the result of transformations across heterogeneous logics. These transformations, called global similarities, are usually motivated by arguments external to the starting system, and can be intertwined to generate a prolific family of similarity relations. We exemplify this framework in the context of shape similarity whose comprehension motivated our work. Finally, the approach developed in this paper sets the basis for a general study of similarity as a group of transformations generated by (primitive) global similarity relations.

Foundations and Trends® in Programming Languages, 2020