Anisotropic Mesh Adaptation for Image Representation

Triangular meshes have gained much interest in image representation and have been widely used in image processing. This paper introduces a framework of anisotropic mesh adaptation (AMA) methods to image representation and proposes a GPRAMA method that is based on AMA and greedy-point removal (GPR) scheme. Different than many other methods that triangulate sample points to form the mesh, the AMA methods start directly with a triangular mesh and then adapt the mesh based on a user-defined metric tensor to represent the image. The AMA methods have clear mathematical framework and provides flexibility for both image representation and image reconstruction. A mesh patching technique is developed for the implementation of the GPRAMA method, which leads to an improved version of the popular GPRFS-ED method. The GPRAMA method can achieve better quality than the GPRFS-ED method but with lower computational cost.Comment: 25 pages, 15 figure

Airborne LiDAR for DEM generation: some critical issues

Airborne LiDAR is one of the most effective and reliable means of terrain data collection. Using LiDAR data for DEM generation is becoming a standard practice in spatial related areas. However, the effective processing of the raw LiDAR data and the generation of an efficient and high-quality DEM remain big challenges. This paper reviews the recent advances of airborne LiDAR systems and the use of LiDAR data for DEM generation, with special focus on LiDAR data filters, interpolation methods, DEM resolution, and LiDAR data reduction. Separating LiDAR points into ground and non-ground is the most critical and difficult step for DEM generation from LiDAR data. Commonly used and most recently developed LiDAR filtering methods are presented. Interpolation methods and choices of suitable interpolator and DEM resolution for LiDAR DEM generation are discussed in detail. In order to reduce the data redundancy and increase the efficiency in terms of storage and manipulation, LiDAR data reduction is required in the process of DEM generation. Feature specific elements such as breaklines contribute significantly to DEM quality. Therefore, data reduction should be conducted in such a way that critical elements are kept while less important elements are removed. Given the highdensity characteristic of LiDAR data, breaklines can be directly extracted from LiDAR data. Extraction of breaklines and integration of the breaklines into DEM generation are presented

A Two-Dimensional Mesh Refinement Method for Problems with One-Dimensional Singularities

This paper introduces a method for resolving internal layers that can occur in the solutions of time-dependent differential equations in two space dimensions. Singular features in these solutions that are essentially one-dimensional in nature but are not oriented with the computational mesh are resolved using one-dimensional mesh refinement techniques with a procedure that is similar to an ADI method. A careful interpolation procedure assures that the resolution obtained in each ADI step is not lost in the succeeding ADI step

A modification of the convective constraint release mechanism in the molecular stress function model giving enhanced vortex growth

The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [J. Rheol. 45 (2001), 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J. non-Newt. Fluid Mech., 3 (1977), 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements

Image interpolation using Shearlet based iterative refinement

This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering, (b) promoting sparsity in a selected dictionary through iterative thresholding, and (c) extracting high frequency information from the approximation to refine the initial estimate. For the sparse modeling, a shearlet dictionary is chosen to yield a multiscale directional representation. The proposed algorithm is compared to several state-of-the-art methods to assess its objective as well as subjective performance. Compared to the cubic spline interpolation method, an average PSNR gain of around 0.8 dB is observed over a dataset of 200 images