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Xiao Liang

Bio: Xiao Liang is an academic researcher from Tsinghua University. The author has contributed to research in topics: Image warping & Invariant (mathematics). The author has an hindex of 3, co-authored 3 publications receiving 477 citations.

Papers
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Journal ArticleDOI
TL;DR: This method can accurately recover both the intrinsic low-rank texture and the unknown transformation, and hence both the geometry and appearance of the associated planar region in 3D in the case of planar regions with significant affine or projective deformation.
Abstract: In this paper, we propose a new tool to efficiently extract a class of "low-rank textures" in a 3D scene from user-specified windows in 2D images despite significant corruptions and warping. The low-rank textures capture geometrically meaningful structures in an image, which encompass conventional local features such as edges and corners as well as many kinds of regular, symmetric patterns ubiquitous in urban environments and man-made objects. Our approach to finding these low-rank textures leverages the recent breakthroughs in convex optimization that enable robust recovery of a high-dimensional low-rank matrix despite gross sparse errors. In the case of planar regions with significant affine or projective deformation, our method can accurately recover both the intrinsic low-rank texture and the unknown transformation, and hence both the geometry and appearance of the associated planar region in 3D. Extensive experimental results demonstrate that this new technique works effectively for many regular and near-regular patterns or objects that are approximately low-rank, such as symmetrical patterns, building facades, printed text, and human faces.

284 citations

Posted Content
TL;DR: In this article, low-rank textures capture geometrically meaningful structures in an image, which encompass conventional local features such as edges and corners as well as all kinds of regular, symmetric patterns ubiquitous in urban environments and man-made objects.
Abstract: In this paper, we show how to efficiently and effectively extract a class of "low-rank textures" in a 3D scene from 2D images despite significant corruptions and warping. The low-rank textures capture geometrically meaningful structures in an image, which encompass conventional local features such as edges and corners as well as all kinds of regular, symmetric patterns ubiquitous in urban environments and man-made objects. Our approach to finding these low-rank textures leverages the recent breakthroughs in convex optimization that enable robust recovery of a high-dimensional low-rank matrix despite gross sparse errors. In the case of planar regions with significant affine or projective deformation, our method can accurately recover both the intrinsic low-rank texture and the precise domain transformation, and hence the 3D geometry and appearance of the planar regions. Extensive experimental results demonstrate that this new technique works effectively for many regular and near-regular patterns or objects that are approximately low-rank, such as symmetrical patterns, building facades, printed texts, and human faces.

203 citations

Journal ArticleDOI
TL;DR: This algorithm based on convex optimization can automatically and correctly repair the global structure of a corrupted texture, even without precise information about the regions to be completed, through extensive simulations.
Abstract: In this paper, we show how to harness both low-rank and sparse structures in regular or near-regular textures for image completion. Our method is based on a unified formulation for both random and contiguous corruption. In addition to the low rank property of texture, the algorithm also uses the sparse assumption of the natural image: because the natural image is piecewise smooth, it is sparse in certain transformed domain (such as Fourier or wavelet transform). We combine low-rank and sparsity properties of the texture image together in the proposed algorithm. Our algorithm based on convex optimization can automatically and correctly repair the global structure of a corrupted texture, even without precise information about the regions to be completed. This algorithm integrates texture rectification and repairing into one optimization problem. Through extensive simulations, we show our method can complete and repair textures corrupted by errors with both random and contiguous supports better than existing low-rank matrix recovery methods. Our method demonstrates significant advantage over local patch based texture synthesis techniques in dealing with large corruption, non-uniform texture, and large perspective deformation.

4 citations


Cited by
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Journal ArticleDOI
TL;DR: It is shown that the convex program associated with LRR solves the subspace clustering problem in the following sense: When the data is clean, LRR exactly recovers the true subspace structures; when the data are contaminated by outliers, it is proved that under certain conditions LRR can exactly recover the row space of the original data.
Abstract: In this paper, we address the subspace clustering problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to cluster the samples into their respective subspaces and remove possible outliers as well. To this end, we propose a novel objective function named Low-Rank Representation (LRR), which seeks the lowest rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that the convex program associated with LRR solves the subspace clustering problem in the following sense: When the data is clean, we prove that LRR exactly recovers the true subspace structures; when the data are contaminated by outliers, we prove that under certain conditions LRR can exactly recover the row space of the original data and detect the outlier as well; for data corrupted by arbitrary sparse errors, LRR can also approximately recover the row space with theoretical guarantees. Since the subspace membership is provably determined by the row space, these further imply that LRR can perform robust subspace clustering and error correction in an efficient and effective way.

3,085 citations

Proceedings ArticleDOI
23 Jun 2014
TL;DR: Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality.
Abstract: As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each singular value equally to pursue the convexity of the objective function. However, this greatly restricts its capability and flexibility in dealing with many practical problems (e.g., denoising), where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, where the singular values are assigned different weights. The solutions of the WNNM problem are analyzed under different weighting conditions. We then apply the proposed WNNM algorithm to image denoising by exploiting the image nonlocal self-similarity. Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality.

1,876 citations

Journal ArticleDOI
TL;DR: This paper reduces this extremely challenging optimization problem to a sequence of convex programs that minimize the sum of l1-norm and nuclear norm of the two component matrices, which can be efficiently solved by scalable convex optimization techniques.
Abstract: This paper studies the problem of simultaneously aligning a batch of linearly correlated images despite gross corruption (such as occlusion). Our method seeks an optimal set of image domain transformations such that the matrix of transformed images can be decomposed as the sum of a sparse matrix of errors and a low-rank matrix of recovered aligned images. We reduce this extremely challenging optimization problem to a sequence of convex programs that minimize the sum of l1-norm and nuclear norm of the two component matrices, which can be efficiently solved by scalable convex optimization techniques. We verify the efficacy of the proposed robust alignment algorithm with extensive experiments on both controlled and uncontrolled real data, demonstrating higher accuracy and efficiency than existing methods over a wide range of realistic misalignments and corruptions.

846 citations

Proceedings ArticleDOI
16 Jun 2012
TL;DR: A system which detects texts of arbitrary orientations in natural images using a two-level classification scheme and two sets of features specially designed for capturing both the intrinsic characteristics of texts to better evaluate its algorithm and compare it with other competing algorithms.
Abstract: With the increasing popularity of practical vision systems and smart phones, text detection in natural scenes becomes a critical yet challenging task. Most existing methods have focused on detecting horizontal or near-horizontal texts. In this paper, we propose a system which detects texts of arbitrary orientations in natural images. Our algorithm is equipped with a two-level classification scheme and two sets of features specially designed for capturing both the intrinsic characteristics of texts. To better evaluate our algorithm and compare it with other competing algorithms, we generate a new dataset, which includes various texts in diverse real-world scenarios; we also propose a protocol for performance evaluation. Experiments on benchmark datasets and the proposed dataset demonstrate that our algorithm compares favorably with the state-of-the-art algorithms when handling horizontal texts and achieves significantly enhanced performance on texts of arbitrary orientations in complex natural scenes.

750 citations

Journal ArticleDOI
TL;DR: It is proved that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers and presents an automatic weight setting method, which greatly facilitates the practical implementation of WNNM.
Abstract: As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear constrains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting.

608 citations