9,089 research outputs found
Random projection depth for multivariate mathematical morphology
International audienceThe open problem of the generalization of mathematical morphology to vector images is handled in this paper using the paradigm of depth functions. Statistical depth functions provide from the "deepest" point a "center-outward ordering" of a multidimensional data distribution and they can be therefore used to construct morphological operators. The fundamental assumption of this data-driven approach is the existence of "background/foreground" image representation. Examples in real color and hyperspectral images illustrate the results
Vector ordering and multispectral morphological image processing
International audienceThis chapter illustrates the suitability of recent multivariate ordering approaches to morphological analysis of colour and multispectral images working on their vector representation. On the one hand, supervised ordering renders machine learning no-tions and image processing techniques, through a learning stage to provide a total ordering in the colour/multispectral vector space. On the other hand, anomaly-based ordering, automatically detects spectral diversity over a majority background, al-lowing an adaptive processing of salient parts of a colour/multispectral image. These two multivariate ordering paradigms allow the definition of morphological operators for multivariate images, from algebraic dilation and erosion to more advanced techniques as morphological simplification, decomposition and segmentation. A number of applications are reviewed and implementation issues are discussed in detail
Linear chemically sensitive electron tomography using DualEELS and dictionary-based compressed sensing
We have investigated the use of DualEELS in elementally sensitive tilt series tomography in the scanning transmission electron microscope. A procedure is implemented using deconvolution to remove the effects of multiple scattering, followed by normalisation by the zero loss peak intensity. This is performed to produce a signal that is linearly dependent on the projected density of the element in each pixel. This method is compared with one that does not include deconvolution (although normalisation by the zero loss peak intensity is still performed). Additionaly, we compare the 3D reconstruction using a new compressed sensing algorithm, DLET, with the well-established SIRT algorithm. VC precipitates, which are extracted from a steel on a carbon replica, are used in this study. It is found that the use of this linear signal results in a very even density throughout the precipitates. However, when deconvolution is omitted, a slight density reduction is observed in the cores of the precipitates (a so-called cupping artefact). Additionally, it is clearly demonstrated that the 3D morphology is much better reproduced using the DLET algorithm, with very little elongation in the missing wedge direction. It is therefore concluded that reliable elementally sensitive tilt tomography using EELS requires the appropriate use of DualEELS together with a suitable reconstruction algorithm, such as the compressed sensing based reconstruction algorithm used here, to make the best use of the limited data volume and signal to noise inherent in core-loss EELS
Characterization of complex networks: A survey of measurements
Each complex network (or class of networks) presents specific topological
features which characterize its connectivity and highly influence the dynamics
of processes executed on the network. The analysis, discrimination, and
synthesis of complex networks therefore rely on the use of measurements capable
of expressing the most relevant topological features. This article presents a
survey of such measurements. It includes general considerations about complex
network characterization, a brief review of the principal models, and the
presentation of the main existing measurements. Important related issues
covered in this work comprise the representation of the evolution of complex
networks in terms of trajectories in several measurement spaces, the analysis
of the correlations between some of the most traditional measurements,
perturbation analysis, as well as the use of multivariate statistics for
feature selection and network classification. Depending on the network and the
analysis task one has in mind, a specific set of features may be chosen. It is
hoped that the present survey will help the proper application and
interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of
measurements for inclusion are welcomed by the author
Recurrent Pixel Embedding for Instance Grouping
We introduce a differentiable, end-to-end trainable framework for solving
pixel-level grouping problems such as instance segmentation consisting of two
novel components. First, we regress pixels into a hyper-spherical embedding
space so that pixels from the same group have high cosine similarity while
those from different groups have similarity below a specified margin. We
analyze the choice of embedding dimension and margin, relating them to
theoretical results on the problem of distributing points uniformly on the
sphere. Second, to group instances, we utilize a variant of mean-shift
clustering, implemented as a recurrent neural network parameterized by kernel
bandwidth. This recurrent grouping module is differentiable, enjoys convergent
dynamics and probabilistic interpretability. Backpropagating the group-weighted
loss through this module allows learning to focus on only correcting embedding
errors that won't be resolved during subsequent clustering. Our framework,
while conceptually simple and theoretically abundant, is also practically
effective and computationally efficient. We demonstrate substantial
improvements over state-of-the-art instance segmentation for object proposal
generation, as well as demonstrating the benefits of grouping loss for
classification tasks such as boundary detection and semantic segmentation
On the Probability Distributions of Ellipticity
In this paper we derive an exact full expression for the 2D probability
distribution of the ellipticity of an object measured from data, only assuming
Gaussian noise in pixel values. This is a generalisation of the probability
distribution for the ratio of single random variables, that is well-known, to
the multivariate case. This expression is derived within the context of the
measurement of weak gravitational lensing from noisy galaxy images. We find
that the third flattening, or epsilon-ellipticity, has a biased maximum
likelihood but an unbiased mean; and that the third eccentricity, or normalised
polarisation chi, has both a biased maximum likelihood and a biased mean. The
very fact that the bias in the ellipticity is itself a function of the
ellipticity requires an accurate knowledge of the intrinsic ellipticity
distribution of the galaxies in order to properly calibrate shear measurements.
We use this expression to explore strategies for calibration of biases caused
by measurement processes in weak gravitational lensing. We find that upcoming
weak lensing surveys like KiDS or DES require calibration fields of order of
several square degrees and 1.2 magnitude deeper than the wide survey in order
to correct for the noise bias. Future surveys like Euclid will require
calibration fields of order 40 square degree and several magnitude deeper than
the wide survey. We also investigate the use of the Stokes parameters to
estimate the shear as an alternative to the ellipticity. We find that they can
provide unbiased shear estimates at the cost of a very large variance in the
measurement. The python code used to compute the distributions presented in the
paper and to perform the numerical calculations are available on request.Comment: 24 pages, 18 figures, 2 Tables. Accepted for publication in Monthly
Notices of the Royal Astronomical Society Main Journa
Shape Descriptors for classification of functional data
Curve discrimination is an important task in engineering and other sciences. We
propose several shape descriptors for classifying functional data, inspired by form anal-
ysis from the image analysis eld: statistical moments, coe cients of the components
of independent component analysis (ICA) and two mathematical morphology descrip-
tors (morphological covariance and spatial size distributions). They are applied to
three problems: an arti cial problem, a speech recognition problem and a biomechan-
ical application. Shape descriptors are compared with other methods in the literature,
obtaining better or similar performance
Automatic Gridding for DNA Microarray Image Using Image Projection Profile
DNA microarray is powerful tool and widely used in many areas.
DNA microarray is produced from control and test tissue sample cDNAs, which
are labeled with two different fluorescent dyes. After hybridization using a laser
scanner, microarray images are obtained. Image analysis play an important role
in extracting fluorescence intensity from microarray image. First step in
microarray image analysis is addressing, that is finding areas in the image on
which contain one spot using gird lines. This step can be done by either
manually or automatically. In this paper we propose an efficient and simple
automatic gridding for microarray image analysis using image projection profile,
base on fact that microarray image has local minimum and maximum intensity
at background and foreground areas respectively. Grid lines are obtained by
finding local minimum of vertical and horizontal projection profile. This
algorithm has been implemented in MATLAB and tested with several
microarray image
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