Edge Potential Functions (EPF) and Genetic Algorithms (GA) for Edge-Based Matching of Visual Objects

Edges are known to be a semantically rich representation of the contents of a digital image. Nevertheless, their use in practical applications is sometimes limited by computation and complexity constraints. In this paper, a new approach is presented that addresses the problem of matching visual objects in digital images by combining the concept of Edge Potential Functions (EPF) with a powerful matching tool based on Genetic Algorithms (GA). EPFs can be easily calculated starting from an edge map and provide a kind of attractive pattern for a matching contour, which is conveniently exploited by GAs. Several tests were performed in the framework of different image matching applications. The results achieved clearly outline the potential of the proposed method as compared to state of the art methodologies. (c) 2007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works

Partial shape matching using CCP map and weighted graph transformation matching

La détection de la similarité ou de la différence entre les images et leur mise en correspondance sont des problèmes fondamentaux dans le traitement de l'image. Pour résoudre ces problèmes, on utilise, dans la littérature, différents algorithmes d'appariement. Malgré leur nouveauté, ces algorithmes sont pour la plupart inefficaces et ne peuvent pas fonctionner correctement dans les situations d’images bruitées. Dans ce mémoire, nous résolvons la plupart des problèmes de ces méthodes en utilisant un algorithme fiable pour segmenter la carte des contours image, appelée carte des CCPs, et une nouvelle méthode d'appariement. Dans notre algorithme, nous utilisons un descripteur local qui est rapide à calculer, est invariant aux transformations affines et est fiable pour des objets non rigides et des situations d’occultation. Après avoir trouvé le meilleur appariement pour chaque contour, nous devons vérifier si ces derniers sont correctement appariés. Pour ce faire, nous utilisons l'approche « Weighted Graph Transformation Matching » (WGTM), qui est capable d'éliminer les appariements aberrants en fonction de leur proximité et de leurs relations géométriques. WGTM fonctionne correctement pour les objets à la fois rigides et non rigides et est robuste aux distorsions importantes. Pour évaluer notre méthode, le jeu de données ETHZ comportant cinq classes différentes d'objets (bouteilles, cygnes, tasses, girafes, logos Apple) est utilisé. Enfin, notre méthode est comparée à plusieurs méthodes célèbres proposées par d'autres chercheurs dans la littérature. Bien que notre méthode donne un résultat comparable à celui des méthodes de référence en termes du rappel et de la précision de localisation des frontières, elle améliore significativement la précision moyenne pour toutes les catégories du jeu de données ETHZ.Matching and detecting similarity or dissimilarity between images is a fundamental problem in image processing. Different matching algorithms are used in literature to solve this fundamental problem. Despite their novelty, these algorithms are mostly inefficient and cannot perform properly in noisy situations. In this thesis, we solve most of the problems of previous methods by using a reliable algorithm for segmenting image contour map, called CCP Map, and a new matching method. In our algorithm, we use a local shape descriptor that is very fast, invariant to affine transform, and robust for dealing with non-rigid objects and occlusion. After finding the best match for the contours, we need to verify if they are correctly matched. For this matter, we use the Weighted Graph Transformation Matching (WGTM) approach, which is capable of removing outliers based on their adjacency and geometrical relationships. WGTM works properly for both rigid and non-rigid objects and is robust to high order distortions. For evaluating our method, the ETHZ dataset including five diverse classes of objects (bottles, swans, mugs, giraffes, apple-logos) is used. Finally, our method is compared to several famous methods proposed by other researchers in the literature. While our method shows a comparable result to other benchmarks in terms of recall and the precision of boundary localization, it significantly improves the average precision for all of the categories in the ETHZ dataset

Robust elastic 2D/3D geometric graph matching

We present an algorithm for geometric matching of graphs embedded in 2D or 3D space. It is applicable for registering any graph-like structures appearing in biomedical images, such as blood vessels, pulmonary bronchi, nerve fibers, or dendritic arbors. Our approach does not rely on the similarity of local appearance features, so it is suitable for multimodal registration with a large difference in appearance. Unlike earlier methods, the algorithm uses edge shape, does not require an initial pose estimate, can handle partial matches, and can cope with nonlinear deformations and topological differences. The matching consists of two steps. First, we find an affine transform that roughly aligns the graphs by exploring the set of all consistent correspondences between the nodes. This can be done at an acceptably low computational expense by using parameter uncertainties for pruning, backtracking as needed. Parameter uncertainties are updated in a Kalman-like scheme with each match. In the second step we allow for a nonlinear part of the deformation, modeled as a Gaussian Process. Short sequences of edges are grouped into superedges, which are then matched between graphs. This allows for topological differences. A maximum consistent set of superedge matches is found using a dedicated branch-and-bound solver, which is over 100 times faster than a standard linear programming approach. Geometrical and topological consistency of candidate matches is determined in a fast hierarchical manner. We demonstrate the effectiveness of our technique at registering angiography and retinal fundus images, as well as neural image stacks.Peer ReviewedPostprint (author’s final draft

Dictionary-based Tensor Canonical Polyadic Decomposition

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images

Best network chirplet-chain: Near-optimal coherent detection of unmodeled gravitation wave chirps with a network of detectors

The searches of impulsive gravitational waves (GW) in the data of the ground-based interferometers focus essentially on two types of waveforms: short unmodeled bursts and chirps from inspiralling compact binaries. There is room for other types of searches based on different models. Our objective is to fill this gap. More specifically, we are interested in GW chirps with an arbitrary phase/frequency vs. time evolution. These unmodeled GW chirps may be considered as the generic signature of orbiting/spinning sources. We expect quasi-periodic nature of the waveform to be preserved independent of the physics which governs the source motion. Several methods have been introduced to address the detection of unmodeled chirps using the data of a single detector. Those include the best chirplet chain (BCC) algorithm introduced by the authors. In the next years, several detectors will be in operation. The joint coherent analysis of GW by multiple detectors can improve the sight horizon, the estimation of the source location and the wave polarization angles. Here, we extend the BCC search to the multiple detector case. The method amounts to searching for salient paths in the combined time-frequency representation of two synthetic streams. The latter are time-series which combine the data from each detector linearly in such a way that all the GW signatures received are added constructively. We give a proof of principle for the full sky blind search in a simplified situation which shows that the joint estimation of the source sky location and chirp frequency is possible.Comment: 22 pages, revtex4, 6 figure

Revisiting Complex Moments For 2D Shape Representation and Image Normalization

When comparing 2D shapes, a key issue is their normalization. Translation and scale are easily taken care of by removing the mean and normalizing the energy. However, defining and computing the orientation of a 2D shape is not so simple. In fact, although for elongated shapes the principal axis can be used to define one of two possible orientations, there is no such tool for general shapes. As we show in the paper, previous approaches fail to compute the orientation of even noiseless observations of simple shapes. We address this problem. In the paper, we show how to uniquely define the orientation of an arbitrary 2D shape, in terms of what we call its Principal Moments. We show that a small subset of these moments suffice to represent the underlying 2D shape and propose a new method to efficiently compute the shape orientation: Principal Moment Analysis. Finally, we discuss how this method can further be applied to normalize grey-level images. Besides the theoretical proof of correctness, we describe experiments demonstrating robustness to noise and illustrating the method with real images.Comment: 69 pages, 20 figure