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

Reconstructing vectorised photographic images

We address the problem of representing captured images in the continuous mathematical space more usually associated with certain forms of drawn ('vector') images. Such an image is resolution-independent so can be used as a master for varying resolution-specific formats. We briefly describe the main features of a vectorising codec for photographic images, whose significance is that drawing programs can access images and image components as first-class vector objects. This paper focuses on the problem of rendering from the isochromic contour form of a vectorised image and demonstrates a new fill algorithm which could also be used in drawing generally. The fill method is described in terms of level set diffusion equations for clarity. Finally we show that image warping is both simplified and enhanced in this form and that we can demonstrate real histogram equalisation with genuinely rectangular histograms

Improvement of Spatial Resolution with Staggered Arrays As Used in The Airborne Optical Sensor Ads40

Using pushbroom sensors onboard aircrafts or satellites requires, especially for photogrammetric applications, wide image swaths with a high geometric resolution. One approach to satisfy both demands is to use staggered line arrays, which are constructed from two identical CCD lines shifted against each other by half a picel in line direction. Practical applications of such arrays in remote sensing include SPOT, and in the commercial environment the Airborne Digital Sensor, or ADS40, from Leica Geosystems. Theoretically, the usefulness of staggered arrays depends from spatial reslution, which is defined by the total point spread function of the imaging system and Shannon's sampling theorem. Due to the two shifted sensor lines staggering results in a double number of sampling points perpendicular to the flight direction. In order to simultaneously double the sample number in the flight direction, the line readout rate, or integration time, has to produce half a pixel spacing on ground. Staggering in combination with a high-resolution optical system can be used to fulfil the sampling condition, which means that no spectral components above the critical spatial frequency 2/D are present. Theoretically, the resolution is as good for a non-staggered line with half pixel size D/2, but radiometric dynamics should be twice as high. In practice, the slightly different viewing angle of both lines of a staggered array can result in a deteration of image quality due to aircraft motion, attitude fluctuations or terrain undulation. Fulfilling the sampling condition further means that no aliasing occurs. This is essential for the image quality in quasiperiodical textured image areas and for photogrammetric sub-pixel accuracy. Furthermore, image restoration methods for enhancing the image quality can be applied more efficently. The panchromatic resolution of the ADS40 opties is optimised for image collection by a staggered array. This means, it transfers spatial frequencies of twice the Nyquist frequency of its 12k sensors. First experiments, which were carried out some years ago, indicated alrady a spatial resolution improvement by using image restitution the ADS 40 staggered 12k pairs. The results of the restitution algorithm, which is integrated in the ADS image processing flow, has now been analysed quantitatively. This paper presents the theory of high resolution image restitution from staggered lines and practical results with ADS40 high resolution panchromatic images and high resolution colour images, created by sharpening 12k colour images with high resolution pan-chromatic ones

Statistical and systematic uncertainties in pixel-based source reconstruction algorithms for gravitational lensing

Gravitational lens modeling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the source and constraining lens model parameters. Using test data for four canonical lens configurations, we explore statistical and systematic uncertainties associated with gridding, source regularisation, interpolation errors, noise, and telescope pointing. Specifically, we compare two gridding schemes in the source plane: a fully adaptive grid that follows the lens mapping but is irregular, and an adaptive Cartesian grid. We also consider regularisation schemes that minimise derivatives of the source (using two finite difference methods) and introduce a scheme that minimises deviations from an analytic source profile. Careful choice of gridding and regularisation can reduce "discreteness noise" in the $\chi^2$ surface that is inherent in the pixel-based methodology. With a gridded source, some degree of interpolation is unavoidable, and errors due to interpolation need to be taken into account (especially for high signal-to-noise data). Different realisations of the noise and telescope pointing lead to slightly different values for lens model parameters, and the scatter between different "observations" can be comparable to or larger than the model uncertainties themselves. The same effects create scatter in the lensing magnification at the level of a few percent for a peak signal-to-noise ratio of 10, which decreases as the data quality improves.Comment: 20 pages, 18 figures, accepted to MNRAS, see http://physics.rutgers.edu/~tagoreas/papers/ for high resolution image

Delaunay triangulation based image enhancement for echocardiography images

A novel image enhancement approach for automatic echocardiography image processing is proposed. The main steps include undecimated wavelet based speckle noise reduction, edge detection, followed by a regional enhancement process that employs Delaunay triangulation based thresholding. The edge detection is performed using a fuzzy logic based center point detection and a subsequent radial search based fuzzy multiscale edge detection. The edges obtained are used as the vertices for Delaunay triangulation for enhancement purposes. This method enhances the heart wall region in the echo image. This technique is applied to both synthetic and real image sets that were obtained from a local hospital

Airborne photogrammetry and LIDAR for DSM extraction and 3D change detection over an urban area : a comparative study

A digital surface model (DSM) extracted from stereoscopic aerial images, acquired in March 2000, is compared with a DSM derived from airborne light detection and ranging (lidar) data collected in July 2009. Three densely built-up study areas in the city centre of Ghent, Belgium, are selected, each covering approximately 0.4 km(2). The surface models, generated from the two different 3D acquisition methods, are compared qualitatively and quantitatively as to what extent they are suitable in modelling an urban environment, in particular for the 3D reconstruction of buildings. Then the data sets, which are acquired at two different epochs t(1) and t(2), are investigated as to what extent 3D (building) changes can be detected and modelled over the time interval. A difference model, generated by pixel-wise subtracting of both DSMs, indicates changes in elevation. Filters are proposed to differentiate 'real' building changes from false alarms provoked by model noise, outliers, vegetation, etc. A final 3D building change model maps all destructed and newly constructed buildings within the time interval t(2) - t(1). Based on the change model, the surface and volume of the building changes can be quantified