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Author |
Debora Gil; Petia Radeva |
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Title |
Shape Restoration via a Regularized Curvature Flow |
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Journal Article |
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2004 |
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Journal of Mathematical Imaging and Vision |
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21 |
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3 |
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205-223 |
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Any image filtering operator designed for automatic shape restoration should satisfy robustness (whatever the nature and degree of noise is) as well as non-trivial smooth asymptotic behavior. Moreover, a stopping criterion should be determined by characteristics of the evolved image rather than dependent on the number of iterations. Among the several PDE based techniques, curvature flows appear to be highly reliable for strongly noisy images compared to image diffusion processes.
In the present paper, we introduce a regularized curvature flow (RCF) that admits non-trivial steady states. It is based on a measure of the local curve smoothness that takes into account regularity of the curve curvature and serves as stopping term in the mean curvature flow. We prove that this measure decreases over the orbits of RCF, which endows the method with a natural stop criterion in terms of the magnitude of this measure. Further, in its discrete version it produces steady states consisting of piece-wise regular curves. Numerical experiments made on synthetic shapes corrupted with different kinds of noise show the abilities and limitations of each of the current geometric flows and the benefits of RCF. Finally, we present results on real images that illustrate the usefulness of the present approach in practical applications. |
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IAM;MILAB |
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IAM @ iam @ GiR2004c |
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1532 |
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Author |
Carme Julia; Angel Sappa; Felipe Lumbreras; Joan Serrat; Antonio Lopez |
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Title |
An iterative multiresolution scheme for SFM with missing data |
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Journal Article |
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Year |
2009 |
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Journal of Mathematical Imaging and Vision |
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JMIV |
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34 |
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3 |
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240–258 |
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Several techniques have been proposed for tackling the Structure from Motion problem through factorization in the case of missing data. However, when the percentage of unknown data is high, most of them may not perform as well as expected. Focussing on this problem, an iterative multiresolution scheme, which aims at recovering missing entries in the originally given input matrix, is proposed. Information recovered following a coarse-to-fine strategy is used for filling in the missing entries. The objective is to recover, as much as possible, missing data in the given matrix.
Thus, when a factorization technique is applied to the partially or totally filled in matrix, instead of to the originally given input one, better results will be obtained. An evaluation study about the robustness to missing and noisy data is reported.
Experimental results obtained with synthetic and real video sequences are presented to show the viability of the proposed approach. |
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ADAS |
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ADAS @ adas @ JSL2009a |
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1163 |
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Author |
Carme Julia; Angel Sappa; Felipe Lumbreras; Joan Serrat; Antonio Lopez |
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Title |
Rank Estimation in Missing Data Matrix Problems |
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Journal Article |
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2011 |
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Journal of Mathematical Imaging and Vision |
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JMIV |
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39 |
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2 |
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140-160 |
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A novel technique for missing data matrix rank estimation is presented. It is focused on matrices of trajectories, where every element of the matrix corresponds to an image coordinate from a feature point of a rigid moving object at a given frame; missing data are represented as empty entries. The objective of the proposed approach is to estimate the rank of a missing data matrix in order to fill in empty entries with some matrix completion method, without using or assuming neither the number of objects contained in the scene nor the kind of their motion. The key point of the proposed technique consists in studying the frequency behaviour of the individual trajectories, which are seen as 1D signals. The main assumption is that due to the rigidity of the moving objects, the frequency content of the trajectories will be similar after filling in their missing entries. The proposed rank estimation approach can be used in different computer vision problems, where the rank of a missing data matrix needs to be estimated. Experimental results with synthetic and real data are provided in order to empirically show the good performance of the proposed approach. |
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0924-9907 |
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ADAS |
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Admin @ si @ JSL2011; |
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1710 |
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Author |
Naveen Onkarappa; Angel Sappa |
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Title |
A Novel Space Variant Image Representation |
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Journal Article |
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2013 |
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Journal of Mathematical Imaging and Vision |
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JMIV |
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47 |
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1-2 |
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48-59 |
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Space-variant representation; Log-polar mapping; Onboard vision applications |
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Traditionally, in machine vision images are represented using cartesian coordinates with uniform sampling along the axes. On the contrary, biological vision systems represent images using polar coordinates with non-uniform sampling. For various advantages provided by space-variant representations many researchers are interested in space-variant computer vision. In this direction the current work proposes a novel and simple space variant representation of images. The proposed representation is compared with the classical log-polar mapping. The log-polar representation is motivated by biological vision having the characteristic of higher resolution at the fovea and reduced resolution at the periphery. On the contrary to the log-polar, the proposed new representation has higher resolution at the periphery and lower resolution at the fovea. Our proposal is proved to be a better representation in navigational scenarios such as driver assistance systems and robotics. The experimental results involve analysis of optical flow fields computed on both proposed and log-polar representations. Additionally, an egomotion estimation application is also shown as an illustrative example. The experimental analysis comprises results from synthetic as well as real sequences. |
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Springer US |
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0924-9907 |
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ADAS; 600.055; 605.203; 601.215 |
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Admin @ si @ OnS2013a |
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2243 |
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Author |
Maria Oliver; G. Haro; Mariella Dimiccoli; B. Mazin; C. Ballester |
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Title |
A Computational Model for Amodal Completion |
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Journal Article |
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2016 |
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Journal of Mathematical Imaging and Vision |
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JMIV |
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56 |
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3 |
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511–534 |
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Perception; visual completion; disocclusion; Bayesian model;relatability; Euler elastica |
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Abstract |
This paper presents a computational model to recover the most likely interpretation
of the 3D scene structure from a planar image, where some objects may occlude others. The estimated scene interpretation is obtained by integrating some global and local cues and provides both the complete disoccluded objects that form the scene and their ordering according to depth.
Our method first computes several distal scenes which are compatible with the proximal planar image. To compute these different hypothesized scenes, we propose a perceptually inspired object disocclusion method, which works by minimizing the Euler's elastica as well as by incorporating the relatability of partially occluded contours and the convexity of the disoccluded objects. Then, to estimate the preferred scene we rely on a Bayesian model and define probabilities taking into account the global complexity of the objects in the hypothesized scenes as well as the effort of bringing these objects in their relative position in the planar image, which is also measured by an Euler's elastica-based quantity. The model is illustrated with numerical experiments on, both, synthetic and real images showing the ability of our model to reconstruct the occluded objects and the preferred perceptual order among them. We also present results on images of the Berkeley dataset with provided figure-ground ground-truth labeling. |
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MILAB; 601.235 |
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Admin @ si @ OHD2016b |
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2745 |
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Author |
Katerine Diaz; Jesus Martinez del Rincon; Aura Hernandez-Sabate; Marçal Rusiñol; Francesc J. Ferri |
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Title |
Fast Kernel Generalized Discriminative Common Vectors for Feature Extraction |
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Journal Article |
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2018 |
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Journal of Mathematical Imaging and Vision |
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JMIV |
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60 |
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4 |
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512-524 |
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This paper presents a supervised subspace learning method called Kernel Generalized Discriminative Common Vectors (KGDCV), as a novel extension of the known Discriminative Common Vectors method with Kernels. Our method combines the advantages of kernel methods to model complex data and solve nonlinear
problems with moderate computational complexity, with the better generalization properties of generalized approaches for large dimensional data. These attractive combination makes KGDCV specially suited for feature extraction and classification in computer vision, image processing and pattern recognition applications. Two different approaches to this generalization are proposed, a first one based on the kernel trick (KT) and a second one based on the nonlinear projection trick (NPT) for even higher efficiency. Both methodologies
have been validated on four different image datasets containing faces, objects and handwritten digits, and compared against well known non-linear state-of-art methods. Results show better discriminant properties than other generalized approaches both linear or kernel. In addition, the KGDCV-NPT approach presents a considerable computational gain, without compromising the accuracy of the model. |
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DAG; ADAS; 600.086; 600.130; 600.121; 600.118; 600.129 |
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Admin @ si @ DMH2018a |
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3062 |
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Author |
Katerine Diaz; Jesus Martinez del Rincon; Marçal Rusiñol; Aura Hernandez-Sabate |
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Title |
Feature Extraction by Using Dual-Generalized Discriminative Common Vectors |
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Journal Article |
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2019 |
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Journal of Mathematical Imaging and Vision |
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JMIV |
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61 |
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3 |
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331-351 |
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Online feature extraction; Generalized discriminative common vectors; Dual learning; Incremental learning; Decremental learning |
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In this paper, a dual online subspace-based learning method called dual-generalized discriminative common vectors (Dual-GDCV) is presented. The method extends incremental GDCV by exploiting simultaneously both the concepts of incremental and decremental learning for supervised feature extraction and classification. Our methodology is able to update the feature representation space without recalculating the full projection or accessing the previously processed training data. It allows both adding information and removing unnecessary data from a knowledge base in an efficient way, while retaining the previously acquired knowledge. The proposed method has been theoretically proved and empirically validated in six standard face recognition and classification datasets, under two scenarios: (1) removing and adding samples of existent classes, and (2) removing and adding new classes to a classification problem. Results show a considerable computational gain without compromising the accuracy of the model in comparison with both batch methodologies and other state-of-art adaptive methods. |
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DAG; ADAS; 600.084; 600.118; 600.121; 600.129 |
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Admin @ si @ DRR2019 |
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3172 |
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