Graph edit distance from spectral seriation

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

Shape-from-shading using the heat equation

This paper offers two new directions to shape-from-shading, namely the use of the heat equation to smooth the field of surface normals and the recovery of surface height using a low-dimensional embedding. Turning our attention to the first of these contributions, we pose the problem of surface normal recovery as that of solving the steady state heat equation subject to the hard constraint that Lambert's law is satisfied. We perform our analysis on a plane perpendicular to the light source direction, where the z component of the surface normal is equal to the normalized image brightness. The x - y or azimuthal component of the surface normal is found by computing the gradient of a scalar field that evolves with time subject to the heat equation. We solve the heat equation for the scalar potential and, hence, recover the azimuthal component of the surface normal from the average image brightness, making use of a simple finite difference method. The second contribution is to pose the problem of recovering the surface height function as that of embedding the field of surface normals on a manifold so as to preserve the pattern of surface height differences and the lattice footprint of the surface normals. We experiment with the resulting method on a variety of real-world image data, where it produces qualitatively good reconstructed surfaces

Directionality in van der Waals Interactions: the Case of 4-Acetylbiphenyl Adsorbed on Au(111)

We report on a theoretical study of adsorption of 4-Acetylbiphenyl molecule and its diffusion properties in the main directions of the Au(111) surface. Structural changes of the molecule, which are induced by adsorption lead to stronger conjugation of the $\pi$-system. The molecule is adsorbed in a flat configuration on the surface with roughly the same binding energy along the [110] and [112] directions, in good agreement with experiments. Furthermore, the diffusion barriers imply an important directionality of the molecule-surface interactions. This is somewhat surprising because our calculations show that the prevailing interaction is the long-range molecule-surface van der Waals interaction. Despite of its weakness, the van der Waals interaction discriminates the preferential adsorption sites as well as imposes a molecular geometry that needs to be considered when rationalizing the diffusion barriers

The artistic use of parallax and lenses revealing the invisible in holography

There are many artistic resources offered by holography: third-dimension registration and reconstruction, immateriality, color interpretation, holographic space, realism, etc. But there are a few of them which are very characteristic and singular of that media such as the inversion of parallax, and the possibility of making invisible to turn into visible. Current paper aims to discuss key issues concerning with the aesthetic use of those special features. It is based on theoretical as well as critical analysis of the production by some of the most outstanding holographic artists who have made use of such interesting resources

A graph-spectral approach to shape-from-shading

In this paper, we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximizes the sum of curvature-dependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert's law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and real-world imagery

A spacecraft-borne gradiometer mission analysis

Numerical simulations were performed to obtain the orbit- and attitude-determination requirements of a spacecraft-borne gradiometer mission. Results demonstrated that position determination of 300 meters in the along-track and cross-track directions and 50 meters in the radial direction are mission requirements. The optimal orientation of the gradiometer sensing plane is achieved when the spin vector elevation is 0 degrees. The attitude-determination requirements are 5 degrees resolution for spin-vector azimuth and 0.2 degree resolution for spin-vector elevation. When these requirements are met, 3-degree gravity anomalies can be recovered globally with an accuracy of 0.025/mm/sq s (2.5 mgals). The Appendix documents the mathematical procedures for estimating detailed gravity fields from gradiometer data

On extracting brightness temperature maps from scanning radiometer data

The extraction of brightness temperature maps from scanning radiometer data is described as a typical linear inverse problem. Spatial quantization and parameter estimation is described and is suggested as an advantageous approach to a solution. Since this approach takes into explicit account the multivariate nature of the problem, it permits an accurate determination of the most detailed resolution extractable from the data as well as explicitly defining the possible compromises between accuracy and resolution. To illustrate the usefulness of the method described for algorithm design and accuracy prediction, it was applied to the problem of providing brightness temperature maps during the NOSS flight segment. The most detained possible resolution was determined and a curve which displays the possible compromises between accuracy and resolution was provided

On estimating gravity anomalies from gradiometer data

The Gravsat-gradiometer mission involves flying a gradiometer on a gravity satellite (Gravsat) which is in a low, polar, and circular orbit. Results are presented of a numerical simulation of the mission which demonstrates that, if the satellite is in a 250-km orbit, 3- and 5-degree gravity anomalies may be estimated with accuracies of 0.03 and 0.01 mm/square second (3 and 1 mgal), respectively. At an altitude of 350 km, the results are 0.07 and 0.025 mm.square second (7 and 2.5 mgal), respectively. These results assume a rotating type gradiometer with a 0.1 -etvos unit accuracy. The results can readily be scaled to reflect another accuracy level