Superposition of local zoom models and simultaneous calibration for 1D–2D shallow water flows

We address the problem of coupling 2D shallow water equations with 1D shallow water equations (St-Venant equations), as applied to river-floodplain flows. Mathematical coupling conditions are derived classicaly from the 3D Navier–Stokes equations by integrating over the vertical wet section, when overflowing occurs. It leads to extra source terms in the 1D equations. Next we assume to be in a variational data assimilation context, then the optimal control process allows to couple both models and assimilate data simultaneously (Joint Assimilation Coupling algorithms). Two different versions of JAC algorithms are presented and compared. In a numerical test case, we superimpose the local 2D model on the 1D global model. The results show the efficiency of the present simultaneous superposition–assimilation approach.     

Restoring warped document images through 3D shape modeling

Scanning a document page from a thick bound volume often results in two kinds of distortions in the scanned image, i.e., shade along the "spine" of the book and warping in the shade area. In this paper, we propose an efficient restoration method based on the discovery of the 3D shape of a book surface from the shading information in a scanned document image. From a technical point of view, this shape from shading (SFS) problem in real-world environments is characterized by 1) a proximal and moving light source, 2) Lambertian reflection, 3) nonuniform albedo distribution, and 4) document skew. Taking all these factors into account, we first build practical models (consisting of a 3D geometric model and a 3D optical model) for the practical scanning conditions to reconstruct the 3D shape of the book surface. We next restore the scanned document image using this shape based on deshading and dewarping models. Finally, we evaluate the restoration results by comparing our estimated surface shape with the real shape as well as the OCR performance on original and restored document images. The results show that the geometric and photometric distortions are mostly removed and the OCR results are improved markedly.     

Symmetry-seeking models and 3D object reconstruction

We propose models of 3D shape which may be viewed as deformable bodies composed of simulated elastic material. In contrast to traditional, purely geometric models of shape, deformable models are active—their shapes change in response to externally applied forces. We develop a deformable model for 3D shape which has a preference for axial symmetry. Symmetry is represented even though the model does not belong to a parametric shape family such as (generalized) cylinders. Rather, a symmetry-seeking property is designed into internal forces that constrain the deformations of the model. We develop a framework for 3D object reconstruction based on symmetry-seeking models. Instances of these models are formed from monocular image data through the action of external forces derived from the data. The forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2D silhouette of an object of interest. The effectiveness of our approach is demonstrated using natural images.     

Face Editing Using Part-Based Optimization of the Latent Space

We propose an approach for interactive 3D face editing based on deep generative models. Most of the current face modeling methods rely on linear methods and cannot express complex and non-linear deformations. In contrast to 3D morphable face models based on Principal Component Analysis (PCA), we introduce a novel architecture based on variational autoencoders. Our architecture has multiple encoders (one for each part of the face, such as the nose and mouth) which feed a single decoder. As a result, each sub-vector of the latent vector represents one part. We train our model with a novel loss function that further disentangles the space based on different parts of the face. The output of the network is a whole 3D face. Hence, unlike part-based PCA methods, our model learns to merge the parts intrinsically and does not require an additional merging process. To achieve interactive face modeling, we optimize for the latent variables given vertex positional constraints provided by a user. To avoid unwanted global changes elsewhere on the face, we only optimize the subset of the latent vector that corresponds to the part of the face being modified. Our editing optimization converges in less than a second. Our results show that the proposed approach supports a broader range of editing constraints and generates more realistic 3D faces.     

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.     

Decision trees for accelerating unimodal, hybrid and multimodal rendering models

This paper deals with the rendering of segmented unimodal, hybrid and aligned multimodal voxel models. We propose a data structure that classifies the segmented voxels into categories, so that whenever the model has to be traversed, only the selected categories are visited and the empty and non-selected voxels are skipped. This strategy is based on: (i) a decision tree, called the rendering decision tree (RDT), which represents the hierarchy of the classification process and (ii) an intermediate run-length encoding (RLE) of the classified voxel model. The traversal of the voxel model given a user query consists of two steps: first, the RDT is traversed and the set of selected categories computed; next, the RLE is visited, but the non-selected runs are skipped and only the voxels of the original model that are codified are accessed in selected runs of the RLE. This strategy has been used to render a voxel model by back-to-front traversal and splatting as well as to construct 3D textures for hardware-driven 3D texture mapping. The results show that the voxel model traversal is significantly accelerated.     

Videoshop: A new framework for spatio-temporal video editing in gradient domain

This paper proposes a new framework for video editing in gradient domain. The spatio-temporal gradient fields of target videos are modified and/or mixed to generate a new gradient field which is usually not integrable. We compare two methods to solve this “mixed gradient problem”, i.e., the variational method and loopy belief propagation. We propose a 3D video integration algorithm, which uses the variational method to find the potential function whose gradient field is closest to the mixed gradient field in the sense of least squares. The video is reconstructed by solving a 3D Poisson equation. The main contributions of our framework lie in three aspects: first, we derive a straightforward extension of current 2D gradient technique to 3D space, thus resulting in a novel video editing framework, which is very different from all current video editing software; secondly, we propose using a fast and accurate 3D discrete Poisson solver which uses diagonal multigrids to solve the 3D Poisson equation, which is up to twice as fast as a simple conventional multigrid algorithm; finally, we introduce a set of new applications, such as face replacement and painting, high dynamic range video compression and graphcut based video compositing. A set of gradient operators is also provided to the user for editing purposes. We evaluate our algorithm using a variety of examples for image/video or video/video pairs. The resulting video can be seamlessly reconstructed.     

Regularized Laplacian Zero Crossings as Optimal Edge Integrators

We view the fundamental edge integration problem for object segmentation in a geometric variational framework. First we show that the classical zero-crossings of the image Laplacian edge detector as suggested by Marr and Hildreth, inherently provides optimal edge-integration with regard to a very natural geometric functional. This functional accumulates the inner product between the normal to the edge and the gray level image-gradient along the edge. We use this observation to derive new and highly accurate active contours based on this functional and regularized by previously proposed geodesic active contour geometric variational models. We also incorporate a 2D geometric variational explanation to the Haralick edge detector into the geometric active contour framework.     

三维图像多相分割的变分水平集方法

变分水平集方法是图像分割等领域出现的新的建模方法,借助多个水平集函数可有效地实现图像多相分割.但在区域/相的通用表达、不同区域内图像模型的表达、通用的能量函的设计、高维图像分割中的拓展研究等方面仍是图像处理的变分方法、水平集方法、偏微分方程方法等研究的热点问题.文中以三维图像为研究对象,系统地建立了一种新的三维图像多相分割的变分水平集方法.该方法用n-1个水平集函数划分n个区域,并基于Heaviside函数设汁出区域划分的通用的特征函数;其能量泛函包括通用的区域模型、边缘检测模型和水平集函数为符号距离函数的约束项3部分;最后,针对所得到的曲面演化方程,采用半隐式差分格式进行离散,并对多种类型三维图像进行分割验证了所提出模型的通用性和有效性.     

Mapping 2D midship drawings into a 3D ship hull model based on STEP AP218

Standard for the exchange of product model data (STEP) AP218 has a standard schema to represent the structural model of a midship section. While its schema facilitate the exchange of ship structural models among heterogeneous systems, most shipyards and classification societies exchange information using 2D paper drawings. We propose a feature parameter input method to generate a 3D STEP model of a ship structure from 2D drawings. We have analyzed the ship structure information contained in 2D drawings and have defined a data model to express the contents of the drawing. We also developed a GUI for the feature parameter input. To translate 2D information extracted from the drawing into a STEP AP218 model, we have developed a shape generation library and have generated the 3D ship model through this library. The generated 3D STEP model of a ship structure can be used to exchange information between design departments in a shipyard as well as between classification societies and shipyards.     

Coupling finite elements and auxiliary sources

We consider second-order scalar elliptic boundary value problems on unbounded domains, which model, for instance, electrostatic fields. We propose a discretization that relies on a Trefftz approximation by multipole auxiliary sources in some parts of the domain and on standard mesh-based primal Lagrangian finite elements in other parts. Several approaches are developed and, based on variational saddle point theory, rigorously analyzed to couple both discretizations across the common interface:1. Least-squares-based coupling using techniques from PDE-constrained optimization.2. Coupling through Dirichlet-to-Neumann operators.3. Three-field variational formulation in the spirit of mortar finite element methods.We compare these approaches in a series of numerical experiments.     

3D clipping algorithm for feature mapping across domains

This paper describes an algorithm based on 3D clipping for mapping feature models across domains. The problem is motivated by the need to identify feature models corresponding to different domains. Feature mapping (also referred to as feature conversion) involves obtaining a feature model in one domain given a feature model in another. This is in contrast to feature extraction which works from the boundary representation of the part. Most techniques for feature mapping have focused on obtaining negative feature models only. We propose an algorithm that can convert a feature model with mixed features (both positive and negative) to a feature model containing either only positive or only negative features.The input to the algorithm is a feature model in one domain. The algorithm for mapping this model to another feature model is based on classification of faces of features in the model and 3D clipping. 3D clipping refers to the splitting of a solid by a surface. The feature mapping process involves three major steps. In the first step, faces forming the features in the input model are classified with respect to one another. The spatial arrangement of faces is used next to derive the dependency relationship amongst features in the input model and a Feature Relationship Graph (FRG) is constructed. In the second step, using the FRG, features are clustered and interactions between features (if any) are resolved. In the final step, the 3D clipping algorithm is used to determine the volumes corresponding to the features in the target domain. These volumes are then classified to identify the features for obtaining the feature model in the target domain. Multiple feature sets (where possible) can be obtained by varying the sequence of faces used for clipping. Results of implementation are presented.     

Fast Global Minimization of the Active Contour/Snake Model

The active contour/snake model is one of the most successful variational models in image segmentation. It consists of evolving a contour in images toward the boundaries of objects. Its success is based on strong mathematical properties and efficient numerical schemes based on the level set method. The only drawback of this model is the existence of local minima in the active contour energy, which makes the initial guess critical to get satisfactory results. In this paper, we propose to solve this problem by determining a global minimum of the active contour model. Our approach is based on the unification of image segmentation and image denoising tasks into a global minimization framework. More precisely, we propose to unify three well-known image variational models, namely the snake model, the Rudin–Osher–Fatemi denoising model and the Mumford–Shah segmentation model. We will establish theorems with proofs to determine the existence of a global minimum of the active contour model. From a numerical point of view, we propose a new practical way to solve the active contour propagation problem toward object boundaries through a dual formulation of the minimization problem. The dual formulation, easy to implement, allows us a fast global minimization of the snake energy. It avoids the usual drawback in the level set approach that consists of initializing the active contour in a distance function and re-initializing it periodically during the evolution, which is time-consuming. We apply our segmentation algorithms on synthetic and real-world images, such as texture images and medical images, to emphasize the performances of our model compared with other segmentation models. Research supported by NIH U54RR021813, NSF DMS-0312222, NSF ACI-0321917 and NSF DMI-0327077.     

A hybrid data assimilation scheme for model parameter estimation: Application to morphodynamic modelling

We present a novel algorithm for joint state-parameter estimation using sequential three dimensional variational data assimilation (3D Var) and demonstrate its application in the context of morphodynamic modelling using an idealised two parameter 1D sediment transport model. The new scheme combines a static representation of the state background error covariances with a flow dependent approximation of the state-parameter cross-covariances. For the case presented here, this involves calculating a local finite difference approximation of the gradient of the model with respect to the parameters. The new method is easy to implement and computationally inexpensive to run. Experimental results are positive with the scheme able to recover the model parameters to a high level of accuracy. We expect that there is potential for successful application of this new methodology to larger, more realistic models with more complex parameterisations.     

Dynamic Trees for unsupervised segmentation and matching of image regions

We present a probabilistic framework namely, multiscale generative models known as dynamic trees (DT), for unsupervised image segmentation and subsequent matching of segmented regions in a given set of images. Beyond these novel applications of DTs, we propose important additions for this modeling paradigm. First, we introduce a novel DT architecture, where multilayered observable data are incorporated at all scales of the model. Second, we derive a novel probabilistic inference algorithm for DTs, structured variational approximation (SVA), which explicitly accounts for the statistical dependence of node positions and model structure in the approximate posterior distribution, thereby relaxing poorly justified independence assumptions in previous work. Finally, we propose a similarity measure for matching dynamic-tree models, representing segmented image regions, across images. Our results for several data sets show that DTs are capable of capturing important component-subcomponent relationships among objects and their parts, and that DTs perform well in segmenting images into plausible pixel clusters. We demonstrate the significantly improved properties of the SVA algorithm, both in terms of substantially faster convergence rates and larger approximate posteriors for the inferred models, when compared with competing inference algorithms. Furthermore, results on unsupervised object recognition demonstrate the viability of the proposed similarity measure for matching dynamic-structure statistical models.     

Variational Segmentation of Image Sequences Using Region-Based Active Contours and Deformable Shape Priors

In this paper we address the problem of segmentation in image sequences using region-based active contours and level set methods. We propose a novel method for variational segmentation of image sequences containing nonrigid, moving objects. The method is based on the classical Chan-Vese model augmented with a novel frame-to-frame interaction term, which allow us to update the segmentation result from one image frame to the next using the previous segmentation result as a shape prior. The interaction term is constructed to be pose-invariant and to allow moderate deformations in shape. It is expected to handle the appearance of occlusions which otherwise can make segmentation fail. The performance of the model is illustrated with experiments on synthetic and real image sequences.     

Blood glucose level prediction for diabetes based on modified fuzzy time series and particle swarm optimization

Blood glucose control is an essential goal for the patients who have Type‐1 diabetes (T1D). The prediction of the blood glucose levels for the next 30‐minute is crucial. If the predicted blood glucose level is in the critical ranges, and these predictions can be known in advance, then the patients can take the necessary cautions to prevent from it. In this article, we propose a modified fuzzy particle swarm optimization algorithm for the prediction of blood glucose levels of 30‐minute after the last measurement. We form the average and patient‐specific models to predict the blood glucose level of the patients. Both models are tested on two different datasets which contain patients with T1D. The experimental results are evaluated in terms of root mean squared error and Clarke error grid analysis metrics. The results indicate that our proposed modified algorithm is feasible to be applied to the prediction of blood glucose levels. In addition, this approach can assist patients with T1D for their blood glucose control.     

Multi‐product supply chain horizontal network integration: models,theory, and computational results

In this paper, we develop multi‐product supply chain network models with explicit capacities, before and after their horizontal integration. In addition, we propose a measure, which allows one to quantify and assess, from a supply chain network perspective, the synergy benefits associated with the integration of multi‐product firms through mergers/acquisitions. We utilize a system‐optimization perspective for the model development and provide the variational inequality formulations, which are then utilized to propose a computational procedure which fully exploits the underlying network structure. We illustrate the theoretical and computational framework with numerical examples. This paper is a contribution to the literatures of supply chain integration and mergers and acquisitions.     

Coupling superposed 1D and 2D shallow-water models: Source terms in finite volume schemes

We study the superposition of 1D and 2D shallow-water equations with non-flat topographies, in the context of river-flood modeling. Since we superpose both models in the bi-dimensional areas, we focus on the definition of the coupling term required in the 1D equations. Using explicit finite volume schemes, we propose a definition of the discrete coupling term leading to schemes globally well-balanced (the global scheme preserves water at rest whatever if overflowing or not). For both equations (1D and 2D), we can consider independent finite volume schemes based on well-balanced Roe, HLL, Rusanov or other scheme, then the resulting global scheme remains well-balanced. We perform a few numerical tests showing on the one hand the well-balanced property of the resulting global numerical model, on the other hand the accuracy and robustness of our superposition approach. Therefore, the definition of the coupling term we present allows to superpose a local 2D model over a 1D main channel model, with non-flat topographies and mix incoming-outgoing lateral fluxes, using independent grids and finite volume solvers.