Segmentation Given Partial Grouping Constraints

We consider data clustering problems where partial grouping is known a priori. We formulate such biased grouping problems as a constrained optimization problem, where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping. We enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data. Considering the normalized cuts criterion in particular, our formulation leads to a constrained eigenvalue problem. By generalizing the Rayleigh-Ritz theorem to projected matrices, we find the global optimum in the relaxed continuous domain by eigendecomposition, from which a near-global optimum to the discrete labeling problem can be obtained effectively. We apply our method to real image segmentation problems, where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations. We demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process, but also that objects can be segregated from the background without specific object knowledge

Solving Markov Random Fields with Spectral Relaxation

Markov Random Fields (MRFs) are used in a large array of computer vision and maching learning applications. Finding the Maximum Aposteriori (MAP) solution of an MRF is in general intractable, and one has to resort to approximate solutions, such as Belief Prop- agation, Graph Cuts, or more recently, ap- proaches based on quadratic programming. We propose a novel type of approximation, Spectral relaxation to Quadratic Program- ming (SQP). We show our method offers tighter bounds than recently published work, while at the same time being computationally efficient. We compare our method to other algorithms on random MRFs in various settings

Spectral Segmentation with Multiscale Graph Decomposition

We present a multiscale spectral image segmentation algorithm. In contrast to most multiscale image processing, this algorithm works on multiple scales of the image in parallel, without iteration, to capture both coarse and fine level details. The algorithm is computationally efficient, allowing to segment large images. We use the Normalized Cut graph partitioning framework of image segmentation. We construct a graph encoding pairwise pixel affinity, and partition the graph for image segmentation.We demonstrate that large image graphs can be compressed into multiple scales capturing image structure at increasingly large neighborhood. We show that the decomposition of the image segmentation graph into different scales can be determined by ecological statistics on the image grouping cues. Our segmentation algorithm works simultaneously across the graph scales, with an inter-scale constraint to ensure communication and consistency between the segmentations at each scale. As the results show, we incorporate long-range connections with linear-time complexity, providing high-quality segmentations efficiently. Images that previously could not be processed because of their size have been accurately segmented thanks to this method

Clustering Spectral avec Contraintes de Paires réglées par Noyaux Gaussiens

International audienceRésumé Nous considérons le problème du clustering spectral partielle-ment supervisé par des contraintes de la forme « must-link » et « cannot-link ». De telles contraintes apparaissent fréquemment dans divers pro-blèmes, comme la résolution de la coréférence en traitement automatique du langage naturel. L'approche développée dans ce papier consiste à ap-prendre une nouvelle représentation de l'espace pour les données, ainsi qu'une nouvelle distance dans cet espace. Cette représentation est ob-tenue via une transformation linéaire de l'enveloppe spectrale des don-nées. Les contraintes sont exprimées avec des fonctions Gaussiennes qui réajustent localement les similarités entre les objets. Un problème d'op-timisation global et non convexe est alors obtenu et l'apprentissage du modèle se fait grâce à des techniques de descentes de gradient. Nous évaluons notre algorithme sur des jeux de données standards et le com-parons à divers algorithmes de l'état de l'art, comme [14,18,32]. Les ré-sultats sur ces jeux de données, ainsi que sur le jeu de données de la tâche de coréférence CoNLL-2012, montrent que notre algorithme amé-liore significativement la qualité des clusters obtenus par les précédentes approches, et est plus robuste en montée en charge

Fast Gaussian Pairwise Constrained Spectral Clustering

International audienceWe consider the problem of spectral clustering with partial supervision in the form of must-link and cannot-link constraints. Such pairwise constraints are common in problems like coreference resolution in natural language processing. The approach developed in this paper is to learn a new representation space for the data together with a dis-tance in this new space. The representation space is obtained through a constraint-driven linear transformation of a spectral embedding of the data. Constraints are expressed with a Gaussian function that locally reweights the similarities in the projected space. A global, non-convex optimization objective is then derived and the model is learned via gradi-ent descent techniques. Our algorithm is evaluated on standard datasets and compared with state of the art algorithms, like [14,18,31]. Results on these datasets, as well on the CoNLL-2012 coreference resolution shared task dataset, show that our algorithm significantly outperforms related approaches and is also much more scalable