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Furukawa Y.,Google | Ponce J.,CNRS ENS Informatics Department
IEEE Transactions on Pattern Analysis and Machine Intelligence | Year: 2010

This paper proposes a novel algorithm for multiview stereopsis that outputs a dense set of small rectangular patches covering the surfaces visible in the images. Stereopsis is implemented as a match, expand, and filter procedure, starting from a sparse set of matched keypoints, and repeatedly expanding these before using visibility constraints to filter away false matches. The keys to the performance of the proposed algorithm are effective techniques for enforcing local photometric consistency and global visibility constraints. Simple but effective methods are also proposed to turn the resulting patch model into a mesh which can be further refined by an algorithm that enforces both photometric consistency and regularization constraints. The proposed approach automatically detects and discards outliers and obstacles and does not require any initialization in the form of a visual hull, a bounding box, or valid depth ranges. We have tested our algorithm on various data sets including objects with fine surface details, deep concavities, and thin structures, outdoor scenes observed from a restricted set of viewpoints, and crowded scenes where moving obstacles appear in front of a static structure of interest. A quantitative evaluation on the Middlebury benchmark [CHECK END OF SENTENCE] shows that the proposed method outperforms all others submitted so far for four out of the six data sets. © 2010 IEEE. Source

Arlot S.,CNRS ENS Informatics Department | Celisse A.,Lille University of Science and Technology
Statistics and Computing | Year: 2011

This paper tackles the problem of detecting abrupt changes in the mean of a heteroscedastic signal by model selection, without knowledge on the variations of the noise. A new family of change-point detection procedures is proposed, showing that cross-validation methods can be successful in the heteroscedastic framework, whereas most existing procedures are not robust to heteroscedasticity. The robustness to heteroscedasticity of the proposed procedures is supported by an extensive simulation study, together with recent partial theoretical results. An application to Comparative Genomic Hybridization (CGH) data is provided, showing that robustness to heteroscedasticity can indeed be required for their analysis. © 2010 Springer Science+Business Media, LLC. Source

Bach F.,CNRS ENS Informatics Department
Journal of Machine Learning Research | Year: 2014

In this paper, we consider supervised learning problems such as logistic regression and study the stochastic gradient method with averaging, in the usual stochastic approximation setting where observations are used only once. We show that after N iterations, with a constant step-size proportional to 1=R 2 √N where N is the number of observations and R is the maximum norm of the observations, the convergence rate is always of order O(1= √N), and improves to O(R2=μN) where μ is the lowest eigenvalue of the Hessian at the global optimum (when this eigenvalue is greater than R2= √N). Since μ does not need to be known in advance, this shows that averaged stochastic gradient is adaptive to unknown local strong convexity of the objective function. Our proof relies on the generalized selfconcordance properties of the logistic loss and thus extends to all generalized linear models with uniformly bounded features. © 2014 Francis Bach. Source

Philbin J.,University of Oxford | Sivic J.,CNRS ENS Informatics Department | Zisserman A.,University of Oxford
International Journal of Computer Vision | Year: 2011

Given a large-scale collection of images our aim is to efficiently associate images which contain the same entity, for example a building or object, and to discover the significant entities. To achieve this, we introduce the Geometric Latent Dirichlet Allocation (gLDA) model for unsupervised discovery of particular objects in unordered image collections. This explicitly represents images as mixtures of particular objects or facades, and builds rich latent topic models which incorporate the identity and locations of visual words specific to the topic in a geometrically consistent way. Applying standard inference techniques to this model enables images likely to contain the same object to be probabilistically grouped and ranked. Additionally, to reduce the computational cost of applying the gLDA model to large datasets, we propose a scalable method that first computes a matching graph over all the images in a dataset. This matching graph connects images that contain the same object, and rough image groups can be mined from this graph using standard clustering techniques. The gLDA model can then be applied to generate a more nuanced representation of the data. We also discuss how "hub images" (images representative of an object or landmark) can easily be extracted from our matching graph representation. We evaluate our techniques on the publicly available Oxford buildings dataset (5K images) and show examples of automatically mined objects. The methods are evaluated quantitatively on this dataset using a ground truth labeling for a number of Oxford landmarks. To demonstrate the scalability of the matching graph method, we show qualitative results on two larger datasets of images taken of the Statue of Liberty (37K images) and Rome (1M+ images). © 2010 Springer Science+Business Media, LLC. Source

Bach F.,CNRS ENS Informatics Department
SIAM Journal on Optimization | Year: 2015

Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is done through convex duality and implies notably that for certain problems, such as for supervised machine learning problems with nonsmooth losses or problems regularized by nonsmooth regularizers, the primal subgradient method and the dual conditional gradient method are formally equivalent. The dual interpretation leads to a form of line search for mirror descent, as well as guarantees of convergence for primal-dual certificates. © 2015 Society for Industrial and Applied Mathematics. Source

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