3,312 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
Decorrelation of Neutral Vector Variables: Theory and Applications
In this paper, we propose novel strategies for neutral vector variable
decorrelation. Two fundamental invertible transformations, namely serial
nonlinear transformation and parallel nonlinear transformation, are proposed to
carry out the decorrelation. For a neutral vector variable, which is not
multivariate Gaussian distributed, the conventional principal component
analysis (PCA) cannot yield mutually independent scalar variables. With the two
proposed transformations, a highly negatively correlated neutral vector can be
transformed to a set of mutually independent scalar variables with the same
degrees of freedom. We also evaluate the decorrelation performances for the
vectors generated from a single Dirichlet distribution and a mixture of
Dirichlet distributions. The mutual independence is verified with the distance
correlation measurement. The advantages of the proposed decorrelation
strategies are intensively studied and demonstrated with synthesized data and
practical application evaluations
Blending Learning and Inference in Structured Prediction
In this paper we derive an efficient algorithm to learn the parameters of
structured predictors in general graphical models. This algorithm blends the
learning and inference tasks, which results in a significant speedup over
traditional approaches, such as conditional random fields and structured
support vector machines. For this purpose we utilize the structures of the
predictors to describe a low dimensional structured prediction task which
encourages local consistencies within the different structures while learning
the parameters of the model. Convexity of the learning task provides the means
to enforce the consistencies between the different parts. The
inference-learning blending algorithm that we propose is guaranteed to converge
to the optimum of the low dimensional primal and dual programs. Unlike many of
the existing approaches, the inference-learning blending allows us to learn
efficiently high-order graphical models, over regions of any size, and very
large number of parameters. We demonstrate the effectiveness of our approach,
while presenting state-of-the-art results in stereo estimation, semantic
segmentation, shape reconstruction, and indoor scene understanding
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