Image-space Approach Research Articles

Perturbation of Image and conjugate duality for vector optimization

<p style='text-indent:20px;'>This paper aims at employing the image space approach to investigate the conjugate duality theory for general constrained vector optimization problems. We introduce the concepts of conjugate map and subdifferential by using two types of maximums. We also construct the conjugate duality problems via a perturbation method. Moreover, the separation condition is proposed by means of vector weak separation functions. Then, it is proved to be a new sufficient condition, which ensures the strong duality theorem. This separation condition is different from the classical regular conditions in the literature. Simultaneously, the application to a nonconvex multi-objective optimization problem is shown to verify our main results.</p>

Quantified, Interactive Simulation of AMCW ToF Camera Including Multipath Effects.

In the last decade, Time-of-Flight (ToF) range cameras have gained increasing popularity in robotics, automotive industry, and home entertainment. Despite technological developments, ToF cameras still suffer from error sources such as multipath interference or motion artifacts. Thus, simulation of ToF cameras, including these artifacts, is important to improve camera and algorithm development. This paper presents a physically-based, interactive simulation technique for amplitude modulated continuous wave (AMCW) ToF cameras, which, among other error sources, includes single bounce indirect multipath interference based on an enhanced image-space approach. The simulation accounts for physical units down to the charge level accumulated in sensor pixels. Furthermore, we present the first quantified comparison for ToF camera simulators. We present bidirectional reference distribution function (BRDF) measurements for selected, purchasable materials in the near-infrared (NIR) range, craft real and synthetic scenes out of these materials and quantitatively compare the range sensor data.

Characterization of duality for a generalized quasi-equilibrium problem

In this paper, the duality theory of a generalized quasi-equilibrium problem (also called generalized Ky Fan quasi-inequality) is investigated by using the image space approach. Generalized quasi-equilibrium problem is transformed into a minimization problem. The minimization problem is further reformulated as an image problem by virtue of linear/nonlinear separation function. The dual problem of the image problem is constructed in the image space, then zero duality gap between the image problem and its dual problem is derived under saddle point condition as well as the equivalent regular linear/nonlinear separation condition. Finally, some more sufficient conditions guaranteeing zero duality gap are also proposed.

Asymmetric Tensor Field Visualization for Surfaces

Asymmetric tensor field visualization can provide important insight into fluid flows and solid deformations. Existing techniques for asymmetric tensor fields focus on the analysis, and simply use evenly-spaced hyperstreamlines on surfaces following eigenvectors and dual-eigenvectors in the tensor field. In this paper, we describe a hybrid visualization technique in which hyperstreamlines and elliptical glyphs are used in real and complex domains, respectively. This enables a more faithful representation of flow behaviors inside complex domains. In addition, we encode tensor magnitude, an important quantity in tensor field analysis, using the density of hyperstreamlines and sizes of glyphs. This allows colors to be used to encode other important tensor quantities. To facilitate quick visual exploration of the data from different viewpoints and at different resolutions, we employ an efficient image-space approach in which hyperstreamlines and glyphs are generated quickly in the image plane. The combination of these techniques leads to an efficient tensor field visualization system for domain scientists. We demonstrate the effectiveness of our visualization technique through applications to complex simulated engine fluid flow and earthquake deformation data. Feedback from domain expert scientists, who are also co-authors, is provided.

An image space approach to Cartesian based parallel MR imaging with total variation regularization

The Cartesian parallel magnetic imaging problem is formulated variationally using a high-order penalty for coil sensitivities and a total variation like penalty for the reconstructed image. Then the optimality system is derived and numerically discretized. The objective function used is non-convex, but it possesses a bilinear structure that allows the ambiguity among solutions to be resolved technically by regularization and practically by normalizing a pre-estimated norm of the reconstructed image. Since the objective function is convex in each single argument, convex analysis is used to formulate the optimality condition for the image in terms of a primal-dual system. To solve the optimality system, a nonlinear Gauss-Seidel outer iteration is used in which the objective function is minimized with respect to one variable after the other using an inner generalized Newton iteration. Computational results for in vivo MR imaging data show that a significant improvement in reconstruction quality can be obtained by using the proposed regularization methods in relation to alternative approaches.

Image space approach and subdifferentials of integral functionals

We relate the image space approach and the theory of perturbations in the framework of nonconvex duality. We show that both theories can be applied to problems involving integral functionals on L 1. Using simple characterizations of the Fréchet subdifferential and of the limiting subdifferential of an integral functional on some L 1 space, we show that a nonconvex duality theory can be obtained for such functionals. The subdifferential of an integral functional on some L p space cannot be given such a simple characterization but the one obtained by E. Giner uses duality tools and we compare it with the image space approach.

Mapping similarity between parallel and serial architecture kinematics

First the principles of mapping spatial points to surfaces is introduced in the context of the inverse kinematics of a general six revolute serial wrist partitioned robot. Then the advantage of choosing ideal frames is illustrated by showing that in the case of some architectures an image space formulation, though possible, may be an impediment to clear geometric insight and a satisfactory and much simpler solution. After showing how the general point mapping transformation is reduced to classical Blaschke-Grunwald planar mapping a novel three legged planar robot’s direct kinematics is solved in image space and then using conventional “distance” constraints. The purpose is to show why the latter approach yields spurious solutions and how the displacement pole rotation performed with kinematic mapping reliably avoids this problem. In conclusion certain other new and/or interesting reduced mobility parallel robots are discussed briefly to point out some advantages and insights gained with an image space approach. Particular effort is made to expose in detail how mapping simplifies and extends the solution of direct kinematics pertaining to Calvel’s “Delta” 3D translational robot.

Multi‐Image Based Photon Tracing for Interactive Global Illumination of Dynamic Scenes

AbstractImage space photon mapping has the advantage of simple implementation on GPU without pre‐computation of complex acceleration structures. However, existing approaches use only a single image for tracing caustic photons, so they are limited to computing only a part of the global illumination effects for very simple scenes. In this paper we fully extend the image space approach by using multiple environment maps for photon mapping computation to achieve interactive global illumination of dynamic complex scenes. The two key problems due to the introduction of multiple images are 1) selecting the images to ensure adequate scene coverage; and 2) reliably computing ray‐geometry intersections with multiple images. We present effective solutions to these problems and show that, with multiple environment maps, the image‐space photon mapping approach can achieve interactive global illumination of dynamic complex scenes. The advantages of the method are demonstrated by comparison with other existing interactive global illumination methods.

A SEPARATION APPROACH TO VECTOR QUASI-EQUILIBRIUM PROBLEMS: SADDLE POINT AND GAP FUNCTION

The image space approach is applied to the study of vector quasiequilibrium problems. Exploiting separation arguments in the image space, Lagrangian-type optimality conditions and gap functions for vector quasiequilibrium problems are derived.

A SEPARATION APPROACH TO VECTOR QUASI-EQUILIBRIUM PROBLEMS: SADDLE POINT AND GAP FUNCTION

The image space approach is applied to the study of vector quasiequilibrium problems. Exploiting separation arguments in the image space, Lagrangian-type optimality conditions and gap functions for vector quasiequilibrium problems are derived.

GPU-based rendering for deformable translucent objects

In this paper we introduce an approximate image-space approach for real-time rendering of deformable translucent models by flattening the geometry and lighting information of objects into textures to calculate multi-scattering in texture spaces. We decompose the process into two stages, called the gathering and scattering corresponding to the computations for incident and exident irradiance respectively. We derive a simplified illumination model for the gathering of the incident irradiance, which is amenable for deformable models using two auxiliary textures. In the scattering stage, we adopt two modes for efficient accomplishment of the view-dependent scattering. Our approach is implemented by fully exploiting the capabilities of graphics processing units (GPUs). It achieves visually plausible results and real-time frame rates for deformable models on commodity desktop PCs.

Lagrangian Duality and Cone Convexlike Functions

In this paper, we consider first the most important classes of cone convexlike vector-valued functions and give a dual characterization for some of these classes. It turns out that these characterizations are strongly related to the closely convexlike and Ky Fan convex bifunctions occurring within minimax problems. Applying the Lagrangian perturbation approach, we show that some of these classes of cone convexlike vector-valued functions show up naturally in verifying strong Lagrangian duality for finite-dimensional optimization problems. This is achieved by extending classical convexity results for biconjugate functions to the class of so-called almost convex functions. In particular, for a general class of finite-dimensional optimization problems, strong Lagrangian duality holds if some vector-valued function related to this optimization problem is closely K-convexlike and satisfies some additional regularity assumptions. For K a full-dimensional convex cone, it turns out that the conditions for strong Lagrangian duality simplify. Finally, we compare the results obtained by the Lagrangian perturbation approach worked out in this paper with the results achieved by the so-called image space approach initiated by Giannessi.

Image-based streamline generation and rendering

Seeding streamlines in 3D flow fields without considering their projections in screen space can produce visually cluttered rendering results. Streamlines will overlap or intersect with each other in the output image, which makes it difficult for the user to perceive the underlying flow structure. This paper presents a method to control the seeding and generation of streamlines in image space to avoid visual cluttering and allow a more flexible exploration of flow fields. In our algorithm, 2D images with depth maps generated by a variety of visualization techniques can be used as input from which seeds are placed and streamlines are generated. The density and rendering styles of streamlines can be flexibly controlled based on various criteria to improve visual clarity. With our image space approach, it is straightforward to implement the level of detail rendering, depth peeling, and stylized rendering of streamlines to allow for more effective visualization of 3D flow fields.

Image-Based Streamline Generation and Rendering

Seeding streamlines in 3D flow fields without considering their projections in screen space can produce visually cluttered rendering results. Streamlines will overlap or intersect with each other in the output image, which makes it difficult for the user to perceive the underlying flow structure. This paper presents a method to control the seeding and generation of streamlines in image space to avoid visual cluttering and allow a more flexible exploration of flow fields. In our algorithm, 2D images with depth maps generated by a variety of visualization techniques can be used as input from which seeds are placed and streamlines are generated. The density and rendering styles of streamlines can be flexibly controlled based on various criteria to improve visual clarity. With our image space approach, it is straightforward to implement the level of detail rendering, depth peeling, and stylized rendering of streamlines to allow for more effective visualization of 3D flow fields.

An approximate image-space approach for interactive refraction

Many interactive applications strive for realistic renderings, but framerate constraints usually limit realism to effects that run efficiently in graphics hardware. One effect largely ignored in such applications is refraction. We introduce a simple, image-space approach to refractions that easily runs on modern graphics cards. Our method requires two passes on a GPU, and allows refraction of a distant environment through two interfaces, compared to current interactive techniques that are restricted to a single interface. Like all image-based algorithms, aliasing can occur in certain circumstances, but the plausible refractions generated with our approach should suffice for many applications.

ISA and IBFVS: image space-based visualization of flow on surfaces

We present a side-by-side analysis of two recent image space approaches for the visualization of vector fields on surfaces. The two methods, Image Space Advection (ISA) and Image-Based Flow Visualization for Curved Surfaces (IBFVS) generate dense representations of time-dependent vector fields with high spatio-temporal correlation. While the 3D vector fields are associated with arbitrary surfaces represented by triangular meshes, the generation and advection of texture properties is confined to image space. Fast frame rates are achieved by exploiting frame-to-frame coherency and graphics hardware. In our comparison of ISA and IBFVS, we point out the strengths and weaknesses of each approach and give recommendations as to when and where they are best applied.

Image-based techniques in a hybrid collision detector

Most collision detection methods developed so far are based on geometrical object-space interference tests. While this remains the basic mode of investigation for geometric algorithms, the requirements for interactive rates and complex geometry predominate in commercial applications. In this article, we propose a new mode of collision detection based on an image-space approach. This approach breaks the object-space collision detection bottleneck by distributing the computational load onto the hardware graphics pipeline. The image-space approach, in conjunction with efficient bounding-box strategies in the object-space, has the potential to handle complex object interactions at interactive rates.

Image-Based Techniques in a Hybrid Collision Detector

Most collision detection methods developed so far are based on geometrical object-space interference tests. While this remains the basic mode of investigation for geometric algorithms, the requirements for interactive rates and complex geometry predominate in commercial applications. In this article, we propose a new mode of collision detection based on an image-space approach. This approach breaks the object-space collision detection bottleneck by distributing the computational load onto the hardware graphics pipeline. The image-space approach, in conjunction with efficient bounding-box strategies in the object-space, has the potential to handle complex object interactions at interactive rates.

Quasi-Multiplier Rules for Quasidifferentiable Extremum Problems

The purpose of the present article is to contribute to clarify the role of the Lagrange multipliers within the theory of the first order necessary optimality conditions for nonsmooth constrained optimization, when the directional derivatives of functions involved in the extremum problems are not sublinear. This task is accomplished in the particular case of quasidifferentiable problems with side constraints. In such setting, making use of the image-space approach, it is possible to establish a generalized (nonlinear) separation result by means of which a new Lagrange principle is obtained. According to this principle, which seems to fit better quasidifferentiable extremum problems than the classic one, the concept of linear multiplier is to be replaced with that of quasi-multiplier, a sublinear and continuous functional whose existence can be guaranteed under mild assumptions, even when classic multipliers fail to exist. Such as extension allows to formulate in terms of Lagrange function the known optimality necessary condition for unconstrained quasidifferentiable optimization expressed in form of quasidifferential inclusion. Along with this, other multiplier rules are established.

RECODE: an image-based collision detection algorithm

Object interactions are ubiquitous in interactive computer graphics, 3D object motion simulations, virtual reality and robotics applications. Most collision detection algorithms are based on geometrical object-space interference tests. Some algorithms have employed an image-space approach to the collision detection problem. In this paper we demonstrate an image-space collision detection process that allows substantial computational savings during the image-space interference test. This approach makes efficient use of the graphics rendering hardware for real-time complex object interactions. Copyright © 1999 John Wiley & Sons, Ltd.