Showing papers by "Jian Sun published in 2013"

Guided Image Filtering

Abstract: In this paper, we propose a novel explicit image filter called guided filter. Derived from a local linear model, the guided filter computes the filtering output by considering the content of a guidance image, which can be the input image itself or another different image. The guided filter can be used as an edge-preserving smoothing operator like the popular bilateral filter [1], but it has better behaviors near edges. The guided filter is also a more generic concept beyond smoothing: It can transfer the structures of the guidance image to the filtering output, enabling new filtering applications like dehazing and guided feathering. Moreover, the guided filter naturally has a fast and nonapproximate linear time algorithm, regardless of the kernel size and the intensity range. Currently, it is one of the fastest edge-preserving filters. Experiments show that the guided filter is both effective and efficient in a great variety of computer vision and computer graphics applications, including edge-aware smoothing, detail enhancement, HDR compression, image matting/feathering, dehazing, joint upsampling, etc.

Blessing of Dimensionality: High-Dimensional Feature and Its Efficient Compression for Face Verification

Abstract: Making a high-dimensional (e.g., 100K-dim) feature for face recognition seems not a good idea because it will bring difficulties on consequent training, computation, and storage. This prevents further exploration of the use of a high dimensional feature. In this paper, we study the performance of a high dimensional feature. We first empirically show that high dimensionality is critical to high performance. A 100K-dim feature, based on a single-type Local Binary Pattern (LBP) descriptor, can achieve significant improvements over both its low-dimensional version and the state-of-the-art. We also make the high-dimensional feature practical. With our proposed sparse projection method, named rotated sparse regression, both computation and model storage can be reduced by over 100 times without sacrificing accuracy quality.

K-Means Hashing: An Affinity-Preserving Quantization Method for Learning Binary Compact Codes

Abstract: In computer vision there has been increasing interest in learning hashing codes whose Hamming distance approximates the data similarity. The hashing functions play roles in both quantizing the vector space and generating similarity-preserving codes. Most existing hashing methods use hyper-planes (or kernelized hyper-planes) to quantize and encode. In this paper, we present a hashing method adopting the k-means quantization. We propose a novel Affinity-Preserving K-means algorithm which simultaneously performs k-means clustering and learns the binary indices of the quantized cells. The distance between the cells is approximated by the Hamming distance of the cell indices. We further generalize our algorithm to a product space for learning longer codes. Experiments show our method, named as K-means Hashing (KMH), outperforms various state-of-the-art hashing encoding methods.

Optimized Product Quantization for Approximate Nearest Neighbor Search

Abstract: Product quantization is an effective vector quantization approach to compactly encode high-dimensional vectors for fast approximate nearest neighbor (ANN) search. The essence of product quantization is to decompose the original high-dimensional space into the Cartesian product of a finite number of low-dimensional subspaces that are then quantized separately. Optimal space decomposition is important for the performance of ANN search, but still remains unaddressed. In this paper, we optimize product quantization by minimizing quantization distortions w.r.t. the space decomposition and the quantization codebooks. We present two novel methods for optimization: a non-parametric method that alternatively solves two smaller sub-problems, and a parametric method that is guaranteed to achieve the optimal solution if the input data follows some Gaussian distribution. We show by experiments that our optimized approach substantially improves the accuracy of product quantization for ANN search.

Bundled camera paths for video stabilization

Abstract: We present a novel video stabilization method which models camera motion with a bundle of (multiple) camera paths. The proposed model is based on a mesh-based, spatially-variant motion representation and an adaptive, space-time path optimization. Our motion representation allows us to fundamentally handle parallax and rolling shutter effects while it does not require long feature trajectories or sparse 3D reconstruction. We introduce the 'as-similar-as-possible' idea to make motion estimation more robust. Our space-time path smoothing adaptively adjusts smoothness strength by considering discontinuities, cropping size and geometrical distortion in a unified optimization framework. The evaluation on a large variety of consumer videos demonstrates the merits of our method.

Constant Time Weighted Median Filtering for Stereo Matching and Beyond

Abstract: Despite the continuous advances in local stereo matching for years, most efforts are on developing robust cost computation and aggregation methods. Little attention has been seriously paid to the disparity refinement. In this work, we study weighted median filtering for disparity refinement. We discover that with this refinement, even the simple box filter aggregation achieves comparable accuracy with various sophisticated aggregation methods (with the same refinement). This is due to the nice weighted median filtering properties of removing outlier error while respecting edges/structures. This reveals that the previously overlooked refinement can be at least as crucial as aggregation. We also develop the first constant time algorithm for the previously time-consuming weighted median filter. This makes the simple combination ``box aggregation + weighted median'' an attractive solution in practice for both speed and accuracy. As a byproduct, the fast weighted median filtering unleashes its potential in other applications that were hampered by high complexities. We show its superiority in various applications such as depth up sampling, clip-art JPEG artifact removal, and image stylization.

A Practical Transfer Learning Algorithm for Face Verification

Abstract: Face verification involves determining whether a pair of facial images belongs to the same or different subjects. This problem can prove to be quite challenging in many important applications where labeled training data is scarce, e.g., family album photo organization software. Herein we propose a principled transfer learning approach for merging plentiful source-domain data with limited samples from some target domain of interest to create a classifier that ideally performs nearly as well as if rich target-domain data were present. Based upon a surprisingly simple generative Bayesian model, our approach combines a KL-divergence based regularizer/prior with a robust likelihood function leading to a scalable implementation via the EM algorithm. As justification for our design choices, we later use principles from convex analysis to recast our algorithm as an equivalent structured rank minimization problem leading to a number of interesting insights related to solution structure and feature-transform invariance. These insights help to both explain the effectiveness of our algorithm as well as elucidate a wide variety of related Bayesian approaches. Experimental testing with challenging datasets validate the utility of the proposed algorithm.

Learning Discriminative Part Detectors for Image Classification and Cosegmentation

Abstract: In this paper, we address the problem of learning discriminative part detectors from image sets with category labels. We propose a novel latent SVM model regularized by group sparsity to learn these part detectors. Starting from a large set of initial parts, the group sparsity regularizer forces the model to jointly select and optimize a set of discriminative part detectors in a max-margin framework. We propose a stochastic version of a proximal algorithm to solve the corresponding optimization problem. We apply the proposed method to image classification and co segmentation, and quantitative experiments with standard benchmarks show that it matches or improves upon the state of the art.

Learning to Estimate and Remove Non-uniform Image Blur

Abstract: This paper addresses the problem of restoring images subjected to unknown and spatially varying blur caused by defocus or linear (say, horizontal) motion. The estimation of the global (non-uniform) image blur is cast as a multi-label energy minimization problem. The energy is the sum of unary terms corresponding to learned local blur estimators, and binary ones corresponding to blur smoothness. Its global minimum is found using Ishikawa's method by exploiting the natural order of discretized blur values for linear motions and defocus. Once the blur has been estimated, the image is restored using a robust (non-uniform) deblurring algorithm based on sparse regularization with global image statistics. The proposed algorithm outputs both a segmentation of the image into uniform-blur layers and an estimate of the corresponding sharp image. We present qualitative results on real images, and use synthetic data to quantitatively compare our approach to the publicly available implementation of Chakrabarti~et al.

Area-Preservation Mapping using Optimal Mass Transport

Abstract: We present a novel area-preservation mapping/flattening method using the optimal mass transport technique, based on the Monge-Brenier theory. Our optimal transport map approach is rigorous and solid in theory, efficient and parallel in computation, yet general for various applications. By comparison with the conventional Monge-Kantorovich approach, our method reduces the number of variables from O(n2) to O(n), and converts the optimal mass transport problem to a convex optimization problem, which can now be efficiently carried out by Newton's method. Furthermore, our framework includes the area weighting strategy that enables users to completely control and adjust the size of areas everywhere in an accurate and quantitative way. Our method significantly reduces the complexity of the problem, and improves the efficiency, flexibility and scalability during visualization. Our framework, by combining conformal mapping and optimal mass transport mapping, serves as a powerful tool for a broad range of applications in visualization and graphics, especially for medical imaging. We provide a variety of experimental results to demonstrate the efficiency, robustness and efficacy of our novel framework.

Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations

Abstract: In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE). A link between the discrete optimal transport, discrete Monge-Ampere equation and the power diagram in computational geometry is established.

Rectangling panoramic images via warping

Abstract: Stitched panoramic images mostly have irregular boundaries. Artists and common users generally prefer rectangular boundaries, which can be obtained through cropping or image completion techniques. In this paper, we present a content-aware warping algorithm that generates rectangular images from stitched panoramic images. Our algorithm consists of two steps. The first local step is mesh-free and preliminarily warps the image into a rectangle. With a grid mesh placed on this rectangle, the second global step optimizes the mesh to preserve shapes and straight lines. In various experiments we demonstrate that the results of our approach are often visually plausible, and the introduced distortion is often unnoticeable.

Joint Inverted Indexing

Abstract: Inverted indexing is a popular non-exhaustive solution to large scale search. An inverted file is built by a quantizer such as k-means or a tree structure. It has been found that multiple inverted files, obtained by multiple independent random quantizers, are able to achieve practically good recall and speed. Instead of computing the multiple quantizers independently, we present a method that creates them jointly. Our method jointly optimizes all code words in all quantizers. Then it assigns these code words to the quantizers. In experiments this method shows significant improvement over various existing methods that use multiple independent quantizers. On the one-billion set of SIFT vectors, our method is faster and more accurate than a recent state-of-the-art inverted indexing method.

Hierarchical Nyström methods for constructing Markov state models for conformational dynamics

Abstract: Markov state models (MSMs) have become a popular approach for investigating the conformational dynamics of proteins and other biomolecules. MSMs are typically built from numerous molecular dynamics simulations by dividing the sampled configurations into a large number of microstates based on geometric criteria. The resulting microstate model can then be coarse-grained into a more understandable macrostate model by lumping together rapidly mixing microstates into larger, metastable aggregates. However, finite sampling often results in the creation of many poorly sampled microstates. During coarse-graining, these states are mistakenly identified as being kinetically important because transitions to/from them appear to be slow. In this paper, we propose a formalism based on an algebraic principle for matrix approximation, i.e., the Nystrom method, to deal with such poorly sampled microstates. Our scheme builds a hierarchy of microstates from high to low populations and progressively applies spectral clustering on sets of microstates within each level of the hierarchy. It helps spectral clustering identify metastable aggregates with highly populated microstates rather than being distracted by lowly populated states. We demonstrate the ability of this algorithm to discover the major metastable states on two model systems, the alanine dipeptide and trpzip2 peptide.

Hierarchical Nystrom Methods for Constructing Markov State Models for Conformational Dynamics

Abstract: Markov state models (MSMs) have become a popular approach for investigating the conformational dynamics of proteins and other biomolecules. MSMs are typically built from numerous molecular dynamics simulations by dividing the sampled configurations into a large number of microstates based on geometric criteria. The resulting microstate model can then be coarse-grained into a more understandable macro state model by lumping together rapidly mixing microstates into larger, metastable aggregates. However, finite sampling often results in the creation of many poorly sampled microstates. During coarse-graining, these states are mistakenly identified as being kinetically important because transitions to/from them appear to be slow. In this paper we propose a formalism based on an algebraic principle for matrix approximation, i.e. the Nystrom method, to deal with such poorly sampled microstates. Our scheme builds a hierarchy of microstates from high to low populations and progressively applies spectral clustering on sets of microstates within each level of the hierarchy. It helps spectral clustering identify metastable aggregates with highly populated microstates rather than being distracted by lowly populated states. We demonstrate the ability of this algorithm to discover the major metastable states on two model systems, the alanine dipeptide and TrpZip2.

Sparse-Coded Features for Image Retrieval.

Abstract: The bag-of-features(BOF) image representation [7] is popular in largescale image retrieval. With BOF, the memory to store the inverted index file and the search complexity are both approximately linearly increased with the number of images. To address the retrieval efficiency and the memory constraint problem, besides some improvement work based on BOF, there come alternative approaches which aggregate local descriptors in one image into a single vector using Fisher Vector [6] or Vector of Local Aggregated Descriptor (VLAD) [1]. It has been shown in [1] that with as few as 16 bytes to represent an image, the retrieval performance is still comparable to that of the BOF representation. In this paper, we illustrate that Fisher Vector, VLAD and BOF can be uniformly derived in two steps: i Encoding – separately map each local descriptor into a code, and ii Pooling – aggregate all codes from one image into a single vector. Motivated by the success of these two-step approaches, we propose to use sparse coding(SC) framework to aggregate local feature for image retrieval. SC framework is firstly introduced by [10] for the task of image classification. It is a classical two-step approach: Step 1: Encoding. Each local descriptor x from an image is encoded into an N-dimensional vector u = [u1,u2, ...,uN ] by fitting a linear model with sparsity (L1) constraint:

Separable Markov Random Field Model and Its Applications in Low Level Vision

Abstract: This brief proposes a continuously-valued Markov random field (MRF) model with separable filter bank, denoted as MRFSepa, which significantly reduces the computational complexity in the MRF modeling. In this framework, we design a novel gradient-based discriminative learning method to learn the potential functions and separable filter banks. We learn MRFSepa models with 2-D and 3-D separable filter banks for the applications of gray-scale/color image denoising and color image demosaicing. By implementing MRFSepa model on graphics processing unit, we achieve real-time image denoising and fast image demosaicing with high-quality results.

Area Preserving Brain Mapping

Abstract: Brain mapping transforms the brain cortical surface to canonical planar domains, which plays a fundamental role in morphological study. Most existing brain mapping methods are based on angle preserving maps, which may introduce large area distortions. This work proposes an area preserving brain mapping method based on Monge-Brenier theory. The brain mapping is intrinsic to the Riemannian metric, unique, and diffeomorphic. The computation is equivalent to convex energy minimization and power Voronoi diagram construction. Comparing to the existing approaches based on Monge-Kantorovich theory, the proposed one greatly reduces the complexity (from n2 unknowns to n ), and improves the simplicity and efficiency. Experimental results on caudate nucleus surface mapping and cortical surface mapping demonstrate the efficacy and efficiency of the proposed method. Conventional methods for caudate nucleus surface mapping may suffer from numerical instability, in contrast, current method produces diffeomorpic mappings stably. In the study of cortical surface classification for recognition of Alzheimer's Disease, the proposed method outperforms some other morphometry features.

A fast parallel clustering algorithm for molecular simulation trajectories

Abstract: We implemented a GPU-powered parallel k-centers algorithm to perform clustering on the conformations of molecular dynamics (MD) simulations. The algorithm is up to two orders of magnitude faster than the CPU implementation. We tested our algorithm on four protein MD simulation datasets ranging from the small Alanine Dipeptide to a 370-residue Maltose Binding Protein (MBP). It is capable of grouping 250,000 conformations of the MBP into 4000 clusters within 40 seconds. To achieve this, we effectively parallelized the code on the GPU and utilize the triangle inequality of metric spaces. Furthermore, the algorithm's running time is linear with respect to the number of cluster centers. In addition, we found the triangle inequality to be less effective in higher dimensions and provide a mathematical rationale. Finally, using Alanine Dipeptide as an example, we show a strong correlation between cluster populations resulting from the k-centers algorithm and the underlying density. © 2012 Wiley Periodicals, Inc.

Content-Aware Rotation

Abstract: We present an image editing tool called Content-Aware Rotation. Casually shot photos can appear tilted, and are often corrected by rotation and cropping. This trivial solution may remove desired content and hurt image integrity. Instead of doing rigid rotation, we propose a warping method that creates the perception of rotation and avoids cropping. Human vision studies suggest that the perception of rotation is mainly due to horizontal/vertical lines. We design an optimization-based method that preserves the rotation of horizontal/vertical lines, maintains the completeness of the image content, and reduces the warping distortion. An efficient algorithm is developed to address the challenging optimization. We demonstrate our content-aware rotation method on a variety of practical cases.

Creation of Rectangular Images from Input Images

Abstract: Stitched images generated from combinations of multiple separate images mostly have irregular boundaries. Users generally prefer rectangular boundaries. Techniques for warping an image with irregular boundaries to give the image rectangular boundaries are disclosed herein. Preliminary warping of the image into the rectangle provides a rectangular shape on which to overlay a mesh. The image is reverted to its original shape with irregular boundaries and the mesh is warped accordingly. Global optimization is applied to the image by finding an energy minimum, or reduced energy below a threshold, for a function that gives the image a rectangular shape while preserving shapes and preserving straight lines. The mesh is warped according to the solution of the function and the image is stretched and/or compressed along with the mesh. This approach generates results that are qualitatively more visually attractive than other contemporary techniques.

Convergence of the Point Integral Method for the Poisson Equation on Manifolds II: the Dirichlet Boundary

Abstract: The Poisson equation on manifolds plays an fundamental role in many applications. Recently, we proposed a novel numerical method called the Point Integral method (PIM) to solve the Poisson equations on manifolds from point clouds. In this paper, we prove the convergence of the point integral method for solving the Poisson equation with the Dirichlet boundary condition.

Rigidity of Infinite Hexagonal Triangulation of the Plane

Abstract: In the paper, we consider the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by Luo in [5]. Our result shows that if a geometric hexagonal triangulation of the plane is PL conformal to the regular hexagonal triangulation and all inner angles are in $[\delta, \pi/2 -\delta]$ for any constant $\delta > 0$, then it is the regular hexagonal triangulation. This partially solves a conjecture of Luo [4]. The proof uses the concept of \emph{quasi-harmonic} functions to unfold the properties of the mesh.

Joint modeling for facial recognition

Abstract: This disclosure describes a system for jointly modeling images for use in performing facial recognition. A facial recognition system may jointly model a first image and a second image using a face prior to generate a joint distribution. Conditional joint probabilities are determined based on the joint distribution. A log likelihood ratio of the first image and the second image are calculated based on the conditional joint probabilities and the subject of the first image and the second image are verified as the same person or as different people based on results of the log likelihood ratio.

Gromov-Hausdorff Approximation of Metric Spaces with Linear Structure

Abstract: In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary structures from data sampled around them. We prove that they can be approximated, with respect to the Gromov-Hausdorff distance by well-chosen Reeb graphs (and some of their variants) and we provide an efficient and easy to implement algorithm to compute such approximations in almost linear time. We illustrate the performances of our algorithm on a few synthetic and real data sets.

Learning Regularized, Query-Dependent Bilinear Similarities for Large Scale Image Retrieval

Abstract: An effective way to improve the quality of image retrieval is by employing a query-dependent similarity measure. However, implementing this in a large scale system is non-trivial because we want neither hurting the efficiency nor relying on too many training samples. In this paper, we introduce a query-dependent bilinear similarity measure to address the first issue. Based on our bilinear similarity model, query adaptation can be achieved by simply applying any existing efficient indexing/retrieval method to a transformed version (surrogate) of a query. To address the issue of limited training samples, we further propose a novel angular regularization constraint for learning the similarity measure. The learning is formulated as a Quadratic Programming (QP) problem and can be solved efficiently by a SMO-type algorithm. Experiments on two public datasets and our 1-million web-image dataset validate that our proposed method can consistently bring improvements and the whole solution is practical in large scale applications.

A Variational Principle for Improving 2D Triangle Meshes based on Hyperbolic Volume.

Abstract: In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle structures whose maximizer is unique and consists only of equilateral triangles. This energy functional is related to hyperbolic volume of ideal 3-simplex. Even with extra constraints on the angles for embedding the mesh into the plane and preserving the boundary, the energy functional remains well-behaved. We devise an efficient algorithm for maximizing the energy functional over these extra constraints. We apply our algorithm to various datasets and compare its performance with that of CVT. The experimental results show that our algorithm produces the meshes with both the angles and the aspect ratios of triangles lying in tighter intervals.

Convergence of Finite Integral Method for Poisson Equation and Corresponding Eigenproblems

Abstract: In this paper, we introduce nite integral method (FIM) for solving PDE’s on submanifolds isometrically embedded in Euclidean spaces. We show the convergence of FIM for solving Poisson equation and Helmholtz equation (aka the eigensystem of LaplaceBeltrami operator) with Neumann boundary. Being a meshless method, FIM avoids the process of meshing the underlying domain, which can be very dicult for curved submanifolds. Therefore it is a good alternative to