This paper presents the MinUnc method to construct m-/belief functions in the framework of the Dempster-Shafer theory to represent the uncertainty in a given body of evidence. Using the Aprinciple of minimum uncertainty and the concepts of entropy and non-specificity, the MinUnc method specifies a partition of a finite interval on the real line and assigns belief masses to the uniform subintervals. The proposed MinUnc method is illustrated using a simple example and applied to uncertainty representation of air flight arrival delay data set.

In this paper, we apply compressed sensing (CS) to video compression. CS techniques exploit the observation that one needs much fewer random measurements than given by the Shannon-Nyquist sampling theory to recover an object if this object is compressible (i.e., sparse in the spatial domain or in a transform domain). In the CS framework, we can achieve sensing, compression, and denoising simultaneously. We propose a fast and simple online encoding by the application of pseudorandom downsampling of the 2-D fast Fourier transform to video frames. For offline decoding, we apply a modification of the recently proposed approximate message passing (AMP) algorithm. The AMP method has been derived using the statistical concept of “state evolution,” and it has been shown to considerably accelerate the convergence rate in special CS-decoding applications. We shall prove that the AMP method can be rewritten as a forward-backward splitting algorithm. This new representation enables us to give conditions that ensure convergence of the AMP method and to modify the algorithm in order to achieve higher robustness. The success of reconstruction methods for video decoding also essentially depends on the chosen transform, where sparsity of the video signals is assumed. We propose incorporating the 3-D dual-tree complex wavelet transform that possesses sufficiently good directional selectivity while being computationally less expensive and less redundant than other directional 3-D wavelet transforms.

A new hybrid scheme, called Lagrangian-Eulerian advection (LEA), that combines the advantages of the Eulerian and Lagrangian frameworks is applied to the visualization of dense representations of time-dependent vector fields. The algorithm encodes the particles into a texture that is then advected. By treating every particle equally, we can handle texture advection and dye advection within a single framework. High temporal and spatial correlation is achieved through the blending of successive frames. A combination of particle and dye advection enables the simultaneous visualization of streamlines, particle paths and streak-lines. We demonstrate various experimental techniques on several physical flow fields. The simplicity of both the resulting data structures and the implementation suggest that LEA could become a useful component of any scientific visualization toolkit concerned with the display of unsteady flows.

In this paper, we propose a new technique to visualize dense representations of time-dependent vector fields based on a Lagrangian-Eulerian Advection (LEA) scheme. The algorithm produces animations with high spatio-temporal correlation at interactive rates. With this technique, every still frame depicts the instantaneous structure of the flow, whereas an animated sequence of frames reveals the motion a dense collection of particles would take when released into the flow. The simplicity of both the resulting data structures and the implementation suggest that LEA could become a useful component of any scientific visualization toolkit concerned with the display of unsteady flows.

We present a novel hardware-accelerated texture advection algorithm to visualize the motion of two-dimensional unsteady flows. Making use of several proposed extensions to the OpenGL-1.2 specification, we demonstrate animations of over 65,000 particles at 2 frames/sec on an SGI Octane with EMXI graphics. High image quality is achieved by careful attention to edge effects, noise frequency, and image enhancement. We provide a detailed description of the hardware implementation, including temporal and spatial coherence techniques, dye advection techniques, and feature extraction.