Second-Order Random Graphs for Modeling Sets of Attributed Graphs and Their Application to Object Learning and Recognition

Abstract

Abstract. The aim of this article is to present a random graph representation, that is based on 2 nd order relations between graph elements, for modeling sets of attributed graphs (AGs). We refer to these models as second-order random graphs (SORGs). The basic feature of SORGs is that they include both marginal probability functions of graph elements and 2 ndorder joint probability functions. This allows a more precise description of both the structural and semantic information contents in a set of AGs and, consequently, an expected improvement in graph matching and object recognition. The article presents a probabilistic formulation of SORGs that includes as particular cases the two previously proposed approaches based on random graphs, namely the first-order random graphs (FORGs) and the function-described graphs (FDGs). We then propose a distance measure derived from the probability of instantiating a SORG into an AG and an incremental procedure to synthesize SORGs from sequences of AGs.Finally, SORGs are shown to improve the performance of FORGs, FDGs and direct AG-to-AG matching in three experimental recognition tasks: one -2 -in which AGs are randomly generated and the other two in which AGs represent multiple views of 3D objects (either synthetic or real) that have been extracted from color images. In the last case, object learning is achieved through the synthesis of SORG models.

Combining Neural Networks and Clustering Techniques for Object Recognition in Indoor Video Sequences

“…For each one of the classes (or objects) o and for each frame f, a weighted mass center wmc(o,f) was computed as (1) where ns(o,f) is the number of spots classified as object o in frame f, p(o|s) is the aposteriori class probability of object o for spot s given by the net, and a(s) and mc(s) are respectively the area and mass center of s.…”

“…For instance, the result of a color image segmentation process, consisting of a set of regions (spots, from now on) characterized by different features (related to color, size and shape), may be a good starting point to learn the model. Although structured models like adjacency attributed graphs or random graphs can be synthesized for each object from several segmented images [1], we have decided to investigate first a much simpler approach in which the object is just represented as an unstructured set of spots. One of the main drawbacks of the structural methods is that the segmented images from one frame to the other can be quite different, and so, it is difficult to match the actual spots (usually represented by nodes of the graphs) with the previous ones.…”

The Use of Graph Techniques for Identifying Objects and Scenes in Indoor Building Environments for Mobile Robots

“…Specifically a FDG includes the antagonism, occurrence and existence relations which apply to pairs of vertices and arcs. Finally, we have expanded this representation, [17,18] by means of Second-Order Random Graphs (SORG), which keep more structural and semantic information than FORGs and FDGs. These last types of representation have led to the development of synthesis techniques for model object generation (by means of 2D projections of a 3D object) and graph matching techniques for graph identification.…”

A probabilistic integrated object recognition and tracking framework

“…In [6], they used specific parameters of the object to be tracked. In [7], they track hands using textures.…”

“…A useful object model should be relatively simple and easy to acquire from the result of image processing steps. For instance, the result of a colour image segmentation process, consisting of a set of regions or spots, characterized by simple features related to colour, may be a good starting point to learn the model [7,12]. Although structured models like attributed graphs or skeletons can be synthesized for each object from several segmented images [13,14], we have decided to investigate a much simpler approach in which the object is just represented as an unstructured set of pixels.…”