Image compression with anisotropic diffusion

Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widely-used JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec

Bioinspired engineering of exploration systems for NASA and DoD

A new approach called bioinspired engineering of exploration systems (BEES) and its value for solving pressing NASA and DoD needs are described. Insects (for example honeybees and dragonflies) cope remarkably well with their world, despite possessing a brain containing less than 0.01% as many neurons as the human brain. Although most insects have immobile eyes with fixed focus optics and lack stereo vision, they use a number of ingenious, computationally simple strategies for perceiving their world in three dimensions and navigating successfully within it. We are distilling selected insect-inspired strategies to obtain novel solutions for navigation, hazard avoidance, altitude hold, stable flight, terrain following, and gentle deployment of payload. Such functionality provides potential solutions for future autonomous robotic space and planetary explorers. A BEES approach to developing lightweight low-power autonomous flight systems should be useful for flight control of such biomorphic flyers for both NASA and DoD needs. Recent biological studies of mammalian retinas confirm that representations of multiple features of the visual world are systematically parsed and processed in parallel. Features are mapped to a stack of cellular strata within the retina. Each of these representations can be efficiently modeled in semiconductor cellular nonlinear network (CNN) chips. We describe recent breakthroughs in exploring the feasibility of the unique blending of insect strategies of navigation with mammalian visual search, pattern recognition, and image understanding into hybrid biomorphic flyers for future planetary and terrestrial applications. We describe a few future mission scenarios for Mars exploration, uniquely enabled by these newly developed biomorphic flyers

Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

On Estimating Map Model Errors and GPS Position Errors: (Applying More Science to the Art of Navigation)

In order to decide whether a desired manoeuver can or cannot be safely undertaken, a prudent navigator must be aware of both the current spatial uncertainty of his vehicle's positioning system and the spatial uncertainty of the navigational map model being used to depict the theatre of operations. From this safety to navigation perspective, knowledge of data accuracy is as important as the data itself. This paper discusses the Electronic Chart (EC) implications of both GPS vehicle positioning errors and the relatively large data modeling errors specific to bathymetric map models (charts). It proposes and demonstrates software solutions which statistically evaluate both of these spatial uncertainties and graphically integrates the two stochastic models within an EC environment. The paper also documents an experiment carried out by the Canadian Hydrographic Service, designed to insure that real-time DGPS users compute statistically valid position error estimates. The experiment ground truthed the position error estimates obtained using a conventional real-time error analysis of pseudo-range redundancy. Using this ground-truth information, an improved pseudo-range error model was empirically determined. The new pseudorange error model is continually updated using the estimated pseudo-range variances computed by the Novatel GPS receiver rather than applying the constant a priori pseudo-range variance typical in least-squares adjustments. This dynamic range error model effectively reduced the statistical bias between the observed errors and their predicted error estimates. The improved range error model also significantly improved the performance of the position solution. All DGPS positions computed by the modified software had a positional accuracy of better than 0.5 metres

Photo-densitometry: radiograph digitization and algorithmic enhancement of x-ray images

Industrial investigation of material structure and composition is an integral part of the manufacturing design flow. It is possible to evaluate these properties by both destructive and non-destructive means. Non-destructive evaluation of materials is attractive for obvious reasons and x-ray NDE (Non-Destructive Evaluation) is a well established discipline. X-ray images of materials (represented and stored in the form of radiographs) are capable of providing valuable information regarding the presence of material defects such as, voids, cracks and inclusions. A common medium used to store an x-ray image is the film or radiograph. This is an analog representation of the x-ray image, produced by the photographic effect. This grayscale representation of the material under investigation, when analyzed, is able to provide the necessary information regarding the presence of defects. The human brain has the ability to recognize patterns and differentiate minute variations in the grayscales of the radiograph, so long as these variations are within a particular range. In order to overcome this limitation of the human visual mechanism and to facilitate the objectives of storage, processing and transmission, it is necessary to transform this representation of the x-ray image as a radiograph, into a digital form. This also helps to extract quantitative physical parameters from a digitized image, which is not possible with an analog image which is only good at providing a qualitative overview of an image

Cloud cover typing from environmental satellite imagery. Discriminating cloud structure with Fast Fourier Transforms (FFT)

The use of two dimensional Fast Fourier Transforms (FFTs) subjected to pattern recognition technology for the identification and classification of low altitude stratus cloud structure from Geostationary Operational Environmental Satellite (GOES) imagery was examined. The development of a scene independent pattern recognition methodology, unconstrained by conventional cloud morphological classifications was emphasized. A technique for extracting cloud shape, direction, and size attributes from GOES visual imagery was developed. These attributes were combined with two statistical attributes (cloud mean brightness, cloud standard deviation), and interrogated using unsupervised clustering amd maximum likelihood classification techniques. Results indicate that: (1) the key cloud discrimination attributes are mean brightness, direction, shape, and minimum size; (2) cloud structure can be differentiated at given pixel scales; (3) cloud type may be identifiable at coarser scales; (4) there are positive indications of scene independence which would permit development of a cloud signature bank; (5) edge enhancement of GOES imagery does not appreciably improve cloud classification over the use of raw data; and (6) the GOES imagery must be apodized before generation of FFTs