Section: New Results
Machine learning for computer vision
Online Matrix Factorization for Sparse Coding (J. Mairal, F. Bach, J. Ponce, joint work with G. Sapiro, University of Minnesota)
Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set, adapting it to specific data. Variations of this problem include dictionary learning in signal processing, non-negative matrix factorization and sparse principal component analysis. In this work, we propose to address these tasks with a new online optimization algorithm, based on stochastic approximations, which scales up gracefully to large datasets with millions of training samples, and extends naturally to various matrix factorization formulations, making it suitable for a wide range of learning problems. Experiments with natural images and genomic data demonstrates that it leads to state-of-the-art performance in terms of speed and optimization for both small and large datasets.
A software implementing these algorithms has been developed and registered at APP under the name SPAMS (Sparse Modeling Software).
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Vanishing point detection for road detection (H. Kong, J.-Y. Audibert and J. Ponce)
Given a single image of an arbitrary road, that may not be well-paved, or have clearly delineated edges, or some a priori known color or texture distribution, is it possible for a computer to find this road? In [35] , we address this question by decomposing the road detection process into two steps: the estimation of the vanishing point associated with the main (straight) part of the road, followed by the segmentation of the corresponding road area based on the detected vanishing point. The main technical contributions of the proposed approach are a novel adaptive soft voting scheme based on variable-sized voting region using confidence-weighted Gabor filters, which compute the dominant texture orientation at each pixel, and a new vanishing-point-constrained edge detection technique for detecting road boundaries. The proposed method has been implemented, and experiments with 1003 general road images demonstrate that it is both computationally efficient and effective at detecting road regions in challenging conditions (see Figure 11 ).
Transductive segmentation of textured meshes (J.-Y. Audibert, joint work with A.-L. Jachiet, J.-P. Pons and R. Keriven)
In [25] , we address the problem of segmenting a textured mesh into objects or object classes, consistently with user-supplied seeds. We view this task as transductive learning and use the flexibility of kernel-based weights to incorporate a various number of diverse features. Our method combines a Laplacian graph regularizer that enforces spatial coherence in label propagation and an SVM classifier that ensures dissemination of the seeds characteristics. Our interactive framework allows to easily specify classes seeds with sketches drawn on the mesh and potentially refine the segmentation. We obtain qualitatively good segmentations on several architectural scenes and show the applicability of our method to outliers removing (see Figure 12 ).
