2,283 research outputs found
Background subtraction with Dirichlet processes
Abstract. Background subtraction is an important first step for video analysis, where it is used to discover the objects of interest for fur-ther processing. Such an algorithm often consists of a background model and a regularisation scheme. The background model determines a per-pixel measure of if a pixel belongs to the background or the foreground, whilst the regularisation brings in information from adjacent pixels. A new method is presented that uses a Dirichlet process Gaussian mixture model to estimate a per-pixel background distribution, which is followed by probabilistic regularisation. Key advantages include inferring the per-pixel mode count, such that it accurately models dynamic backgrounds, and that it updates its model continuously in a principled way.
Bayesian Analysis of Femtosecond Pump-Probe Photoelectron-Photoion Coincidence Spectra with Fluctuating Laser Intensities
This paper employs Bayesian probability theory for analyzing data generated
in femtosecond pump-probe photoelectron-photoion coincidence (PEPICO)
experiments. These experiments allow investigating ultrafast dynamical
processes in photoexcited molecules. Bayesian probability theory is
consistently applied to data analysis problems occurring in these types of
experiments such as background subtraction and false coincidences. We
previously demonstrated that the Bayesian formalism has many advantages,
amongst which are compensation of false coincidences, no overestimation of
pump-only contributions, significantly increased signal-to-noise ratio, and
applicability to any experimental situation and noise statistics. Most
importantly, by accounting for false coincidences, our approach allows running
experiments at higher ionization rates, resulting in an appreciable reduction
of data acquisition times. In addition to our previous paper, we include
fluctuating laser intensities, of which the straightforward implementation
highlights yet another advantage of the Bayesian formalism. Our method is
thoroughly scrutinized by challenging mock data, where we find a minor impact
of laser fluctuations on false coincidences, yet a noteworthy influence on
background subtraction. We apply our algorithm to data obtained in experiments
and discuss the impact of laser fluctuations on the data analysis
Background Subtraction via Generalized Fused Lasso Foreground Modeling
Background Subtraction (BS) is one of the key steps in video analysis. Many
background models have been proposed and achieved promising performance on
public data sets. However, due to challenges such as illumination change,
dynamic background etc. the resulted foreground segmentation often consists of
holes as well as background noise. In this regard, we consider generalized
fused lasso regularization to quest for intact structured foregrounds. Together
with certain assumptions about the background, such as the low-rank assumption
or the sparse-composition assumption (depending on whether pure background
frames are provided), we formulate BS as a matrix decomposition problem using
regularization terms for both the foreground and background matrices. Moreover,
under the proposed formulation, the two generally distinctive background
assumptions can be solved in a unified manner. The optimization was carried out
via applying the augmented Lagrange multiplier (ALM) method in such a way that
a fast parametric-flow algorithm is used for updating the foreground matrix.
Experimental results on several popular BS data sets demonstrate the advantage
of the proposed model compared to state-of-the-arts
Black Hole Entropy: Off-Shell vs On-Shell
Different methods of calculation of quantum corrections to the
thermodynamical characteristics of a black hole are discussed and compared. The
relation between on-shell and off-shell approaches is established. The
off-shell methods are used to explicitly demonstrate that the thermodynamical
entropy of a black hole, defined by the first thermodynamical law,
differs from the statistical-mechanical entropy , determined as
S^{SM}=-\mbox{Tr}(\hat{\rho}^H\ln\hat{\rho}^H) for the density matrix
of a black hole. It is shown that the observable thermodynamical
black hole entropy can be presented in the form . Here is the radius of the horizon
shifted because of the quantum backreaction effect, and is
the statistical-mechanical entropy calculated in the Rindler space.Comment: 47 pages, latex, 7 postscript figures have been included since the
first submission of the articl
Horizon divergences of Fields and Strings in Black Hole backgrounds
General arguments based on curved space-time thermodynamics show that any
extensive quantity, like the free energy or the entropy of thermal matter,
always has a divergent boundary contribution in the presence of event horizons,
and this boundary term comes with the Hawking-Bekenstein form. Although the
coefficients depend on the particular geometry we show that intensive
quantities, like the free energy density are universal in the vicinity of the
horizon. {} From the point of view of the matter degrees of freedom this
divergence is of infrared type rather than ultraviolet, and we use this remark
to speculate about the fate of these pathologies in String Theory. Finally we
interpret them as instabilities of the Canonical Ensemble with respect to
gravitational collapse via the Jeans mechanism.Comment: 16 pages, PUPT-1448 (some typos corrected and references added
Probabilistic Clustering of Time-Evolving Distance Data
We present a novel probabilistic clustering model for objects that are
represented via pairwise distances and observed at different time points. The
proposed method utilizes the information given by adjacent time points to find
the underlying cluster structure and obtain a smooth cluster evolution. This
approach allows the number of objects and clusters to differ at every time
point, and no identification on the identities of the objects is needed.
Further, the model does not require the number of clusters being specified in
advance -- they are instead determined automatically using a Dirichlet process
prior. We validate our model on synthetic data showing that the proposed method
is more accurate than state-of-the-art clustering methods. Finally, we use our
dynamic clustering model to analyze and illustrate the evolution of brain
cancer patients over time
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