Real Time Local Approximation of Deformations using Rotations

Additional realism can be achieved in computer generated images using smooth and increasingly complex deformations. Though significant effort has been spent on improving these deformations, no general method has been proposed yet to deal with rigid pieces connected to soft objects. This paper proposes a general framework to solve this problem. We will present several types of applications, such as flowing small objects in a deformation field, animating rigid features connected to some deformed object, or smoothly attached limbs to a deforming body. All the calculations presented here can be applied to any type of deformation, provided that the deformation at each point only depends on the point itself. Even though we can directly compute the result for some analytical deformation fields, we will show that a good sampling of the deformation in the area of interest is generally enough. One intermediate result consists of a practical method to find the best rotation that approximates a linear transformation. The proposed method is a superset of the Gram-Schmidt orthonormalization process, and is much easier to compute than global methods based on Taylor series.     

A Vector-based Representation for Image Warping

A method for image analysis, representation and re-synthesis is introduced. Unlike other schemes it is not pixel based but rather represents a picture as vector data, from which an altered version of the original image can be rendered. Representing an image as vector data allows performing operations such as zooming, retouching or colourising, avoiding common problems associated with pixel image manipulation. This paper brings together methods from the areas of computer vision, image compositing and image based rendering to prove that this type of image representation is a step towards accurate and efficient image manipulation.     

Motion Balance Filtering

This paper presents a new technique called motion balance filtering, which corrects an unbalanced motion to a balanced one while preserving the original motion characteristics as much as possible. Differently from previous approaches that deal only with the balance of static posture, we solve the problem of balancing a dynamic motion. We achieve dynamic balance by analyzing and controlling the trajectory of the zero moment point (ZMP). Our algorithm consists of three steps. First, it analyzes the ZMP trajectory to find out the duration in which dynamic balance is violated. Dynamic imbalance is identified by the ZMP trajectory segments lying out of the supporting area. Next, the algorithm modifies the ZMP trajectory by projecting it into the supporting area. Finally, it generates the balanced motion that satisfies the new ZMP constraint. This process is formulated as a constrained optimization problem so that the new motion resembles the original motion as much as possible. Experiments prove that our motion balance filtering algorithm is a useful method to add physical realism to a kinematically edited motion.     

Representing Epistemic Uncertainty by Means of Dialectical Argumentation

We articulate a dialectical argumentation framework for qualitative representation of epistemic uncertainty in scientific domains. The framework is grounded in specific philosophies of science and theories of rational mutual discourse. We study the formal properties of our framework and provide it with a game theoretic semantics. With this semantics, we examine the relationship between the snaphots of the debate in the framework and the long run position of the debate, and prove a result directly analogous to the standard (Neyman–Pearson) approach to statistical hypothesis testing. We believe this formalism for representating uncertainty has value in domains with only limited knowledge, where experimental evidence is ambiguous or conflicting, or where agreement between different stakeholders on the quantification of uncertainty is difficult to achieve. All three of these conditions are found in assessments of carcinogenic risk for new chemicals.     

以复形为基础的非流形造型与基于物理的造型相结合的物体表示

提出一个新的表示物体的框架。通过非流形造型与基于物理的造型相结合，从拓扑结构和几何信息两个方面扩大了模型的表示范围。以代数拓扑中的复形为基础的非流形造型的作用是生成物体的拓扑框架，既可以表示ＣＡＤ的物体，更适合表示具有复杂拓扑结构的自然物体。基于物理的造型的作用是在拓扑框架上生成最终的几何信息。二者的结合提供了一种新的几何造型手段。     

Representing short-term observations of moving objects by a simple visual language

In a variety of dynamical systems, formations of motion patterns occur. Observing colonies of animals, for instance, for the scientist it is not only of interest which kinds of formations these animals show, but also how they altogether move around. In order to analyse motion patterns for the purpose of making predictions, to describe the behaviour of systems, or to index databases of moving objects, methods are required for dealing with them. This becomes increasingly important since a number of technologies have been devised which allow objects precisely to get traced. However, the indeterminacy of spatial information in real world environments also requires techniques to approximate reasoning, for example, in order to compensate for small and unimportant distinctions which are due to noisy measurements. As a consequence, precise as well as coarse motion patterns have to be dealt with.A set of 16 atomic motion patterns is proposed. On the one hand, a relation algebra is defined on them. On the other hand, these 16 relations form the basis of a visual language using which motion patterns can easily be dealt with in a diagrammatic way. The relations are coarse but crisp and they allow imprecise knowledge about motion patterns to be dealt with, while their diagrammatic realisation also allow precise patterns to get handled. While almost all approaches consider motion patterns along arbitrary time intervals, this paper in particular focuses on short-term motion patterns as we permanently observe them in our everyday life.The bottom line of the current work, however, is yet more general. While it has been widely argued that it makes sense to use both sentential and diagrammatic representations in order to represent different things in the same system adequately (and hence differently), we argue that it makes even sense to represent the same things differently in order to grasp different aspects of one and the same object of interest from different viewpoints. We demonstrate this by providing both a sentential and a diagrammatic representation for the purpose of grasping different aspects of motion patterns. It shows that both representations complement each other.     

Computational methods for database repair by signed formulae*

We introduce a simple and practical method for repairing inconsistent databases. Given a possibly inconsistent database, the idea is to properly represent the underlying problem, i.e., to describe the possible ways of restoring its consistency. We do so by what we call signed formulae, and show how the ‘signed theory’ that is obtained can be used by a variety of off-the-shelf computational models in order to compute the corresponding solutions, i.e., consistent repairs of the database. *This paper is a revised and extended version of [9].     

Representing effects of micro-topography on runoff generation and sub-surface flow patterns by using superficial rill/depression storage height variations

An adequate representation of micro-topography in spatially explicit, physically based models can be crucial in modeling runoff generation, surface/subsurface flow interactions or subsurface flow patterns in hydrological systems with pronounced micro-topography. However, representation of micro-topography in numerical models usually requires high grid resolutions to capture relevant small scale variations in topography at the range of centimeters to meters. High grid resolutions usually result in longer simulation times, especially if fully integrated model approaches are used where the governing partial differential equations for surface and subsurface flow are solved simultaneously. This often restricts the implementation of micro-topography to plot scale models where the overall model domain is small to minimize computational cost resulting from a high grid resolution. In this study an approach is presented where a highly resolved digital elevation model (DEM) for a hummocky topography in a plot scale wetland model (10 m × 21 m × 2 m), is represented by spatially distributed rill/depression storage zones in a numerical model with a planar surface. By replacing the explicit micro-topography with spatially distributed rill/depression storage zones, important effects of micro-topography on surface flow generation and subsurface transport characteristics (e.g. residence time distributions) are being preserved, while at the same time the number of computational nodes is reduced significantly. We demonstrate that the rill/depression storage concept, which has been used for some time to represent time delays in the generation of surface runoff, can also be used to mimic subsurface flow patterns caused by micro-topography. Results further indicate that the rill/depression storage concept is an efficient tool to represent micro-topography in plot scale models because model computation times drop significantly. As important aspects of surface and subsurface flows induced by micro-topography can be mimicked adequately by applying the rill/depression storage concept on a coarser grid, it may also be a useful tool to represent micro-topography in numerical flow models beyond the plot scale.     

Context‐Based Coding of Adaptive Multiresolution Meshes

Multiresolution meshes provide an efficient and structured representation of geometric objects. To increase the mesh resolution only at vital parts of the object, adaptive refinement is widely used. We propose a lossless compression scheme for these adaptive structures that exploits the parent–child relationships inherent to the mesh hierarchy. We use the rules that correspond to the adaptive refinement scheme and store bits only where some freedom of choice is left, leading to compact codes that are free of redundancy. Moreover, we extend the coder to sequences of meshes with varying refinement. The connectivity compression ratio of our method exceeds that of state‐of‐the‐art coders by a factor of 2–7. For efficient compression of vertex positions we adapt popular wavelet‐based coding schemes to the adaptive triangular and quadrangular cases to demonstrate the compatibility with our method. Akin to state‐of‐the‐art coders, we use a zerotree to encode the resulting coefficients. Using improved context modelling we enhanced the zerotree compression, cutting the overall geometry data rate by 7% below those of the successful Progressive Geometry Compression. More importantly, by exploiting the existing refinement structure we achieve compression factors that are four times greater than those of coders which can handle irregular meshes.     

Computation of probabilities of survival/failure of technical,economic systems/structures by means of piecewise linearization of the performance function

The computation of the probability of survival/failure of technical/economic structures and systems is based on an appropriate performance or so-called (limit) state function separating the safe and unsafe states in the space of random model parameters. Starting with the survival conditions, hence, the state equation and the condition for the admissibility of states, an optimizational representation of the state function can be given in terms of the minimum value function of a closely related minimization problem. Selecting a certain number of boundary points of the safe/unsafe domain, hence, on the limit state surface, the safe/unsafe domain is approximated by a convex polyhedron. This convex polyhedron is defined by the intersection of the half spaces in the parameter space generated by the tangent hyperplanes to the safe/unsafe domain at the selected boundary points on the limit state surface. The approximative probability functions are then defined by means of the resulting probabilistic linear constraints in the parameter space. After an appropriate transformation, the probability distribution of the parameter vector can be assumed to be normal with zero mean vector and unit covariance matrix. Working with separate linear constraints, approximation formulas for the probability of survival of the structure are obtained immediately. More exact approximations are obtained by considering joint probability constraints. In a second approximation step, these approximations can be evaluated by using probability inequalities and/or discretizations of the underlying probability distribution.     

Image Interpolation by Pixel-Level Data-Dependent Triangulation

We present a novel image interpolation algorithm. The algorithm can be used in arbitrary resolution enhancement, arbitrary rotation and other applications of still images in continuous space. High‐resolution images are interpolated from the pixel‐level data‐dependent triangulation of lower‐resolution images. It is simpler than other methods and is adaptable to a variety of image manipulations. Experimental results show that the new “mesh image” algorithm is as fast as the bilinear interpolation method. We assess the interpolated images' quality visually and also by the MSE measure which shows our method generates results comparable in quality to slower established methods. We also implement our method in graphics card hardware using OpenGL which leads to real‐time high‐quality image reconstruction. These features give it the potential to be used in gaming and image‐processing applications.