Michela Spagnuolo

From exact to approximate maximum common subgraph

This paper presents an algorithm for the computation of the maximum common subgraph (MCS) between two directed, acyclic graphs with attributes. The core of the contribution resides in the modularity of the proposed algorithm which allows different heuristic techniques to be plugged in, depending on the application domain. Implemented heuristics for robust graph matching with respect to graph structural noise are discussed. n nAs example of its effectiveness, the algorithm is applied to the problem of 3D shape similarity evaluation through structural shape descriptors.

Polyhedral Surface Decomposition Based on Curvature Analysis

This paper describes a method to characterize the shape of a generic surface approximated with a triangulation. Combining classical topological techniques and differential geometry provides simple methods for evaluating several shape descriptors. Based on this idea a qualitative analysis is defined to estimate the curvature “along” edges and “around” triangles in order to identify regions whose shape is classified as concave, convex, plane or saddle. The proposed curvature regions are defined as connected components of the graph surface model and give rise to a unique surface decomposition which is suitable for parallel implementation and has a linear computational complexity.

Shape abstraction using computational topology techniques

This paper investigates the possible role of the new field of computational topology for incorporating abstraction mechanisms in shape modelling. The effectiveness of computational topology techniques is exemplified with an application of discrete differential topology. In particular, a method is proposed for the extraction of a critical point configuration graph from a triangulated surface. Starting from the definition of the Reeb graph in the smooth domain, the concept of critical point is extended to critical areas, which may represent isolated as well as degenerated critical points in the discrete domain. The resulting graph effectively represents the surface shape and has been successfully used as a basis for model compression and restoring purposes.

Discrete Surface Models: Constraint-based Generation and Understanding

A two level description is proposed for natural surface modelling: a geometric model, in terms of low level primitive entities, and a conceptual model, which is a symbolic surface representation based on its prominent shape characteristics. The geometric and conceptual level can exchange information using two operators: the abstraction operator and the generation operator.

Geometric Reasoning for the Extraction of Surface Shape Properties

Shape descriptions are essential in computer graphics to provide effective representations of the objects to be modelled. A geometric reasoning approach is here proposed to extract curvature information from a surface approximated by a triangulation. In particular, a curvature measure is defined which is qualitatively-similar to the mean curvature. This curvature measure enhances the descriptive power of the shape characterisation previously defined by the authors, based on the decomposition of the surface in its convex, concave, plane and saddle regions.

Hybrid Representation of Feature-Based Models

A double description of a feature-based model is proposed which should be equally efficient both 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 generic form features (neutral description) and a set of viewpoint dependent feature-based representations (secondary descriptions) which are created by transformations that are viewpoint specific and apply to the neutral object description.

Shape Analysis and Description Using Real Functions

We discuss how the shape of an object can be analyzed according to the properties of real functions defined on it, and how these properties can be stored in compact and informative geometric/topological descriptors. As examples, we refer to Reeb graphs and persistence diagrams, encoding either the configuration of level sets or sub-level sets of functions. We then move to the case of vector-valued functions, encoding multi-dimensional properties of shapes, showing how this kind of information can be dealt with by means of persistence spaces. Experiments on the retrieval of textured 3D models are presented as a possible application of such tools.

Morphological decomposition of natural surfaces (Invited Paper)

The main goal of surface characterization addresses the reduction of a surface to a compact symbolic description that efficiently stores information about the morphological structure of the surface. In the context of polyhedral surfaces characteristic regions, i.e., regions with convex, concave, planar, and saddle shape, are proposed as structural surface components and are defined taking into account geometric relationships between triangles. Based on these areal features, a symbolic representation of the surface called characteristic region configuration graph is produced where the nodes correspond to the surface regions while the arcs and hyperarcs correspond to the surface characteristic lines and points.