18,580 research outputs found
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
A Learning Framework for Morphological Operators using Counter-Harmonic Mean
We present a novel framework for learning morphological operators using
counter-harmonic mean. It combines concepts from morphology and convolutional
neural networks. A thorough experimental validation analyzes basic
morphological operators dilation and erosion, opening and closing, as well as
the much more complex top-hat transform, for which we report a real-world
application from the steel industry. Using online learning and stochastic
gradient descent, our system learns both the structuring element and the
composition of operators. It scales well to large datasets and online settings.Comment: Submitted to ISMM'1
Robust semi-automated path extraction for visualising stenosis of the coronary arteries
Computed tomography angiography (CTA) is useful for diagnosing and planning treatment of heart disease. However, contrast agent in surrounding structures (such as the aorta and left ventricle) makes 3-D visualisation of the coronary arteries difficult. This paper presents a composite method employing segmentation and volume rendering to overcome this issue. A key contribution is a novel Fast Marching minimal path cost function for vessel centreline extraction. The resultant centreline is used to compute a measure of vessel lumen, which indicates the degree of stenosis (narrowing of a vessel). Two volume visualisation techniques are presented which utilise the segmented arteries and lumen measure. The system is evaluated and demonstrated using synthetic and clinically obtained datasets
Generalized connected operators
This paper deals with the notion of connected operators These operators are becoming popular in image processing because they have the fundamental property of simplifying the signal while preserving the contour information In a rst step we recall the basic notions involved in binary and gray level connected operators. Then we show how one can extend and generalize these operators We focus on two important issues the connectivity and the simplication criterion We will show in particular how to create connectivities that are either more or less strict than the usual ones and how to build new criteriaPeer ReviewedPostprint (published version
A mathematical morphology approach for a qualitative exploration of drought events in space and time
Drought events occur worldwide and possibly incur severe consequences. Trying to understand and characterize drought events is of considerable importance in order to improve the preparedness for coping with future events. In this paper, we present a methodology that allows for the delineation of drought events by exploiting their spatiotemporal nature. To that end, we apply operators borrowed from mathematical morphology to represent drought events as connected components in space and time. As an illustration, we identify drought events on the basis of a 35-year data set of daily soil moisture values covering mainland Australia. We then extract characteristics reflecting the affected area, duration and intensity from the proposed representation of a drought event in order to illustrate the impact of tuning parameters in the methodology presented. Yet, this paper we refrain from comparing with other drought delineation methods
Informed baseline subtraction of proteomic mass spectrometry data aided by a novel sliding window algorithm
Proteomic matrix-assisted laser desorption/ionisation (MALDI) linear
time-of-flight (TOF) mass spectrometry (MS) may be used to produce protein
profiles from biological samples with the aim of discovering biomarkers for
disease. However, the raw protein profiles suffer from several sources of bias
or systematic variation which need to be removed via pre-processing before
meaningful downstream analysis of the data can be undertaken. Baseline
subtraction, an early pre-processing step that removes the non-peptide signal
from the spectra, is complicated by the following: (i) each spectrum has, on
average, wider peaks for peptides with higher mass-to-charge ratios (m/z), and
(ii) the time-consuming and error-prone trial-and-error process for optimising
the baseline subtraction input arguments. With reference to the aforementioned
complications, we present an automated pipeline that includes (i) a novel
`continuous' line segment algorithm that efficiently operates over data with a
transformed m/z-axis to remove the relationship between peptide mass and peak
width, and (ii) an input-free algorithm to estimate peak widths on the
transformed m/z scale. The automated baseline subtraction method was deployed
on six publicly available proteomic MS datasets using six different m/z-axis
transformations. Optimality of the automated baseline subtraction pipeline was
assessed quantitatively using the mean absolute scaled error (MASE) when
compared to a gold-standard baseline subtracted signal. Near-optimal baseline
subtraction was achieved using the automated pipeline. The advantages of the
proposed pipeline include informed and data specific input arguments for
baseline subtraction methods, the avoidance of time-intensive and subjective
piecewise baseline subtraction, and the ability to automate baseline
subtraction completely. Moreover, individual steps can be adopted as
stand-alone routines.Comment: 50 pages, 19 figure
Sabanci-Okan system at ImageClef 2011: plant identication task
We describe our participation in the plant identication task of ImageClef 2011. Our approach employs a variety of texture, shape as well as color descriptors. Due to the morphometric properties of plants, mathematical morphology has been advocated as the main methodology for texture characterization, supported by a multitude of contour-based shape and color features. We submitted a single run, where the focus has been almost exclusively on scan and scan-like images, due primarily to lack of time. Moreover, special care has been taken to obtain a fully automatic system, operating only on image data. While our photo results
are low, we consider our submission successful, since besides being our rst attempt, our accuracy is the highest when considering the average of the scan and scan-like results, upon which we had concentrated our eorts
Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure
A crucial aspect of mass-mapping, via weak lensing, is quantification of the
uncertainty introduced during the reconstruction process. Properly accounting
for these errors has been largely ignored to date. We present results from a
new method that reconstructs maximum a posteriori (MAP) convergence maps by
formulating an unconstrained Bayesian inference problem with Laplace-type
-norm sparsity-promoting priors, which we solve via convex
optimization. Approaching mass-mapping in this manner allows us to exploit
recent developments in probability concentration theory to infer theoretically
conservative uncertainties for our MAP reconstructions, without relying on
assumptions of Gaussianity. For the first time these methods allow us to
perform hypothesis testing of structure, from which it is possible to
distinguish between physical objects and artifacts of the reconstruction. Here
we present this new formalism, demonstrate the method on illustrative examples,
before applying the developed formalism to two observational datasets of the
Abel-520 cluster. In our Bayesian framework it is found that neither Abel-520
dataset can conclusively determine the physicality of individual local massive
substructure at significant confidence. However, in both cases the recovered
MAP estimators are consistent with both sets of data
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