arXiv subjects

Mathieu Salzmann

Publications and source records attributed to Mathieu Salzmann.

198 records · Page 11Linked to original sources

arXiv2016

Built-in Foreground/Background Prior for Weakly-Supervised Semantic Segmentation

Pixel-level annotations are expensive and time consuming to obtain. Hence, weak supervision using only image tags could have a significant impact in semantic segmentation. Recently, CNN-based methods have proposed to fine-tune pre-trained networks using image tags. Without additional information, this leads to poor localization accuracy. This problem, however, was alleviated by making use of objectness priors to generate foreground/background masks. Unfortunately these priors either require training pixel-level annotations/bounding boxes, or still yield inaccurate object boundaries. Here, we propose a novel method to extract markedly more accurate masks from the pre-trained network itself, forgoing external objectness modules. This is accomplished using the activations of the higher-level convolutional layers, smoothed by a dense CRF. We demonstrate that our method, based on these masks and a weakly-supervised loss, outperforms the state-of-the-art tag-based weakly-supervised semantic segmentation techniques. Furthermore, we introduce a new form of inexpensive weak supervision yielding an additional accuracy boost.

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arXiv2016

Semantic-Aware Depth Super-Resolution in Outdoor Scenes

While depth sensors are becoming increasingly popular, their spatial resolution often remains limited. Depth super-resolution therefore emerged as a solution to this problem. Despite much progress, state-of-the-art techniques suffer from two drawbacks: (i) they rely on the assumption that intensity edges coincide with depth discontinuities, which, unfortunately, is only true in controlled environments; and (ii) they typically exploit the availability of high-resolution training depth maps, which can often not be acquired in practice due to the sensors' limitations. By contrast, here, we introduce an approach to performing depth super-resolution in more challenging conditions, such as in outdoor scenes. To this end, we first propose to exploit semantic information to better constrain the super-resolution process. In particular, we design a co-sparse analysis model that learns filters from joint intensity, depth and semantic information. Furthermore, we show how low-resolution training depth maps can be employed in our learning strategy. We demonstrate the benefits of our approach over state-of-the-art depth super-resolution methods on two outdoor scene datasets.

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arXiv2016

Dimensionality Reduction on SPD Manifolds: The Emergence of Geometry-Aware Methods

Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks. Unfortunately, computation on the Riemannian manifold of SPD matrices -especially of high-dimensional ones- comes at a high cost that limits the applicability of existing techniques. In this paper, we introduce algorithms able to handle high-dimensional SPD matrices by constructing a lower-dimensional SPD manifold. To this end, we propose to model the mapping from the high-dimensional SPD manifold to the low-dimensional one with an orthonormal projection. This lets us formulate dimensionality reduction as the problem of finding a projection that yields a low-dimensional manifold either with maximum discriminative power in the supervised scenario, or with maximum variance of the data in the unsupervised one. We show that learning can be expressed as an optimization problem on a Grassmann manifold and discuss fast solutions for special cases. Our evaluation on several classification tasks evidences that our approach leads to a significant accuracy gain over state-of-the-art methods.

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arXiv2016

Structured Prediction of 3D Human Pose with Deep Neural Networks

Most recent approaches to monocular 3D pose estimation rely on Deep Learning. They either train a Convolutional Neural Network to directly regress from image to 3D pose, which ignores the dependencies between human joints, or model these dependencies via a max-margin structured learning framework, which involves a high computational cost at inference time. In this paper, we introduce a Deep Learning regression architecture for structured prediction of 3D human pose from monocular images that relies on an overcomplete auto-encoder to learn a high-dimensional latent pose representation and account for joint dependencies. We demonstrate that our approach outperforms state-of-the-art ones both in terms of structure preservation and prediction accuracy.

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arXiv2016

Sample and Filter: Nonparametric Scene Parsing via Efficient Filtering

Scene parsing has attracted a lot of attention in computer vision. While parametric models have proven effective for this task, they cannot easily incorporate new training data. By contrast, nonparametric approaches, which bypass any learning phase and directly transfer the labels from the training data to the query images, can readily exploit new labeled samples as they become available. Unfortunately, because of the computational cost of their label transfer procedures, state-of-the-art nonparametric methods typically filter out most training images to only keep a few relevant ones to label the query. As such, these methods throw away many images that still contain valuable information and generally obtain an unbalanced set of labeled samples. In this paper, we introduce a nonparametric approach to scene parsing that follows a sample-and-filter strategy. More specifically, we propose to sample labeled superpixels according to an image similarity score, which allows us to obtain a balanced set of samples. We then formulate label transfer as an efficient filtering procedure, which lets us exploit more labeled samples than existing techniques. Our experiments evidence the benefits of our approach over state-of-the-art nonparametric methods on two benchmark datasets.

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arXiv2016

Robust Multi-body Feature Tracker: A Segmentation-free Approach

Feature tracking is a fundamental problem in computer vision, with applications in many computer vision tasks, such as visual SLAM and action recognition. This paper introduces a novel multi-body feature tracker that exploits a multi-body rigidity assumption to improve tracking robustness under a general perspective camera model. A conventional approach to addressing this problem would consist of alternating between solving two subtasks: motion segmentation and feature tracking under rigidity constraints for each segment. This approach, however, requires knowing the number of motions, as well as assigning points to motion groups, which is typically sensitive to the motion estimates. By contrast, here, we introduce a segmentation-free solution to multi-body feature tracking that bypasses the motion assignment step and reduces to solving a series of subproblems with closed-form solutions. Our experiments demonstrate the benefits of our approach in terms of tracking accuracy and robustness to noise.

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arXiv2015

Structured Depth Prediction in Challenging Monocular Video Sequences

In this paper, we tackle the problem of estimating the depth of a scene from a monocular video sequence. In particular, we handle challenging scenarios, such as non-translational camera motion and dynamic scenes, where traditional structure from motion and motion stereo methods do not apply. To this end, we first study the problem of depth estimation from a single image. In this context, we exploit the availability of a pool of images for which the depth is known, and formulate monocular depth estimation as a discrete-continuous optimization problem, where the continuous variables encode the depth of the superpixels in the input image, and the discrete ones represent relationships between neighboring superpixels. The solution to this discrete-continuous optimization problem is obtained by performing inference in a graphical model using particle belief propagation. To handle video sequences, we then extend our single image model to a two-frame one that naturally encodes short-range temporal consistency and inherently handles dynamic objects. Based on the prediction of this model, we then introduce a fully-connected pairwise CRF that accounts for longer range spatio-temporal interactions throughout a video. We demonstrate the effectiveness of our model in both the indoor and outdoor scenarios.

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arXiv2015

Beyond Gauss: Image-Set Matching on the Riemannian Manifold of PDFs

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs) using kernel density estimators. To compare and match image-sets, we exploit Csiszar f-divergences, which bear strong connections to the geodesic distance defined on the space of PDFs, i.e., the statistical manifold. Furthermore, we introduce valid positive definite kernels on the statistical manifolds, which let us make use of more powerful classification schemes to match image-sets. Finally, we introduce a supervised dimensionality reduction technique that learns a latent space where f-divergences reflect the class labels of the data. Our experiments on diverse problems, such as video-based face recognition and dynamic texture classification, evidence the benefits of our approach over the state-of-the-art image-set matching methods.

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arXiv2015

When VLAD met Hilbert

Vectors of Locally Aggregated Descriptors (VLAD) have emerged as powerful image/video representations that compete with or even outperform state-of-the-art approaches on many challenging visual recognition tasks. In this paper, we address two fundamental limitations of VLAD: its requirement for the local descriptors to have vector form and its restriction to linear classifiers due to its high-dimensionality. To this end, we introduce a kernelized version of VLAD. This not only lets us inherently exploit more sophisticated classification schemes, but also enables us to efficiently aggregate non-vector descriptors (e.g., tensors) in the VLAD framework. Furthermore, we propose three approximate formulations that allow us to accelerate the coding process while still benefiting from the properties of kernel VLAD. Our experiments demonstrate the effectiveness of our approach at handling manifold-valued data, such as covariance descriptors, on several classification tasks. Our results also evidence the benefits of our nonlinear VLAD descriptors against the linear ones in Euclidean space using several standard benchmark datasets.

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arXiv2015

Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernels

In this paper, we develop an approach to exploiting kernel methods with manifold-valued data. In many computer vision problems, the data can be naturally represented as points on a Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, usual Euclidean computer vision and machine learning algorithms yield inferior results on such data. In this paper, we define Gaussian radial basis function (RBF)-based positive definite kernels on manifolds that permit us to embed a given manifold with a corresponding metric in a high dimensional reproducing kernel Hilbert space. These kernels make it possible to utilize algorithms developed for linear spaces on nonlinear manifold-valued data. Since the Gaussian RBF defined with any given metric is not always positive definite, we present a unified framework for analyzing the positive definiteness of the Gaussian RBF on a generic metric space. We then use the proposed framework to identify positive definite kernels on two specific manifolds commonly encountered in computer vision: the Riemannian manifold of symmetric positive definite matrices and the Grassmann manifold, i.e., the Riemannian manifold of linear subspaces of a Euclidean space. We show that many popular algorithms designed for Euclidean spaces, such as support vector machines, discriminant analysis and principal component analysis can be generalized to Riemannian manifolds with the help of such positive definite Gaussian kernels.

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arXiv2014

Kernel Methods on the Riemannian Manifold of Symmetric Positive Definite Matrices

Symmetric Positive Definite (SPD) matrices have become popular to encode image information. Accounting for the geometry of the Riemannian manifold of SPD matrices has proven key to the success of many algorithms. However, most existing methods only approximate the true shape of the manifold locally by its tangent plane. In this paper, inspired by kernel methods, we propose to map SPD matrices to a high dimensional Hilbert space where Euclidean geometry applies. To encode the geometry of the manifold in the mapping, we introduce a family of provably positive definite kernels on the Riemannian manifold of SPD matrices. These kernels are derived from the Gaussian ker- nel, but exploit different metrics on the manifold. This lets us extend kernel-based algorithms developed for Euclidean spaces, such as SVM and kernel PCA, to the Riemannian manifold of SPD matrices. We demonstrate the benefits of our approach on the problems of pedestrian detection, ob- ject categorization, texture analysis, 2D motion segmentation and Diffusion Tensor Imaging (DTI) segmentation.

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arXiv2014

A Framework for Shape Analysis via Hilbert Space Embedding

We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these spaces, most existing shape classification algorithms resort to nearest neighbor methods and to learning distances on shape spaces. Here, we propose to map shapes on Kendall's shape manifold to a high dimensional Hilbert space where Euclidean geometry applies. To this end, we introduce a kernel on this manifold that permits such a mapping, and prove its positive definiteness. This kernel lets us extend kernel-based algorithms developed for Euclidean spaces, such as SVM, MKL and kernel PCA, to the shape manifold. We demonstrate the benefits of our approach over the state-of-the-art methods on shape classification, clustering and retrieval.

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arXiv2014

Optimizing Over Radial Kernels on Compact Manifolds

We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However, the number of known positive definite kernels on manifolds remain very limited. Furthermore, most kernels typically depend on at least one parameter that needs to be tuned for the problem at hand. A poor choice of kernel, or of parameter value, may yield significant performance drop-off. Here, we show that positive definite radial kernels on the unit n-sphere, the Grassmann manifold and Kendall's shape manifold can be expressed in a simple form whose parameters can be automatically optimized within a support vector machine framework. We demonstrate the benefits of our kernel learning algorithm on object, face, action and shape recognition.

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arXiv2014

Iteratively Reweighted Graph Cut for Multi-label MRFs with Non-convex Priors

While widely acknowledged as highly effective in computer vision, multi-label MRFs with non-convex priors are difficult to optimize. To tackle this, we introduce an algorithm that iteratively approximates the original energy with an appropriately weighted surrogate energy that is easier to minimize. Our algorithm guarantees that the original energy decreases at each iteration. In particular, we consider the scenario where the global minimizer of the weighted surrogate energy can be obtained by a multi-label graph cut algorithm, and show that our algorithm then lets us handle of large variety of non-convex priors. We demonstrate the benefits of our method over state-of-the-art MRF energy minimization techniques on stereo and inpainting problems.

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arXiv2014

From Manifold to Manifold: Geometry-Aware Dimensionality Reduction for SPD Matrices

Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian manifold of SPD matrices --especially of high-dimensional ones-- comes at a high cost that limits the applicability of existing techniques. In this paper we introduce an approach that lets us handle high-dimensional SPD matrices by constructing a lower-dimensional, more discriminative SPD manifold. To this end, we model the mapping from the high-dimensional SPD manifold to the low-dimensional one with an orthonormal projection. In particular, we search for a projection that yields a low-dimensional manifold with maximum discriminative power encoded via an affinity-weighted similarity measure based on metrics on the manifold. Learning can then be expressed as an optimization problem on a Grassmann manifold. Our evaluation on several classification tasks shows that our approach leads to a significant accuracy gain over state-of-the-art methods.

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arXiv2014

Kernel Coding: General Formulation and Special Cases

Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are typically entangled. In contrast, here, we study the problem of performing coding in a high-dimensional Hilbert space, where the classes are expected to be more easily separable. To this end, we introduce a general coding formulation that englobes the most popular techniques, such as bag of words, sparse coding and locality-based coding, and show how this formulation and its special cases can be kernelized. Importantly, we address several aspects of learning in our general formulation, such as kernel learning, dictionary learning and supervised kernel coding. Our experimental evaluation on several visual recognition tasks demonstrates the benefits of performing coding in Hilbert space, and in particular of jointly learning the kernel, the dictionary and the classifier.

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arXiv2014

Expanding the Family of Grassmannian Kernels: An Embedding Perspective

Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g, support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as we will show- is universal, which limits their ability to approximate a target function arbitrarily well. Here, we introduce several positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing.

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arXiv2014

Bregman Divergences for Infinite Dimensional Covariance Matrices

We introduce an approach to computing and comparing Covariance Descriptors (CovDs) in infinite-dimensional spaces. CovDs have become increasingly popular to address classification problems in computer vision. While CovDs offer some robustness to measurement variations, they also throw away part of the information contained in the original data by only retaining the second-order statistics over the measurements. Here, we propose to overcome this limitation by first mapping the original data to a high-dimensional Hilbert space, and only then compute the CovDs. We show that several Bregman divergences can be computed between the resulting CovDs in Hilbert space via the use of kernels. We then exploit these divergences for classification purposes. Our experiments demonstrate the benefits of our approach on several tasks, such as material and texture recognition, person re-identification, and action recognition from motion capture data.

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