Shape Decomposition Research Articles

The adaptive pyramid: A framework for 2D image analysis

The adaptive pyramid is a new framework for 2D image analysis. It is based on the principle of local evidence accumulation for global interpretation. The adaptive structure of this pyramid is a new approach of reduced resolution. We introduce the concept of surviving cell as a local maximum of an interest operator. A root is then defined as a particular surviving cell. Examples are shown in segmentation for different images. The limits of this technique are presented on an example of a highly textured image. A particular top-down process is presented in the context of shape decomposition.

A uniform approach to represent features in different application contexts

A dual description for feature-based modeling is proposed which should be equally efficient for design with feature systems and automatic recognition of instances of standard or user-defined features. This description consists of a primary representation in terms of shape features ( neutral description) and a set of viewpoint-dependent feature-based representations ( secondary descriptions) which are created by transformations that are viewpoint-specific and which are applied to the shape decomposition model.

Decomposition of complex shapes for their structural recognition

In the author's previous paper a representation of complex shapes and their features (mainly grooves) has been developed. Using this representation, a method for a unique decomposition of complex shapes into the so-called quasiconvex figures has been established. The relationship between these figures describes the inner structure of the decomposed shape. This relationship, expressed by a tree, enables one to find productions of an attributed context-free grammar which uniquely describes the shape. The semantics of this grammar is formulated automatically during the decomposition. The derived grammar may be substantially generalized by means of a trivial procedure. The developed formalism leads to the construction of a self-learning system which recognizes complex shapes in a syntactic way.

The largest convex patches: A boundary-based method for obtaining object parts

The importance of boundaries for shape decomposition into component parts has been discussed from different points of view by Koenderink and van Doorn (1982), and by Hoffman and Richards (1984). The former define part boundaries as parabolic contours, whereas the latter propose that part boundaries should be defined by contours of negative minima (or maxima) of principal curvature. In this article, building on aspects of both approaches, we develop a new method for shape decomposition. This method relies exclusively on global properties of the surface which are fully characterized by local surface properties. We propose that a useful parcellation of shapes into parts can be obtained by decomposing the shape boundary into the largest convex surface patches and the smallest nonconvex surface patches. The essential computational steps of this method are the following: (i) build initial parts from the largest locally convex patches, (ii) consider an initial part as a constituent part if it is essentially convex, and (iii) obtain the remaining constituent parts by merging adjacent initial parts generated by the largest locally convex and the smallest nonconvex patches of nearly the same sizes. The method is illustrated on both smooth and continuous shapes. We show that the decomposition of shapes into the largest convex patches aims to maximize the "thingness" in an object, and to minimize its "non-thingness". The method is conducive to a natural parcellation of shapes into constituent parts useful for recognition and for inferring function.

Shape decomposition by collinearity

The analysis of collinearity with semantic considerations in shape decomposition is presented. The method is based on a lot of heuristics satisfying human intuition about collinearity. Man-made objects which often contain many collinear lines are analyzed to verify this approach.

Manifolds accepting codimension-one- sphere-shape decompositions

A decomposition of a metric space is said to be CS k -shape if each of its members is a compactum shape equivalent to a cohomology k-sphere. We will show that for m⩾2 every CS m−1 -shape decomposition of a closed m-manifold is upper semicontinuous (Theorem 3.1). Consequently, for m≠3, 4, 5, every connected closed m-manifold accepting an S m−1 -shape decomposition is homeomorphic to the total space of an ( m−1)-sphere-fiber bundle over the circle (Theorem 4.2).

Shape comparison of physical spectra: Application to Mössbauer spectra of silicate glasses

A shape comparison method is applied to a group of related spectra in terms of shape decomposition, avoiding reference to any a priori structural model in their interpretation. The method, utilized for a series or iron Mössbauer spectra of silicate glasses of the same bulk composition but varying iron redox ratios, enables the characterization of the varying Fe 3+ structural role. Statistically, it is superior to the fit of glass spectra to a finite number of Lorentzian lines and gives iron redox ratios that are directly comparable to microchemical determinations.

A Graph-Theoretic Method for Decomposing Two-Dimensional Polygonal Shapes into Meaningful Parts

This note gives a new graph-theoretic shape decomposition procedure, extending the idea in the paper ``Decomposition of Two-Dimensional Shapes by Graph-Theoretic Clustering'' by Shapiro and Haralick [1]. A binary matrix is used in order to express the LI relation. A solution for the problems connected with artificial separation of two CS cliques and the presence of a regular concavity is proposed. Our algorithm produces nonoverlapping shape parts in much reduced execution time.

Global Shape Analysis by k-Syntactic Similarity

The k-syntactic similarity approach is couched in graphical representation terms and its ability to provide global recognition capability while retaining a low time complexity is explored. One potential application domain, that of composite shape decomposition into approximately convex subshapes, is described. This is shown to be equivalent to finding cycles within a particular graph. The approach yields valid decompositions in many cases of interest, and is capable of identifying those cases where additional semantic considerations are necessary for proper analysis. The permissible graph structures representing composite shapes given a reasonable set of relations are determined. Experimental results on nonideal data are given.

Two-dimensional shape decomposition using fuzzy subset theory applied to automated chromosome analysis

This paper describes a technique to transform a two-dimensional shape into a generalized fuzzy binary relation whose clusters represent the meaningful simple parts of the shape. The fuzzy binary relation is defined on the set of convex and concave boundary points, implying a piecewise linear approximation of the boundary, and describes the dissemblance of two vertices to a common cluster. Next some fuzzy subsets are defined over the points which determine the connection between the clusters. The decomposition method first determines nearly convex regions, which are subgraphs of the total graph, and then selects the greatest nearly convex region which satisfies best the defined fuzzy subsets and relations. Using this procedure on touching chromosomes defining the simple parts to be the separated chromosomes, the decomposition often corresponds well to the decomposition that a human might make.

Decomposition of Two-Dimensional Shapes by Graph-Theoretic Clustering

This paper describes a technique for transforming a twodimensional shape into a binary relation whose clusters represent the intuitively pleasing simple parts of the shape. The binary relation can be defined on the set of boundary points of the shape or on the set of line segments of a piecewise linear approximation to the boundary. The relation includes all pairs of vertices (or segments) such that the line segment joining the pair lies entirely interior to the boundary of the shape. The graph-theoretic clustering method first determines dense regions, which are local regions of high compactness, and then forms clusters by merging together those dense regions having high enough overlap. Using this procedure on handdrawn colon shapes copied from an X-ray and on handprinted characters, the parts determined by the clustering often correspond well to decompositions that a human might make.

An experimental study of baroclinic wave interactions in a two-layer system

Abstract Baroclinic waves in a rotating two-layer shear flow are observed by measuring fluctuations in the height of the interface using a technique which does not disturb the flow. Decomposition of the shape of the interface into azimuthal Fourier components shows that the wave spectrum is dominated by a single wave number, but other components have significant amplitudes. Nonlinear interactions between these components are isolated by comparing the results with the predictions of a linear stability theory. The observed interactions are reminiscent of those found by Hide, Mason and Plumb (1977) in a different system, thus demonstrating that they are a fundamental property of baroclinic waves.