Proceedings ArticleDOI
Variations on regularization
Daniel Keren,Michael Werman +1 more
- pp 93-98
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TLDR
The authors consider as an example a case in which regularization has been used to reconstruct a surface from sparse data, and attempt to determine how strongly the height of the surface at a certain point can be relied upon.Abstract:
Regularization has become an important tool for solving many ill-posed problems in approximation theory-for example, in computer vision-including surface reconstruction, optical flow, and shape from shading. The authors attempt to determine whether the approach taken in regularization is always the correct one, and to what extent the results of regularization are reliable. They consider as an example a case in which regularization has been used to reconstruct a surface from sparse data, and attempt to determine how strongly the height of the surface at a certain point can be relied upon. These questions are answered by defining a probability distribution on the class of surfaces considered, and computing its expectation and variance. The variance can be used, for instance, to construct a safety strip around the interpolated surface that should not be entered if collision with the surface is to be avoided. >read more
Citations
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Shape Representation and Recognition from Multiscale Curvature
Gregory Dudek,John K. Tsotsos +1 more
TL;DR: A technique for shape representation and the recognition of objects based on multiscale curvature information that provides a single framework for both the decomposition and recognition of both planar curves as well as surfaces in three-dimensional space is presented.
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Discontinuity preserving regularization of inverse visual problems
TL;DR: This paper presents a technique for incorporating discontinuities into the reconstruction problem while maintaining a well-posed and well-conditioned problem statement and the resulting computational problem is a convex functional minimization problem.
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A Bayesian method for fitting parametric and nonparametric models to noisy data
Michael Werman,Daniel Keren +1 more
TL;DR: In this paper, a simple paradigm for fitting models, parametric and nonparametric, to noisy data is presented, which resolves some of the problems associated with classical MSE algorithms.
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Motion-based object segmentation and estimation using the MDL principle
H. Zheng,Steven D. Blostein +1 more
TL;DR: A framework motivated by Rissanen's (1983) minimum description length (MDL) principle is proposed to more tightly couple motion estimation and object segmentation algorithms to the overall objective of minimizing source bit rate.
Proceedings ArticleDOI
A fast algorithm for MDL-based multi-band image segmentation
TL;DR: An incremental polynomial regression that uses computations from the previous stage to compute results in the current stage, resulting in a significant speed up over the non-incremental technique is used.
References
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Determining optical flow
TL;DR: In this paper, a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image, and an iterative implementation is shown which successfully computes the Optical Flow for a number of synthetic image sequences.
Journal ArticleDOI
Determining Three-Dimensional Motion and Structure from Optical Flow Generated by Several Moving Objects
TL;DR: A new approach for the interpretation of optical flow fields is presented, where the flow field is partitioned into connected segments of flow vectors, where each segment is consistent with a rigid motion of a roughly planar surface.
Book
Determining optical flow
TL;DR: An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences and is robust in that it can handle image sequences that are quantified rather coarsely in space and time.
Journal ArticleDOI
Regularization of Inverse Visual Problems Involving Discontinuities
TL;DR: This paper proposes a general class of controlled-continuity stabilizers which provide the necessary control over smoothness in visual reconstruction problems that involve both continuous regions and discontinuities, for which global smoothness constraints fail.