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

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 quasi-random sampling approach to image retrieval

In this paper, we present a novel approach to contentsbased image retrieval. The method hinges in the use of quasi-random sampling to retrieve those images in a database which are related to a query image provided by the user. Departing from random sampling theory, we make use of the EM algorithm so as to organize the images in the database into compact clusters that can then be used for stratified random sampling. For the purposes of retrieval, we use the similarity between the query and the clustered images to govern the sampling process within clusters. In this way, the sampling can be viewed as a stratified sampling one which is random at the cluster level and takes into account the intra-cluster structure of the dataset. This approach leads to a measure of statistical confidence that relates to the theoretical hard-limit of the retrieval performance. We show results on the Oxford Flowers dataset. 1

A NURBS-based spectral reflectance descriptor with applications in computer vision and pattern recognition

In this paper, we present a surface reflectance descriptor based on the control points resulting from the interpolation of Non-Uniform Rational B-Spline (NURBS) curves to multispectral reflectance data. The interpolation is based upon a knot removal scheme in the parameter domain. Thus, we exploit the local support of NURBS so as to recover a compact descriptor robust to noise and local perturbation of the spectra. We demonstrate the utility of our NURBS-based descriptor for material identification. To this end, we perform skin spectra recognition making use of a Support Vector Machine classifier. We also provide results on hyperspectral imagery and elaborate on the preprocessing step for skin segmentation. We compare our results with those obtained using an alternative descriptor

Specularity Removal from Imaging Spectroscopy Data via Entropy Minimisation

In this paper, we present a method to remove specularities from imaging spectroscopy data. We do this by making use of the dichromatic model so as to cast the problem in a linear regression setting. We do this so as to employ the average radiance for each pixel as a means to map the spectra onto a two-dimensional space. This permits the use of an entropy minimisation approach so as to recover the slope of a line described by a linear regressor. We show how this slope can be used to recover the specular coefficient in the dichromatic model and provide experiments on real-world imaging spectroscopy data. We also provide comparison with an alternative and effect a quantitative analysis that shows our method is robust to changes the degree of specularity of the image or the location of the light source in the scene