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19
SIFTBased Local Image Description using Sparse Representations
 in "Proceedings of the IEEE International Workshop on Multimedia Signal Processing (MMSP09), Rio de Janeiro
, 2009
"... Abstract—This paper addresses the problem of efficient SIFTbased image description and searches in large databases within the framework of local querying. A descriptor called the bagoffeatures has been introduced in [1] which first vector quantizes SIFT descriptors and then aggregates the set of re ..."
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Abstract—This paper addresses the problem of efficient SIFTbased image description and searches in large databases within the framework of local querying. A descriptor called the bagoffeatures has been introduced in [1] which first vector quantizes SIFT descriptors and then aggregates the set of resulting codeword indices (socalled visual words) into a histogram of occurence of the different visual words in the image. The aim is to make the image search complexity tractable by transforming the set of local image descriptor vectors into a single sparse vector as sparsity particularly permits efficient inner product calculations. However, aggregating local descriptors into a single histogram decreases the discerning power of the system when performing local queries. In this paper, we propose a new approach that aims to enjoy the complexity benefits of sparsity while at the same time retaining the local quality of the input descriptor vectors. This is accomplished by searching for a sparse approximation of the input SIFT descriptors. The sparse approximation yields a sparse vector per local SIFT descriptor, and helps preserving local description properties by using each sparsetransformed descriptor independently in a voting system to retrieve indexed images. Our system is shown experimentally to perform better than histogram based systems under query locality, albeit at an increased complexity. I.
OPTIMAL IMAGE ALIGNMENT WITH RANDOM MEASUREMENTS
"... We consider the problem of image alignment using random measurements. More specifically, this paper is concerned with estimating a transformation that aligns a given reference image with a query image, assuming that not the images themselves but only random measurements are available. According to t ..."
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We consider the problem of image alignment using random measurements. More specifically, this paper is concerned with estimating a transformation that aligns a given reference image with a query image, assuming that not the images themselves but only random measurements are available. According to the theory behind compressed sensing, random projections of signal manifolds nearly preserve pairwise Euclidean distances when the reduced space is sufficiently large. This suggests that image alignment can be performed effectively based on a sufficient number of random measurements. We build on our previous work in order to show that the corresponding objective function can be decomposed as the difference of two convex functions (DC). Thus, the optimization problem becomes equivalent to a DC program that can be solved by an outerapproximation cutting plane method, which always converges to the globally optimal solution.
1 Discretization of Parametrizable Signal Manifolds
"... Abstract—Transformationinvariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several transformation manifolds representing different classes ..."
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Abstract—Transformationinvariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several transformation manifolds representing different classes provides essential information for the classification of the signal. In many applications the computation of the exact distance to the manifold is costly, whereas an efficient practical solution is the approximation of the manifold distance with the aid of a manifold grid. In this paper, we consider a setting with transformation manifolds of known parameterization. We first present an algorithm for the selection of samples from a single manifold that permits to minimize the average error in the manifold distance estimation. Then we propose a method for the joint discretization of multiple manifolds that represent different signal classes, where we optimize the transformationinvariant classification accuracy yielded by the discrete manifold representation. Experimental results show that sampling each manifold individually by minimizing the manifold distance estimation error outperforms baseline sampling solutions with respect to registration and classification accuracy. Performing an additional joint optimization on all samples improves the classification performance further. Moreover, given a fixed total number of samples to be selected from all manifolds, an asymmetric distribution of samples to different manifolds depending on their geometric structures may also increase the classification accuracy in comparison with the equal distribution of samples. Index Terms—Manifold discretization, transformation manifolds, manifold distance, pattern transformations, pattern classification I.
Optimal image alignment with random projections of manifolds: algorithm and geometric analysis
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LEARNING PATTERN TRANSFORMATION MANIFOLDS WITH PARAMETRIC ATOM SELECTION
"... We address the problem of building a manifold in order to represent a set of geometrically transformed images by selecting a good common sparse approximation of them with parametric atoms. We propose a greedy method to construct a representative pattern such that the total distance between the trans ..."
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We address the problem of building a manifold in order to represent a set of geometrically transformed images by selecting a good common sparse approximation of them with parametric atoms. We propose a greedy method to construct a representative pattern such that the total distance between the transformation manifold of the representative pattern and the input images is minimized. In the progressive construction of the pattern we select atoms from a continuous dictionary by optimizing the atom parameters. Experimental results suggest that the representative pattern built with the proposed method provides an accurate representation of data, where the invariance to geometric transformations is achieved due to the transformation manifold model.
A GEOMETRIC FRAMEWORK FOR REGISTRATION OF SPARSE IMAGES
"... We examine the problem of image registration when images have a sparse representation in a dictionary of geometric features. We propose a novel algorithm for aligning images by pairing their sparse components. We show numerically that this algorithm works well in practice and analyze key properties ..."
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We examine the problem of image registration when images have a sparse representation in a dictionary of geometric features. We propose a novel algorithm for aligning images by pairing their sparse components. We show numerically that this algorithm works well in practice and analyze key properties on the dictionary that drive the registration performance. We compare these properties to existing characterizations of redundant dictionaries (i.e., coherence, restricted isometry property) and show that the newly introduced properties finely capture the behaviour of our registration algorithm. Index Terms — Image alignment, sparse approximation, parametric dictionary, dictionary properties.
APPROXIMATION OF PATTERN TRANSFORMATION MANIFOLDS WITH PARAMETRIC DICTIONARIES
"... The construction of lowdimensional models explaining highdimensional signal observations provides concise and efficient data representations. In this paper, we focus on pattern transformation manifold models generated by inplane geometric transformations of 2D visual patterns. We propose a method ..."
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The construction of lowdimensional models explaining highdimensional signal observations provides concise and efficient data representations. In this paper, we focus on pattern transformation manifold models generated by inplane geometric transformations of 2D visual patterns. We propose a method for computing a manifold by building a representative pattern such that its transformation manifold accurately fits a set of given observations. We present a solution for the progressive construction of the representative pattern with the aid of a parametric dictionary, which in turn provides an analytical representation of the data and the manifold. Experimental results show that the patterns learned with the proposed algorithm can efficiently capture the main characteristics of the input data with high approximation accuracy, where the invariance to the geometric transformations of the data is accomplished due to the transformation manifold model. Index Terms — Pattern transformation manifolds, manifold learning, dimensionality reduction, matching pursuit, sparse representations
Distancebased discretization of parametric signal manifolds
 in IEEE International Conference on Acoustics, Speech and Signal Processing
, 2010
"... The characterization of signals and images in manifolds often lead to efficient dimensionality reduction algorithms based on manifold distance computation for analysis or classification tasks. We propose in this paper a method for the discretization of signal manifolds given in a parametric form. We ..."
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The characterization of signals and images in manifolds often lead to efficient dimensionality reduction algorithms based on manifold distance computation for analysis or classification tasks. We propose in this paper a method for the discretization of signal manifolds given in a parametric form. We present an iterative algorithm for the selection of samples on the manifold that permits to minimize the average error in the manifold distance computation. Experimental results with image appearance manifolds demonstrate that the proposed discretization algorithm outperforms baseline solutions based on random or regular sampling, both in terms of projection accuracy and image registration. Index Terms — Manifold discretization, image appearance manifolds, manifold distance, pattern transformations
An unsupervised algorithm for learning . . .
, 2011
"... We present several theoretical contributions which allow Lie group, or continuous transformation, models to be fit to large high dimensional datasets. We then demonstrate training of Lie group models on natural video. Transformation operators are represented in their eigenbasis, reducing the compu ..."
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We present several theoretical contributions which allow Lie group, or continuous transformation, models to be fit to large high dimensional datasets. We then demonstrate training of Lie group models on natural video. Transformation operators are represented in their eigenbasis, reducing the computational complexity of parameter estimation to that of training a linear transformation model. A transformation specific “blurring” operator is introduced that allows inference to escape local minima via a smoothing of the transformation space. A penalty on traversed manifold distance is added which encourages the discovery of sparse, minimal distance, transformations between states.