271 research outputs found
A stochastic-variational model for soft Mumford-Shah segmentation
In contemporary image and vision analysis, stochastic approaches demonstrate
great flexibility in representing and modeling complex phenomena, while
variational-PDE methods gain enormous computational advantages over Monte-Carlo
or other stochastic algorithms. In combination, the two can lead to much more
powerful novel models and efficient algorithms. In the current work, we propose
a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of
mixture image patterns. Unlike the classical hard Mumford-Shah segmentation,
the new model allows each pixel to belong to each image pattern with some
probability. We show that soft segmentation leads to hard segmentation, and
hence is more general. The modeling procedure, mathematical analysis, and
computational implementation of the new model are explored in detail, and
numerical examples of synthetic and natural images are presented.Comment: 22 page
The chaotic effects in a nonlinear QCD evolution equation
The corrections of gluon fusion to the DGLAP and BFKL equations are discussed
in a united partonic framework. The resulting nonlinear evolution equations are
the well-known GLR-MQ-ZRS equation and a new evolution equation. Using the
available saturation models as input, we find that the new evolution equation
has the chaos solution with positive Lyaponov exponents in the perturbative
range. We predict a new kind of shadowing caused by chaos, which blocks the QCD
evolution in a critical small range. The blocking effect in the evolution
equation may explain the Abelian gluon assumption and even influence our
expectations to the projected Large Hadron Electron Collider (LHeC), Very Large
Hadron Collider (VLHC) and the upgrade (CppC) in a circular collider
(SppC).Comment: 58 pages, 23 figures,. Final version to appear in NP
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