arXiv subjects

Christine Guillemot

Publications and source records attributed to Christine Guillemot.

26 records · Page 2Linked to original sources

arXiv2018

A study of the classification of low-dimensional data with supervised manifold learning

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of supervised manifold learning for classification. We consider nonlinear dimensionality reduction algorithms that yield linearly separable embeddings of training data and present generalization bounds for this type of algorithms. A necessary condition for satisfactory generalization performance is that the embedding allow the construction of a sufficiently regular interpolation function in relation with the separation margin of the embedding. We show that for supervised embeddings satisfying this condition, the classification error decays at an exponential rate with the number of training samples. Finally, we examine the separability of supervised nonlinear embeddings that aim to preserve the low-dimensional geometric structure of data based on graph representations. The proposed analysis is supported by experiments on several real data sets.

cs.LG↗

arXiv2016

Scalable image coding based on epitomes

In this paper, we propose a novel scheme for scalable image coding based on the concept of epitome. An epitome can be seen as a factorized representation of an image. Focusing on spatial scalability, the enhancement layer of the proposed scheme contains only the epitome of the input image. The pixels of the enhancement layer not contained in the epitome are then restored using two approaches inspired from local learning-based super-resolution methods. In the first method, a locally linear embedding model is learned on base layer patches and then applied to the corresponding epitome patches to reconstruct the enhancement layer. The second approach learns linear mappings between pairs of co-located base layer and epitome patches. Experiments have shown that significant improvement of the rate-distortion performances can be achieved compared to an SHVC reference.

cs.CV↗

arXiv2016

Geometry-Aware Neighborhood Search for Learning Local Models for Image Reconstruction

Local learning of sparse image models has proven to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean distance as a dissimilarity metric. However, the Euclidean distance may not always be a good dissimilarity measure for comparing data samples lying on a manifold. In this paper, we propose two algorithms for determining a local subset of training samples from which a good local model can be computed for reconstructing a given input test sample, where we take into account the underlying geometry of the data. The first algorithm, called Adaptive Geometry-driven Nearest Neighbor search (AGNN), is an adaptive scheme which can be seen as an out-of-sample extension of the replicator graph clustering method for local model learning. The second method, called Geometry-driven Overlapping Clusters (GOC), is a less complex nonadaptive alternative for training subset selection. The proposed AGNN and GOC methods are evaluated in image super-resolution, deblurring and denoising applications and shown to outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings.

cs.CV↗

arXiv2015

Face Hallucination using Linear Models of Coupled Sparse Support

Most face super-resolution methods assume that low-resolution and high-resolution manifolds have similar local geometrical structure, hence learn local models on the lowresolution manifolds (e.g. sparse or locally linear embedding models), which are then applied on the high-resolution manifold. However, the low-resolution manifold is distorted by the oneto-many relationship between low- and high- resolution patches. This paper presents a method which learns linear models based on the local geometrical structure on the high-resolution manifold rather than on the low-resolution manifold. For this, in a first step, the low-resolution patch is used to derive a globally optimal estimate of the high-resolution patch. The approximated solution is shown to be close in Euclidean space to the ground-truth but is generally smooth and lacks the texture details needed by state-ofthe-art face recognizers. This first estimate allows us to find the support of the high-resolution manifold using sparse coding (SC), which are then used as support for learning a local projection (or upscaling) model between the low-resolution and the highresolution manifolds using Multivariate Ridge Regression (MRR). Experimental results show that the proposed method outperforms six face super-resolution methods in terms of both recognition and quality. These results also reveal that the recognition and quality are significantly affected by the method used for stitching all super-resolved patches together, where quilting was found to better preserve the texture details which helps to achieve higher recognition rates.

cs.CV↗

arXiv2015

Out-of-sample generalizations for supervised manifold learning for classification

Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes in the learned embedding. Most nonlinear supervised manifold learning methods compute the embedding of the manifolds only at the initially available training points, while the generalization of the embedding to novel points, known as the out-of-sample extension problem in manifold learning, becomes especially important in classification applications. In this work, we propose a semi-supervised method for building an interpolation function that provides an out-of-sample extension for general supervised manifold learning algorithms studied in the context of classification. The proposed algorithm computes a radial basis function (RBF) interpolator that minimizes an objective function consisting of the total embedding error of unlabeled test samples, defined as their distance to the embeddings of the manifolds of their own class, as well as a regularization term that controls the smoothness of the interpolation function in a direction-dependent way. The class labels of test data and the interpolation function parameters are estimated jointly with a progressive procedure. Experimental results on face and object images demonstrate the potential of the proposed out-of-sample extension algorithm for the classification of manifold-modeled data sets.

cs.CV↗

arXiv2008

Information-theoretic resolution of perceptual WSS watermarking of non i.i.d. Gaussian signals

The theoretical foundations of data hiding have been revealed by formulating the problem as message communication over a noisy channel. We revisit the problem in light of a more general characterization of the watermark channel and of weighted distortion measures. Considering spread spectrum based information hiding, we release the usual assumption of an i.i.d. cover signal. The game-theoretic resolution of the problem reveals a generalized characterization of optimum attacks. The paper then derives closed-form expressions for the different parameters exhibiting a practical embedding and extraction technique.

cs.IT↗

arXiv2006

Synchronization recovery and state model reduction for soft decoding of variable length codes

Variable length codes exhibit de-synchronization problems when transmitted over noisy channels. Trellis decoding techniques based on Maximum A Posteriori (MAP) estimators are often used to minimize the error rate on the estimated sequence. If the number of symbols and/or bits transmitted are known by the decoder, termination constraints can be incorporated in the decoding process. All the paths in the trellis which do not lead to a valid sequence length are suppressed. This paper presents an analytic method to assess the expected error resilience of a VLC when trellis decoding with a sequence length constraint is used. The approach is based on the computation, for a given code, of the amount of information brought by the constraint. It is then shown that this quantity as well as the probability that the VLC decoder does not re-synchronize in a strict sense, are not significantly altered by appropriate trellis states aggregation. This proves that the performance obtained by running a length-constrained Viterbi decoder on aggregated state models approaches the one obtained with the bit/symbol trellis, with a significantly reduced complexity. It is then shown that the complexity can be further decreased by projecting the state model on two state models of reduced size.

cs.NI↗

arXiv2005

Entropy coding with Variable Length Re-writing Systems

This paper describes a new set of block source codes well suited for data compression. These codes are defined by sets of productions rules of the form a.l->b, where a in A represents a value from the source alphabet A and l, b are -small- sequences of bits. These codes naturally encompass other Variable Length Codes (VLCs) such as Huffman codes. It is shown that these codes may have a similar or even a shorter mean description length than Huffman codes for the same encoding and decoding complexity. A first code design method allowing to preserve the lexicographic order in the bit domain is described. The corresponding codes have the same mean description length (mdl) as Huffman codes from which they are constructed. Therefore, they outperform from a compression point of view the Hu-Tucker codes designed to offer the lexicographic property in the bit domain. A second construction method allows to obtain codes such that the marginal bit probability converges to 0.5 as the sequence length increases and this is achieved even if the probability distribution function is not known by the encoder.

cs.IT↗