Results 1 
5 of
5
A Theoretical Framework for Convex Regularizers in PDEBased Computation of Image Motion
, 2000
"... Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness consta ..."
Abstract

Cited by 99 (25 self)
 Add to MetaCart
Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for datadriven and flowdriven, isotropic and anisotropic, as well as spatial and spatiotemporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are wellposed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flowdriven regularizers is identified, and a design criterion is proposed for constructing anisotropic flowdriven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.
Relations between Optimization and Gradient Flow Methods with Applications to Image Registration
, 2001
"... Fast multiscale and multigrid methods for the matching of images in 2D and 3D are presented. Especially in medical imaging this problem  denoted as the registration problem  is of fundamental importance in the handling of images from multiple image modalities or of image time series. The paper ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
Fast multiscale and multigrid methods for the matching of images in 2D and 3D are presented. Especially in medical imaging this problem  denoted as the registration problem  is of fundamental importance in the handling of images from multiple image modalities or of image time series. The paper restricts
Accurate optical flow computation under nonuniform brightness varations
 Computer Vision and Image Understanding
, 2005
"... In this paper, we present a very accurate algorithm for computing optical
ow with nonuniform brightness variations. The proposed algorithm is based on a generalized dynamic image model (GDIM) in conjunction with a regularization framework to cope with the problem of nonuniform brightness variati ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
(Show Context)
In this paper, we present a very accurate algorithm for computing optical
ow with nonuniform brightness variations. The proposed algorithm is based on a generalized dynamic image model (GDIM) in conjunction with a regularization framework to cope with the problem of nonuniform brightness variations. To alleviate
ow constraint errors due to image aliasing and noise, we employ a reweighted leastsquares method to suppress unreliable
ow constraints, thus leading to robust estimation of optical
ow. In addition, a dynamic smoothness adjustment scheme is proposed to eciently suppress the smoothness constraint in the vicinity of the motion and brightness variation discontinuities, thereby preserving motion boundaries. We also employ a constraint renement scheme, which aims at reducing the approximation errors in the rstorder dierential
ow equation, to rene the optical
ow estimation especially for large image motions. To eciently minimize the resulting energy function for optical ow computation, we utilize an incomplete Cholesky preconditioned conjugate gradient algorithm to solve the large linear system. Experimental results on some synthetic and real image sequences show that the proposed algorithm compares favorably to most existing techniques
A Theoretical Framework for Convex Regularizers in PDEBased Computation of Image Motion
, 2000
"... Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness consta ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for datadriven and flowdriven, isotropic and anisotropic, as well as spatial and spatiotemporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are wellposed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flowdriven regularizers is identified, and a design criterion is proposed for constructing anisotropic flowdriven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.
Computing Optic Flow by ScaleSpace Integration of Normal Flow
 in `Proc. ScaleSpace'01
, 2001
"... In this paper we will present a least committed multiscale method for computation of optic flow fields. We extract optic flow fields from normal flow, by fitting the normal components of a local polynomial model of the optic flow to the normal flow. This fitting is based on an analytically solvable ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
In this paper we will present a least committed multiscale method for computation of optic flow fields. We extract optic flow fields from normal flow, by fitting the normal components of a local polynomial model of the optic flow to the normal flow. This fitting is based on an analytically solvable optimization problem, in which an integration scalespace over the normal flow field regularizes the solution. An automatic local scale selection mechanism is used in order to adapt to the local structure of the flow field. The performance profile of the method is compared with that of existing optic flow techniques and we show that the proposed method performs at least as well as the leading algorithms on the benchmark image sequences proposed by Barron et al. [3]. We also do a performance comparison on a synthetic fire particle sequence and apply our method to a real sequence of smoke circulation in a pigsty. Both consist of highly complex nonrigid motion.