22,644 research outputs found
Reflection methods for user-friendly submodular optimization
Recently, it has become evident that submodularity naturally captures widely
occurring concepts in machine learning, signal processing and computer vision.
Consequently, there is need for efficient optimization procedures for
submodular functions, especially for minimization problems. While general
submodular minimization is challenging, we propose a new method that exploits
existing decomposability of submodular functions. In contrast to previous
approaches, our method is neither approximate, nor impractical, nor does it
need any cumbersome parameter tuning. Moreover, it is easy to implement and
parallelize. A key component of our method is a formulation of the discrete
submodular minimization problem as a continuous best approximation problem that
is solved through a sequence of reflections, and its solution can be easily
thresholded to obtain an optimal discrete solution. This method solves both the
continuous and discrete formulations of the problem, and therefore has
applications in learning, inference, and reconstruction. In our experiments, we
illustrate the benefits of our method on two image segmentation tasks.Comment: Neural Information Processing Systems (NIPS), \'Etats-Unis (2013
Linear Shape Deformation Models with Local Support Using Graph-based Structured Matrix Factorisation
Representing 3D shape deformations by linear models in high-dimensional space
has many applications in computer vision and medical imaging, such as
shape-based interpolation or segmentation. Commonly, using Principal Components
Analysis a low-dimensional (affine) subspace of the high-dimensional shape
space is determined. However, the resulting factors (the most dominant
eigenvectors of the covariance matrix) have global support, i.e. changing the
coefficient of a single factor deforms the entire shape. In this paper, a
method to obtain deformation factors with local support is presented. The
benefits of such models include better flexibility and interpretability as well
as the possibility of interactively deforming shapes locally. For that, based
on a well-grounded theoretical motivation, we formulate a matrix factorisation
problem employing sparsity and graph-based regularisation terms. We demonstrate
that for brain shapes our method outperforms the state of the art in local
support models with respect to generalisation ability and sparse shape
reconstruction, whereas for human body shapes our method gives more realistic
deformations.Comment: Please cite CVPR 2016 versio
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