Abstract—This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graph-matching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems. Index Terms—Graph edit distance, graph seriation, maximum a posteriori probability (MAP), graph-spectral methods. 1

This paper proposes a comparative study of 3D and 2D/3D shape descriptors (SDs) for of 3D mesh model indexing and retrieval. Seven state of the art SDs are considered and compared, among which five are 3D (Optimized 3D Hough Descriptor-O3DHTD, Extended Gaussian Images- EGIs, cords length and spherical angles histograms, random triangles histogram, MPEG-7 3D shape spectrum descriptor – 3DSSD), and two 2D/3D, based on the MPEG-7 2D SDs (Contour Scale Space- CSS, and Angular Radial Transform- ART). A low complexity vector quantized (VQ) OH3DD is also proposed and considered for this comparison. Experimental results were carried out upon the categorized MPEG-7 3D test database. By computing Bull-Eye Score (BES) and First Tier (FT) criteria, it is objectively established that the O3DHTD (even in its VQ version) outperforms (BES = 81 % or 79%).all other SDs. The 2D/3D CSS-based descriptor exhibits a highly discriminant behavior (BES = 74%) outperforming the other both 3D and 2D/3D approaches. Apply to the industrial framework of the French national project SEMANTIC-3D, the O3DHTD demonstrated its relevance together with its scalability and robustness properties.