4,721 research outputs found
Pruned Continuous Haar Transform of 2D Polygonal Patterns with Application to VLSI Layouts
We introduce an algorithm for the efficient computation of the continuous
Haar transform of 2D patterns that can be described by polygons. These patterns
are ubiquitous in VLSI processes where they are used to describe design and
mask layouts. There, speed is of paramount importance due to the magnitude of
the problems to be solved and hence very fast algorithms are needed. We show
that by techniques borrowed from computational geometry we are not only able to
compute the continuous Haar transform directly, but also to do it quickly. This
is achieved by massively pruning the transform tree and thus dramatically
decreasing the computational load when the number of vertices is small, as is
the case for VLSI layouts. We call this new algorithm the pruned continuous
Haar transform. We implement this algorithm and show that for patterns found in
VLSI layouts the proposed algorithm was in the worst case as fast as its
discrete counterpart and up to 12 times faster.Comment: 4 pages, 5 figures, 1 algorith
A Wavelet Visible Difference Predictor
In this paper, we describe a model of the human visual system (HVS) based on the wavelet transform. This model is largely based on a previously proposed model, but has a number of modifications that make it more amenable to potential integration into a wavelet based image compression scheme. These modifications include the use of a separable wavelet transform instead of the cortex transform, the application of a wavelet contrast sensitivity function (CSF), and a simplified definition of subband contrast that allows us to predict noise visibility directly from wavelet coefficients. Initially, we outline the luminance, frequency, and masking sensitivities of the HVS and discuss how these can be incorporated into the wavelet transform. We then outline a number of limitations of the wavelet transform as a model of the HVS, namely the lack of translational invariance and poor orientation sensitivity. In order to investigate the efficacy of this wavelet based model, a wavelet visible difference predictor (WVDP) is described. The WVDP is then used to predict visible differences between an original and compressed (or noisy) image. Results are presented to emphasize the limitations of commonly used measures of image quality and to demonstrate the performance of the WVDP. The paper concludes with suggestions on how the WVDP can be used to determine a visually optimal quantization strategy for wavelet coefficients and produce a quantitative measure of image quality
Optimising Spatial and Tonal Data for PDE-based Inpainting
Some recent methods for lossy signal and image compression store only a few
selected pixels and fill in the missing structures by inpainting with a partial
differential equation (PDE). Suitable operators include the Laplacian, the
biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The
quality of such approaches depends substantially on the selection of the data
that is kept. Optimising this data in the domain and codomain gives rise to
challenging mathematical problems that shall be addressed in our work.
In the 1D case, we prove results that provide insights into the difficulty of
this problem, and we give evidence that a splitting into spatial and tonal
(i.e. function value) optimisation does hardly deteriorate the results. In the
2D setting, we present generic algorithms that achieve a high reconstruction
quality even if the specified data is very sparse. To optimise the spatial
data, we use a probabilistic sparsification, followed by a nonlocal pixel
exchange that avoids getting trapped in bad local optima. After this spatial
optimisation we perform a tonal optimisation that modifies the function values
in order to reduce the global reconstruction error. For homogeneous diffusion
inpainting, this comes down to a least squares problem for which we prove that
it has a unique solution. We demonstrate that it can be found efficiently with
a gradient descent approach that is accelerated with fast explicit diffusion
(FED) cycles. Our framework allows to specify the desired density of the
inpainting mask a priori. Moreover, is more generic than other data
optimisation approaches for the sparse inpainting problem, since it can also be
extended to nonlinear inpainting operators such as EED. This is exploited to
achieve reconstructions with state-of-the-art quality.
We also give an extensive literature survey on PDE-based image compression
methods
Seismic Ray Impedance Inversion
This thesis investigates a prestack seismic inversion scheme implemented in the ray
parameter domain. Conventionally, most prestack seismic inversion methods are
performed in the incidence angle domain. However, inversion using the concept of
ray impedance, as it honours ray path variation following the elastic parameter
variation according to Snell’s law, shows the capacity to discriminate different
lithologies if compared to conventional elastic impedance inversion.
The procedure starts with data transformation into the ray-parameter domain and then
implements the ray impedance inversion along constant ray-parameter profiles. With
different constant-ray-parameter profiles, mixed-phase wavelets are initially estimated
based on the high-order statistics of the data and further refined after a proper well-to-seismic
tie. With the estimated wavelets ready, a Cauchy inversion method is used to
invert for seismic reflectivity sequences, aiming at recovering seismic reflectivity
sequences for blocky impedance inversion. The impedance inversion from reflectivity
sequences adopts a standard generalised linear inversion scheme, whose results are
utilised to identify rock properties and facilitate quantitative interpretation. It has also
been demonstrated that we can further invert elastic parameters from ray impedance
values, without eliminating an extra density term or introducing a Gardner’s relation
to absorb this term.
Ray impedance inversion is extended to P-S converted waves by introducing the
definition of converted-wave ray impedance. This quantity shows some advantages in
connecting prestack converted wave data with well logs, if compared with the shearwave
elastic impedance derived from the Aki and Richards approximation to the
Zoeppritz equations. An analysis of P-P and P-S wave data under the framework of
ray impedance is conducted through a real multicomponent dataset, which can reduce
the uncertainty in lithology identification.Inversion is the key method in generating those examples throughout the entire thesis
as we believe it can render robust solutions to geophysical problems. Apart from the
reflectivity sequence, ray impedance and elastic parameter inversion mentioned above,
inversion methods are also adopted in transforming the prestack data from the offset
domain to the ray-parameter domain, mixed-phase wavelet estimation, as well as the
registration of P-P and P-S waves for the joint analysis.
The ray impedance inversion methods are successfully applied to different types of
datasets. In each individual step to achieving the ray impedance inversion, advantages,
disadvantages as well as limitations of the algorithms adopted are detailed. As a
conclusion, the ray impedance related analyses demonstrated in this thesis are highly
competent compared with the classical elastic impedance methods and the author
would like to recommend it for a wider application
Digital Image-Based Frameworks for Monitoring and Controlling of Particulate Systems
Particulate processes have been widely involved in various industries and most products in the chemical industry today are manufactured as particulates. Previous research and practise illustrate that the final product quality can be influenced by particle properties such as size and shape which are related to operating conditions. Online characterization of these particles is an important step for maintaining desired product quality in particulate processes. Image-based characterization method for the purpose of monitoring and control particulate processes is very promising and attractive. The development of a digital image-based framework, in the context of this research, can be envisioned in two parts. One is performing image analysis and designing advanced algorithms for segmentation and texture analysis. The other is formulating and implementing modern predictive tools to establish the correlations between the texture features and the particle characteristics. According to the extent of touching and overlapping between particles in images, two image analysis methods were developed and tested. For slight touching problems, image segmentation algorithms were developed by introducing Wavelet Transform de-noising and Fuzzy C-means Clustering detecting the touching regions, and by adopting the intensity and geometry characteristics of touching areas. Since individual particles can be identified through image segmentation, particle number, particle equivalent diameter, and size distribution were used as the features. For severe touching and overlapping problems, texture analysis was carried out through the estimation of wavelet energy signature and fractal dimension based on wavelet decomposition on the objects. Predictive models for monitoring and control for particulate processes were formulated and implemented. Building on the feature extraction properties of the wavelet decomposition, a projection technique such as principal component analysis (PCA) was used to detect off-specification conditions which generate particle mean size deviates the target value. Furthermore, linear and nonlinear predictive models based on partial least squares (PLS) and artificial neural networks (ANN) were formulated, implemented and tested on an experimental facility to predict particle characteristics (mean size and standard deviation) from the image texture analysis
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