Miguel Angel Lozano

A robust Graph Transformation Matching for non-rigid registration

In this paper, we propose a simple and highly robust point-matching method named Graph Transformation Matching (GTM) relying on finding a consensus nearest-neighbour graph emerging from candidate matches. The method iteratively eliminates dubious matches in order to obtain the consensus graph. The proposed technique is compared against both the Softassign algorithm and a combination of RANSAC and epipolar constraint. Among these three techniques, GTM demonstrates to yield the best results in terms of elimination of outliers. The algorithm is shown to be able to deal with difficult cases such as duplication of patterns and non-rigid deformations of objects. An execution time comparison is also presented, where GTM shows to be also superior to RANSAC for high outlier rates. In order to improve the performance of GTM for lower outlier rates, we present an optimised version of the algorithm. Lastly, GTM is successfully applied in the context of constructing mosaics of retinal images, where feature points are extracted from properly segmented binary images. Similarly, the proposed method could be applied to a number of other important applications.

Protein classification by matching and clustering surface graphs

In this paper, we address the problem of comparing and classifying protein surfaces with graph-based methods. Comparison relies on matching surface graphs, extracted from the surfaces by considering concave and convex patches, through a kernelized version of the Softassign graph-matching algorithm. On the other hand, classification is performed by clustering the surface graphs with an EM-like algorithm, also relying on kernelized Softassign, and then calculating the distance of an input surface graph to the closest prototype. We present experiments showing the suitability of kernelized Softassign for both comparing and classifying surface graphs.

Constellations and the unsupervised learning of graphs

In this paper, we propose a novel method for the unsupervised clustering of graphs in the context of the constellation approach to object recognition. Such method is an EM central clustering algorithm which builds prototypical graphs on the basis of fast matching with graph transformations. Our experiments, both with random graphs and in realistic situations (visual localization), show that our prototypes improve the set median graphs and also the prototypes derived from our previous incremental method. We also discuss how the method scales with a growing number of images.

Graph matching through entropic manifold alignment

In this paper we cast the problem of graph matching as one of non-rigid manifold alignment. The low dimensional manifolds are from the commute time embedding and are matched though coherent point drift. Although there have been a number of attempts to realise graph matching in this way, in this paper we propose a novel information-theoretic measure of alignment, the so-called symmetrized normalized-entropy-square variation. We succesfully test this dissimilarity measure between manifolds on a a challenging database. The measure is estimated by means of the bypass Leonenko entropy functional. In addition we prove that the proposed measure induces a positive definite kernel between the probability density functions associated with the manifolds and hence between graphs after deformation. In our experiments we find that the optimal embedding is associated to the commute time distance and we also find that our approach, which is purely topological, outperforms several state-of-the-art graph-based algorithms for point matching.

Graph-based methods for retinal mosaicing and vascular characterization

In this paper, we propose a highly robust point-matching method (Graph Transformation Matching - GTM) relying on finding the consensus graph emerging from putative matches. Such method is a two-phased one in the sense that after finding the consensus graph it tries to complete it as much as possible. We successfully apply GTM to image registration in the context of finding mosaics from retinal images. Feature points are obtained after properly segmenting such images. In addition, we also introduce a novel topological descriptor for quantifying disease by characterizing the arterial/venular trees. Such descriptor relies on diffusion kernels on graphs. Our experiments have showed only statistical significance for the case of arterial trees, which is consistent with previous findings.

ACM attributed graph clustering for learning classes of images

In a previous work we have adapted the Asymmetric Clustering Model (ACM) to the domain of non-attributed graphs. We use our Comb algorithm for graph matching, a population-based method which performs multi-point explorations of the discrete space of feasible solutions. Given this algorithm we define an incremental method to obtain a prototypical graph by fusing the elements of the ensemble weighted by their prior probabilities of belonging to the class. Graph-matching and incremental fusion are integrated in a EM clustering algorithm. In this paper, we adapt the latter ACM clustering model to deal with attributed graphs, where these attributes are probability density functions associated to nodes and edges. In order to do so, we modify the incremental method for obtaining a prototypical graph to update these pdfs provided that they are statistically compatible with those of the corresponding nodes and edges. This graph-clustering approach is successfully tested in the domain of Mondrian images (images built on rectangular patches of colored textures) because our final purpose is to the unsupervised learning of image classes.

Aerial Obstacle Detection With 3 - D Mobile Devices

In this paper, we present a novel approach for aerial obstacle detection (e.g., branches or awnings) using a 3-D smartphone in the context of the visually impaired (VI) people assistance. This kind of obstacles are especially challenging because they cannot be detected by the walking stick or the guide dog. The algorithm captures the 3-D data of the scene through stereo vision. To our knowledge, this is the first work that presents a technology able to obtain real 3-D measures with smartphones in real time. The orientation sensors of the device (magnetometer and accelerometer) are used to approximate the walking direction of the user, in order to look for the obstacles only in such a direction. The obtained 3-D data are compressed and then linearized for detecting the potential obstacles. Potential obstacles are tracked in order to accumulate enough evidence to alert the user only when a real obstacle is found. In the experimental section, we show the results of the algorithm in several situations using real data and helped by VI users.

A Significant Improvement of Softassign with Diffusion Kernels

In this paper we propose a simple way of significantly improving the performance of the Softassign graph-matching algorithm of Gold and Rangarajan. Exploiting recent theoretical results in spectral graph theory we use diffusion kernels to transform a matching problem between unweighted graphs into a matching between weighted ones in which the weights rely on the entropies of the probability distributions associated to the vertices after kernel computation. In our experiments, we report that weighting the original quadratic cost function results in a notable improvement of the matching performance, even in medium and high noise conditions.

EM Algorithm for Clustering an Ensemble of Graphs with Comb Matching

In this paper we address the unsupervised clustering of an ensemble of graphs. We adapt to the domain of graphs the Asymmetric Clustering Model (ACM). Firstly, we use an improvement of our Comb algorithm for graph matching, a population-based method which performs multi-point explorations of the discrete space of feasible solutions. Given this algorithm we define an incremental method to obtain a prototypical graph by fusing the elements of the ensemble weighted by their prior probabilities of belonging to the class. Graph-matching and incremental fusion are integrated in a EM clustering algorithm: In the E-step we re-estimate the class-membership variables by computing the distances of input graphs to current prototypes through graph-matching, and in the M-step we re-estimate the prototypes by considering the latter class-membership variables in order to perform graph fusions. We introduce adaptation: The algorithm starts with a high number of classes and in each epoch tries to fuse the two classes with closer prototypes. We present several results of Comb-matching, incremental fusion and clustering.

Flow Complexity: Fast Polytopal Graph Complexity and 3D Object Clustering

In this paper, we introduce a novel descriptor of graph complexity which can be computed in real time and has the same qualitative behavior of polytopal (Birkhoff) complexity, which has been successfully tested in the context of Bioinformatics. We also show how the phase-change point may be characterized in terms of the Laplacian spectrum, by analyzing the derivatives of the complexity function. In addition, the new complexity notion (flow complexity ) is applied to cluster a database of Reeb graphs coming from analyzing 3D objects.