scholarly journals Image Completion with Hybrid Interpolation in Tensor Representation

2020 ◽  
Vol 10 (3) ◽  
pp. 797 ◽  
Author(s):  
Rafał Zdunek ◽  
Tomasz Sadowski
Keyword(s):  
Polynomial Interpolation ◽  
State Of The Art ◽  
Tensor Decomposition ◽  
Good Alternative ◽  
Low Rank ◽  
Decomposition Algorithms ◽  
Image Completion ◽  
The Matrix ◽  
Low Rank Approximations ◽  
Incomplete Images

The issue of image completion has been developed considerably over the last two decades, and many computational strategies have been proposed to fill-in missing regions in an incomplete image. When the incomplete image contains many small-sized irregular missing areas, a good alternative seems to be the matrix or tensor decomposition algorithms that yield low-rank approximations. However, this approach uses heuristic rank adaptation techniques, especially for images with many details. To tackle the obstacles of low-rank completion methods, we propose to model the incomplete images with overlapping blocks of Tucker decomposition representations where the factor matrices are determined by a hybrid version of the Gaussian radial basis function and polynomial interpolation. The experiments, carried out for various image completion and resolution up-scaling problems, demonstrate that our approach considerably outperforms the baseline and state-of-the-art low-rank completion methods.

scholarly journals Three-Way Tensor Decompositions: A Generalized Minimum Noise Subspace Based Approach

2018 ◽  
Author(s):  
Le Trung Thanh ◽  
Viet-Dung Nguyen ◽  
Nguyen Linh-Trung ◽  
Karim Abed-Meraim
Keyword(s):  
Computational Complexity ◽  
State Of The Art ◽  
Tensor Decomposition ◽  
Decomposition Algorithms ◽  
Subspace Analysis ◽  
Tensor Decompositions ◽  
Noise Subspace ◽  
Parallel Factor ◽  
Value Decomposition ◽  
Minimum Noise

Tensor decomposition has recently become a popular method of multi-dimensional data analysis in various applications. The main interest in tensor decomposition is for dimensionality reduction, approximation or subspace purposes. However, the emergence of “big data” now gives rise to increased computational complexity for performing tensor decomposition. In this paper, motivated by the advantages of the generalized minimum noise subspace (GMNS) method, recently proposed for array processing, we proposed two algorithms for principal subspace analysis (PSA) and two algorithms for tensor decomposition using parallel factor analysis (PARAFAC) and higher-order singular value decomposition (HOSVD). The proposed decomposition algorithms can preserve several desired properties of PARAFAC and HOSVD while substantially reducing the computational complexity. Performance comparisons of PSA and tensor decomposition of our proposed algorithms against the state-of-the-art ones were studied via numerical experiments. Experimental results indicated that the proposed algorithms are of practical values.

scholarly journals Beyond Unfolding: Exact Recovery of Latent Convex Tensor Decomposition Under Reshuffling

2020 ◽  
Vol 34 (04) ◽  
pp. 4602-4609
Author(s):  
Chao Li ◽  
Mohammad Emtiyaz Khan ◽  
Zhun Sun ◽  
Gang Niu ◽  
Bo Han ◽  
...  
Keyword(s):  
State Of The Art ◽  
Synthetic Data ◽  
Tensor Decomposition ◽  
Scientific Data ◽  
Image Steganography ◽  
Real World Data ◽  
Practical Applications ◽  
Scientific Data Analysis ◽  
The Matrix ◽  
Td Methods

Exact recovery of tensor decomposition (TD) methods is a desirable property in both unsupervised learning and scientific data analysis. The numerical defects of TD methods, however, limit their practical applications on real-world data. As an alternative, convex tensor decomposition (CTD) was proposed to alleviate these problems, but its exact-recovery property is not properly addressed so far. To this end, we focus on latent convex tensor decomposition (LCTD), a practically widely-used CTD model, and rigorously prove a sufficient condition for its exact-recovery property. Furthermore, we show that such property can be also achieved by a more general model than LCTD. In the new model, we generalize the classic tensor (un-)folding into reshuffling operation, a more flexible mapping to relocate the entries of the matrix into a tensor. Armed with the reshuffling operations and exact-recovery property, we explore a totally novel application for (generalized) LCTD, i.e., image steganography. Experimental results on synthetic data validate our theory, and results on image steganography show that our method outperforms the state-of-the-art methods.

scholarly journals Enhancing Matrix Completion Using a Modified Second-Order Total Variation

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wendong Wang ◽  
Jianjun Wang
Keyword(s):  
Total Variation ◽  
Optimization Problem ◽  
State Of The Art ◽  
Matrix Completion ◽  
Second Order ◽  
Low Rank ◽  
Superior Performance ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
The Matrix

In this paper, we propose a new method to deal with the matrix completion problem. Different from most existing matrix completion methods that only pursue the low rank of underlying matrices, the proposed method simultaneously optimizes their low rank and smoothness such that they mutually help each other and hence yield a better performance. In particular, the proposed method becomes very competitive with the introduction of a modified second-order total variation, even when it is compared with some recently emerged matrix completion methods that also combine the low rank and smoothness priors of matrices together. An efficient algorithm is developed to solve the induced optimization problem. The extensive experiments further confirm the superior performance of the proposed method over many state-of-the-art methods.

scholarly journals ShadingNet: Image Intrinsics by Fine-Grained Shading Decomposition

2021 ◽  
Author(s):  
Anil S. Baslamisli ◽  
Partha Das ◽  
Hoang-An Le ◽  
Sezer Karaoglu ◽  
Theo Gevers
Keyword(s):  
Neural Network ◽  
Large Scale ◽  
State Of The Art ◽  
Image Decomposition ◽  
Natural Environments ◽  
Decomposition Algorithms ◽  
Ambient Light ◽  
Fine Grained ◽  
Large Scale Dataset ◽  
Direct Illumination

AbstractIn general, intrinsic image decomposition algorithms interpret shading as one unified component including all photometric effects. As shading transitions are generally smoother than reflectance (albedo) changes, these methods may fail in distinguishing strong photometric effects from reflectance variations. Therefore, in this paper, we propose to decompose the shading component into direct (illumination) and indirect shading (ambient light and shadows) subcomponents. The aim is to distinguish strong photometric effects from reflectance variations. An end-to-end deep convolutional neural network (ShadingNet) is proposed that operates in a fine-to-coarse manner with a specialized fusion and refinement unit exploiting the fine-grained shading model. It is designed to learn specific reflectance cues separated from specific photometric effects to analyze the disentanglement capability. A large-scale dataset of scene-level synthetic images of outdoor natural environments is provided with fine-grained intrinsic image ground-truths. Large scale experiments show that our approach using fine-grained shading decompositions outperforms state-of-the-art algorithms utilizing unified shading on NED, MPI Sintel, GTA V, IIW, MIT Intrinsic Images, 3DRMS and SRD datasets.

Computing Robust Principal Components by A* Search

2018 ◽  
Vol 27 (07) ◽  
pp. 1860013 ◽  
Author(s):  
Swair Shah ◽  
Baokun He ◽  
Crystal Maung ◽  
Haim Schweitzer
Keyword(s):  
State Of The Art ◽  
Principal Component ◽  
Low Rank ◽  
A Algorithm ◽  
Running Time ◽  
Current State ◽  
Dimensionality Reduction Technique ◽  
Related Variant ◽  
Low Rank Representation ◽  
The Cost

Principal Component Analysis (PCA) is a classical dimensionality reduction technique that computes a low rank representation of the data. Recent studies have shown how to compute this low rank representation from most of the data, excluding a small amount of outlier data. We show how to convert this problem into graph search, and describe an algorithm that solves this problem optimally by applying a variant of the A* algorithm to search for the outliers. The results obtained by our algorithm are optimal in terms of accuracy, and are shown to be more accurate than results obtained by the current state-of-the- art algorithms which are shown not to be optimal. This comes at the cost of running time, which is typically slower than the current state of the art. We also describe a related variant of the A* algorithm that runs much faster than the optimal variant and produces a solution that is guaranteed to be near the optimal. This variant is shown experimentally to be more accurate than the current state-of-the-art and has a comparable running time.

scholarly journals Low-Rank and Sparse Based Deep-Fusion Convolutional Neural Network for Crowd Counting

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Siqi Tang ◽  
Zhisong Pan ◽  
Xingyu Zhou
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
State Of The Art ◽  
Regression Method ◽  
Low Rank ◽  
Counting Method ◽  
Direct Integral ◽  
Crowd Counting ◽  
Counting Methods ◽  
Density Map

This paper proposes an accurate crowd counting method based on convolutional neural network and low-rank and sparse structure. To this end, we firstly propose an effective deep-fusion convolutional neural network to promote the density map regression accuracy. Furthermore, we figure out that most of the existing CNN based crowd counting methods obtain overall counting by direct integral of estimated density map, which limits the accuracy of counting. Instead of direct integral, we adopt a regression method based on low-rank and sparse penalty to promote accuracy of the projection from density map to global counting. Experiments demonstrate the importance of such regression process on promoting the crowd counting performance. The proposed low-rank and sparse based deep-fusion convolutional neural network (LFCNN) outperforms existing crowd counting methods and achieves the state-of-the-art performance.

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