68,792 research outputs found
Systematic approach to nonlinear filtering associated with aggregation operators. Part 2. Frechet MIMO-filters
Median filtering has been widely used in scalar-valued image processing as an edge preserving operation. The basic idea is that the pixel value is replaced by the median of the pixels contained in a window around it. In this work, this idea is extended onto vector-valued images. It is based on the fact that the median is also the value that minimizes the sum of distances between all grey-level pixels in the window. The Frechet median of a discrete set of vector-valued pixels in a metric space with a metric is the point minimizing the sum of metric distances to the all sample pixels. In this paper, we extend the notion of the Frechet median to the general Frechet median, which minimizes the Frechet cost function (FCF) in the form of aggregation function of metric distances, instead of the ordinary sum. Moreover, we propose use an aggregation distance instead of classical metric distance. We use generalized Frechet median for constructing new nonlinear Frechet MIMO-filters for multispectral image processing. (C) 2017 The Authors. Published by Elsevier Ltd.This work was supported by grants the RFBR No 17-07-00886, No 17-29-03369 and by Ural State Forest University Engineering's Center of Excellence in "Quantum and Classical Information Technologies for Remote Sensing Systems"
Optimum non linear binary image restoration through linear grey-scale operations
Non-linear image processing operators give excellent results in a number of image processing tasks such as restoration and object recognition. However they are frequently excluded from use in solutions because the system designer does not wish to introduce additional hardware or algorithms and because their design can appear to be ad hoc. In practice the median filter is often used though it is rarely optimal. This paper explains how various non-linear image processing operators may be implemented on a basic linear image processing system using only convolution and thresholding operations. The paper is aimed at image processing system developers wishing to include some non-linear processing operators without introducing additional system capabilities such as extra hardware components or software toolboxes. It may also be of benefit to the interested reader wishing to learn more about non-linear operators and alternative methods of design and implementation. The non-linear tools include various components of mathematical morphology, median and weighted median operators and various order statistic filters. As well as describing novel algorithms for implementation within a linear system the paper also explains how the optimum filter parameters may be estimated for a given image processing task. This novel approach is based on the weight monotonic property and is a direct rather than iterated method
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
Flat zones filtering, connected operators, and filters by reconstruction
This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version
Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms
By introducing Hilbert space and operators, we show how probabilities,
approximations and entropy encoding from signal and image processing allow
precise formulas and quantitative estimates. Our main results yield orthogonal
bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur
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
Discrete spherical means of directional derivatives and Veronese maps
We describe and study geometric properties of discrete circular and spherical
means of directional derivatives of functions, as well as discrete
approximations of higher order differential operators. For an arbitrary
dimension we present a general construction for obtaining discrete spherical
means of directional derivatives. The construction is based on using the
Minkowski's existence theorem and Veronese maps. Approximating the directional
derivatives by appropriate finite differences allows one to obtain finite
difference operators with good rotation invariance properties. In particular,
we use discrete circular and spherical means to derive discrete approximations
of various linear and nonlinear first- and second-order differential operators,
including discrete Laplacians. A practical potential of our approach is
demonstrated by considering applications to nonlinear filtering of digital
images and surface curvature estimation
Formal Representation of the SS-DB Benchmark and Experimental Evaluation in EXTASCID
Evaluating the performance of scientific data processing systems is a
difficult task considering the plethora of application-specific solutions
available in this landscape and the lack of a generally-accepted benchmark. The
dual structure of scientific data coupled with the complex nature of processing
complicate the evaluation procedure further. SS-DB is the first attempt to
define a general benchmark for complex scientific processing over raw and
derived data. It fails to draw sufficient attention though because of the
ambiguous plain language specification and the extraordinary SciDB results. In
this paper, we remedy the shortcomings of the original SS-DB specification by
providing a formal representation in terms of ArrayQL algebra operators and
ArrayQL/SciQL constructs. These are the first formal representations of the
SS-DB benchmark. Starting from the formal representation, we give a reference
implementation and present benchmark results in EXTASCID, a novel system for
scientific data processing. EXTASCID is complete in providing native support
both for array and relational data and extensible in executing any user code
inside the system by the means of a configurable metaoperator. These features
result in an order of magnitude improvement over SciDB at data loading,
extracting derived data, and operations over derived data.Comment: 32 pages, 3 figure
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A computer-based product classification and component detection for demanufacturing processes
This is an Author's Accepted Manuscript of an article published in International Journal of Computer Integrated
Manufacturing, 24(10), 900-914, 2011 [copyright Taylor & Francis], available online at:
http://www.tandfonline.com/10.1080/0951192X.2011.579169.The aim of this paper is to propose a novel computer-based product classification, component detection and tracking for demanufacturing and disassembly process. This is achieved by introducing a series of automated and sequential product scanning, component identification, image analysis and sorting – leading to the development of a bill of material (BOM). The produced BOM can then be associated with the relevant disassembly/demanufacture proviso. The proposed integrated image sorting and product classification (ISPC) approach can be considered as a step forward in automation of demanufacturing activities. The ISPC model proposed in this paper utilises and builds on the state-of-the-art technology and current body of research in computer-integrated demanufacturing and remanufacturing (CIDR). An appraisal of the latest research material and the factors that inhibit CIDR methods inpractice are presented. A novel solution for the integration of imaging and material identification techniques toovercome some of the existing shortcomings of automated recycling processes is proposed in this paper. The proposed product scanning and component detection ISPC software consists of four distinct models: the repertory database, the search engine, the product-attributes updater and the image sorting and classification algorithm. The software framework that integrates the four components is presented in this paper. Finally, an overall assessment of applying ISPC at various stages of CIDR processes concludes the article.University of Ibadan MacArthur Foundation Gran
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