APPlications of Transform and Ant一transform Methods in Remote Sensing Image Processing

遥感图像处理中有许多正变换与逆变换处理，富立叶变换与逆变换、RGB来统与IHS系统之间的彩色空间变换以及主成分变换与逆变换就是典型的变换与逆变换处理技术。灵活地运用这些技术十分重要，分析了这些变换技术的特点，给出了在图像处理中的具休应用实例。     

Local and Nonlocal Discrete Regularization on Weighted Graphs for Image and Mesh Processing

We propose a discrete regularization framework on weighted graphs of arbitrary topology, which unifies local and nonlocal processing of images, meshes, and more generally discrete data. The approach considers the problem as a variational one, which consists in minimizing a weighted sum of two energy terms: a regularization one that uses the discrete p-Dirichlet form, and an approximation one. The proposed model is parametrized by the degree p of regularity, by the graph structure and by the weight function. The minimization solution leads to a family of simple linear and nonlinear processing methods. In particular, this family includes the exact expression or the discrete version of several neighborhood filters, such as the bilateral and the nonlocal means filter. In the context of images, local and nonlocal regularizations, based on the total variation models, are the continuous analog of the proposed model. Indirectly and naturally, it provides a discrete extension of these regularization methods for any discrete data or functions.     

Cooperative Object Segmentation and Behavior Inference in Image Sequences

In this paper, we propose a general framework for fusing bottom-up segmentation with top-down object behavior inference over an image sequence. This approach is beneficial for both tasks, since it enables them to cooperate so that knowledge relevant to each can aid in the resolution of the other, thus enhancing the final result. In particular, the behavior inference process offers dynamic probabilistic priors to guide segmentation. At the same time, segmentation supplies its results to the inference process, ensuring that they are consistent both with prior knowledge and with new image information. The prior models are learned from training data and they adapt dynamically, based on newly analyzed images. We demonstrate the effectiveness of our framework via particular implementations that we have employed in the resolution of two hand gesture recognition applications. Our experimental results illustrate the robustness of our joint approach to segmentation and behavior inference in challenging conditions involving complex backgrounds and occlusions of the target object.     

The Flexible, Extensible and Efficient Toolbox of Level Set Methods

Level set methods are a popular and powerful class of numerical algorithms for dynamic implicit surfaces and solution of Hamilton-Jacobi PDEs. While the advanced level set schemes combine both efficiency and accuracy, their implementation complexity makes it difficult for the community to reproduce new results and make quantitative comparisons between methods. This paper describes the Toolbox of Level Set Methods, a collection of Matlab routines implementing the basic level set algorithms on fixed Cartesian grids for rectangular domains in arbitrary dimension. The Toolbox’s code and interface are designed to permit flexible combinations of different schemes and PDE forms, allow easy extension through the addition of new algorithms, and achieve efficient execution despite the fact that the code is entirely written as m-files. The current contents of the Toolbox and some coding patterns important to achieving its flexibility, extensibility and efficiency are briefly explained, as is the process of adding two new algorithms. Code for both the Toolbox and the new algorithms is available from the Web.     

Orientation-Matching Minimization for Image Denoising and Inpainting

In this paper, we propose an orientation-matching functional minimization for image denoising and image inpainting. Following the two-step TV-Stokes algorithm (Rahman et al. in Scale space and variational methods in computer vision, pp. 473–482, Springer, Heidelberg, 2007; Tai et al. in Image processing based on partial differential equations, pp. 3–22, Springer, Heidelberg, 2006; Bertalmio et al. in Proc. conf. comp. vision pattern rec., pp. 355–362, 2001), a regularized tangential vector field with zero divergence condition is first obtained. Then a novel approach to reconstruct the image is proposed. Instead of finding an image that fits the regularized normal direction from the first step, we propose to minimize an orientation matching cost measuring the alignment between the image gradient and the regularized normal direction. This functional yields a new nonlinear partial differential equation (PDE) for reconstructing denoised and inpainted images. The equation has an adaptive diffusivity depending on the orientation of the regularized normal vector field, providing reconstructed images which have sharp edges and smooth regions. The additive operator splitting (AOS) scheme is used for discretizing Euler-Lagrange equations. We present the results of various numerical experiments that illustrate the improvements obtained with the new functional.     

New Possibilities in Image Diffusion and Sharpening via High-Order Sobolev Gradient Flows

We study the use of high-order Sobolev gradients for PDE-based image smoothing and sharpening, extending our previous work on this problem. In particular, we study the gradient descent equation on the heat equation energy functional obtained by modifying the usual metric on the space of images, which is the L ² metric, to a weighted H ^k Sobolev metric. We present existence and uniqueness results which show that the Sobolev diffusion PDE are well-posed both in the forward and backward direction. Furthermore, we perform a Fourier analysis on the scale space generated by the Sobolev PDE and show that as the order of the Sobolev metric tends to infinity, the Sobolev gradients converge to a Gaussian smoothed L ² gradient. We then present experimental results which exploit the theoretical stability results by applying the various Sobolev gradient flows in the backward direction for image sharpening effects. Furthermore, we show that as the Sobolev order is increased, the sharpening effects become more global in nature and more immune to noise.     

An Efficient Algorithm for ℓ 0 Minimization in Wavelet Frame Based Image Restoration

Wavelet frame based models for image restoration have been extensively studied for the past decade (Chan et al. in SIAM J. Sci. Comput. 24(4):1408–1432, 2003; Cai et al. in Multiscale Model. Simul. 8(2):337–369, 2009; Elad et al. in Appl. Comput. Harmon. Anal. 19(3):340–358, 2005; Starck et al. in IEEE Trans. Image Process. 14(10):1570–1582, 2005; Shen in Proceedings of the international congress of mathematicians, vol. 4, pp. 2834–2863, 2010; Dong and Shen in IAS lecture notes series, Summer program on “The mathematics of image processing”, Park City Mathematics Institute, 2010). The success of wavelet frames in image restoration is mainly due to their capability of sparsely approximating piecewise smooth functions like images. Most of the wavelet frame based models designed in the past are based on the penalization of the ? ₁ norm of wavelet frame coefficients, which, under certain conditions, is the right choice, as supported by theories of compressed sensing (Candes et al. in Appl. Comput. Harmon. Anal., 2010; Candes et al. in IEEE Trans. Inf. Theory 52(2):489–509, 2006; Donoho in IEEE Trans. Inf. Theory 52:1289–1306, 2006). However, the assumptions of compressed sensing may not be satisfied in practice (e.g. for image deblurring and CT image reconstruction). Recently in Zhang et al. (UCLA CAM Report, vol. 11-32, 2011), the authors propose to penalize the ? ₀ “norm” of the wavelet frame coefficients instead, and they have demonstrated significant improvements of their method over some commonly used ? ₁ minimization models in terms of quality of the recovered images. In this paper, we propose a new algorithm, called the mean doubly augmented Lagrangian (MDAL) method, for ? ₀ minimizations based on the classical doubly augmented Lagrangian (DAL) method (Rockafellar in Math. Oper. Res. 97–116, 1976). Our numerical experiments show that the proposed MDAL method is not only more efficient than the method proposed by Zhang et al. (UCLA CAM Report, vol. 11-32, 2011), but can also generate recovered images with even higher quality. This study reassures the feasibility of using the ? ₀ “norm” for image restoration problems.     

Primal Discontinuous Galerkin Methods for Time-Dependent Coupled Surface and Subsurface Flow

This paper introduces and analyzes a numerical method based on discontinuous finite element methods for solving the two-dimensional coupled problem of time-dependent incompressible Navier-Stokes equations with the Darcy equations through Beaver-Joseph-Saffman’s condition on the interface. The proposed method employs Crank-Nicolson discretization in time (which requires one step of a first order scheme namely backward Euler) and primal DG method in space. With the correct assumption on the first time step optimal error estimates are obtained that are high order in space and second order in time.     

Image Comparison by Compound Disjoint Information with Applications to Perceptual Visual Quality Assessment, Image Registration and Tracking

In this paper, we study (normalized) disjoint information as a metric for image comparison and its applications to perceptual image quality assessment, image registration, and video tracking. Disjoint information is the joint entropy of random variables excluding the mutual information. This measure of statistical dependence and information redundancy satisfies more rigorous metric conditions than mutual information, including self-similarity, minimality, symmetry and triangle inequality. It is applicable to two or more random variables, and can be computed by vector histogramming, vector Parzen window density approximation, and upper bound approximation involving fewer variables. We show such a theoretic advantage does have implications in practice. In the domain of digital image and video, multiple visual features are extracted and (normalized) compound disjoint information is derived from a set of marginal densities of the image distributions, thus enriching the vocabulary of content representation. The proposed metric matching functions are applied to several domain applications to demonstrate their efficacy.     

Performance Modeling and Algorithm Characterization for Robust Image Segmentation

This paper presents a probabilistic framework based on Bayesian theory for the performance prediction and selection of an optimal segmentation algorithm. The framework models the optimal algorithm selection process as one that accounts for the information content of an input image as well as the behavioral properties of a particular candidate segmentation algorithm. The input image information content is measured in terms of image features while the candidate segmentation algorithm’s behavioral characteristics are captured through the use of segmentation quality features. Gaussian probability distribution models are used to learn the required relationships between the extracted image and algorithm features and the framework tested on the Berkeley Segmentation Dataset using four candidate segmentation algorithms.     

A Quaternion Framework for Color Image Smoothing and Segmentation

In this paper, we present feature/detail preserving models for color image smoothing and segmentation using the Hamiltonian quaternion framework. First, we introduce a novel quaternionic Gabor filter (QGF) which can combine the color channels and the orientations in the image plane. We show that these filters are optimally localized both in the spatial and frequency domains and provide a good approximation to quaternionic quadrature filters. Using the QGFs, we extract the local orientation information in the color images. Second, in order to model this derived orientation information, we propose continuous mixtures of appropriate exponential basis functions and derive analytic expressions for these models. These analytic expressions take the form of spatially varying kernels which, when convolved with a color image or the signed distance function of an evolving contour (placed in the color image), yield a detail preserving smoothing and segmentation, respectively. Several examples on widely used image databases are shown to depict the performance of our algorithms.     

Generalized Rigid and Generalized Affine Image Registration and Interpolation by Geometric Multigrid

Generalized rigid and generalized affine registration and interpolation obtained by finite displacements and by optical flow are here developed variationally and numerically as well as with respect to a geometric multigrid solution process. For high order optimality systems under natural boundary conditions, it is shown that the convergence criteria of Hackbusch (Iterative Solution of Large Sparse Systems of Equations. Springer, Berlin, 1993) are met. Specifically, the Galerkin formalism is used together with a multi-colored ordering of unknowns to permit vectorization of a symmetric successive over-relaxation on image processing systems. The geometric multigrid procedure is situated as an inner iteration within an outer Newton or lagged diffusivity iteration, which in turn is embedded within a pyramidal scheme that initializes each outer iteration from predictions obtained on coarser levels. Differences between results obtainable by finite displacements and by optical flows are elucidated. Specifically, independence of image order can be shown for optical flow but in general not for finite displacements. Also, while autonomous optical flows are used in practice, it is shown explicitly that finite displacements generate a broader class of registrations. This work is motivated by applications in histological reconstruction and in dynamic medical imaging, and results are shown for such realistic examples.     

On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods

We examine four nodal versions of tensor product discontinuous Galerkin spectral element approximations to systems of conservation laws for quadrilateral or hexahedral meshes. They arise from the two choices of Gauss or Gauss-Lobatto quadrature and integrate by parts once (I) or twice (II) formulations of the discontinuous Galerkin method. We show that the two formulations are in fact algebraically equivalent with either Gauss or Gauss-Lobatto quadratures when global polynomial interpolations are used to approximate the solutions and fluxes within the elements. Numerical experiments confirm the equivalence of the approximations and indicate that using Gauss quadrature with integration by parts once is the most efficient of the four approximations.     

A Variational Framework for Structure from Motion in Omnidirectional Image Sequences

We address the problem of depth and ego-motion estimation from omnidirectional images. We propose a correspondence-free structure-from-motion problem for sequences of images mapped on the 2-sphere. A novel graph-based variational framework is first proposed for depth estimation between pairs of images. The estimation is cast as a TV-L1 optimization problem that is solved by a fast graph-based algorithm. The ego-motion is then estimated directly from the depth information without explicit computation of the optical flow. Both problems are finally addressed together in an iterative algorithm that alternates between depth and ego-motion estimation for fast computation of 3D information from motion in image sequences. Experimental results demonstrate the effective performance of the proposed algorithm for 3D reconstruction from synthetic and natural omnidirectional images.     

The Processing and Improvement of Multi-Statement Queries in Chiql

Chiql is a novel Chinese relational database query language for Chinese users.It supports procedural query style in which users can specify a complex database request in multiple simple statements.This facility renders Chiql simple-to-use and easy-to-remember.However,direct execution of multi-statemen Chiql rueries(i.e.statement by statement)is often inefficient as potential index-based operations(e.g.join) are by-passed.Furthermore,it often incurs additional database operations,such as scan and projection.To improve this situation,the SMA(Statement Merging Algorithm)is proposed.The goal of SMA is to merge as many dependent statments within Chiql query as possible to form a more efficient Chiql query.The ability in achieving improved effciency without sacrificing the simplicity of the language is the major advantage of this algorithm.     

Application of Discontinuous Galerkin Methods for Reaction-Diffusion Systems in Developmental Biology

Nonlinear reaction-diffusion systems which are often employed in mathematical modeling in developmental biology are usually highly stiff in both diffusion and reaction terms. Moreover, they are typically considered on multidimensional complex geometrical domains because of complex shapes of embryos. We overcome these computational challenges by combining discontinuous Galerkin (DG) finite element methods with Strang type symmetrical operator splitting technique, on triangular meshes. This allows us to avoid directly solving a coupled nonlinear system, as is necessary with the standard implicit schemes. Numerical solutions of two reaction-diffusion systems, the well-studied Schnakenberg model, which has been applied to several problems in developmental biology, and a new biologically based system for skeletal pattern formation in the vertebrate limb, are presented to demonstrate effects of various domain geometries on the resulting biological patterns.     

Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media

We present fully adaptive multiresolution methods for a class of spatially two-dimensional reaction-diffusion systems which describe excitable media and often give rise to the formation of spiral waves. A novel model ingredient is a strongly degenerate diffusion term that controls the degree of spatial coherence and serves as a mechanism for obtaining sharper wave fronts. The multiresolution method is formulated on the basis of two alternative reference schemes, namely a classical finite volume method, and Barkley’s approach (Barkley in Phys. D 49:61–70, 1991), which consists in separating the computation of the nonlinear reaction terms from that of the piecewise linear diffusion. The proposed methods are enhanced with local time stepping to attain local adaptivity both in space and time. The computational efficiency and the numerical precision of our methods are assessed. Results illustrate that the fully adaptive methods provide stable approximations and substantial savings in memory storage and CPU time while preserving the accuracy of the discretizations on the corresponding finest uniform grid.     

Geodesic Matting: A Framework for Fast Interactive Image and Video Segmentation and Matting

An interactive framework for soft segmentation and matting of natural images and videos is presented in this paper. The proposed technique is based on the optimal, linear time, computation of weighted geodesic distances to user-provided scribbles, from which the whole data is automatically segmented. The weights are based on spatial and/or temporal gradients, considering the statistics of the pixels scribbled by the user, without explicit optical flow or any advanced and often computationally expensive feature detectors. These could be naturally added to the proposed framework as well if desired, in the form of weights in the geodesic distances. An automatic localized refinement step follows this fast segmentation in order to further improve the results and accurately compute the corresponding matte function. Additional constraints into the distance definition permit to efficiently handle occlusions such as people or objects crossing each other in a video sequence. The presentation of the framework is complemented with numerous and diverse examples, including extraction of moving foreground from dynamic background in video, natural and 3D medical images, and comparisons with the recent literature.     

Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations

Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the last two decades, a growing interest has been devoted to a new family of methods, called spectral stochastic methods, for the propagation of uncertainties through physical models governed by stochastic partial differential equations. These approaches rely on a fruitful marriage of probability theory and approximation theory in functional analysis. This paper provides a review of some recent developments in computational stochastic methods, with a particular emphasis on spectral stochastic approaches. After a review of different choices for the functional representation of random variables, we provide an overview of various numerical methods for the computation of these functional representations: projection, collocation, Galerkin approaches…. A detailed presentation of Galerkin-type spectral stochastic approaches and related computational issues is provided. Recent developments on model reduction techniques in the context of spectral stochastic methods are also discussed. The aim of these techniques is to circumvent several drawbacks of spectral stochastic approaches (computing time, memory requirements, intrusive character) and to allow their use for large scale applications. We particularly focus on model reduction techniques based on spectral decomposition techniques and their generalizations. This work is supported by the French National Research Agency (grant ANR-06-JCJC-0064) and by GdR MoMaS with partners ANDRA, BRGM, CEA, CNRS, EDF, IRSN.