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31
Diffeomorphic Demons: Efficient Nonparametric Image Registration
, 2008
"... We propose an efficient nonparametric diffeomorphic image registration algorithm based on Thirion’s demons algorithm. In the first part of this paper, we show that Thirion’s demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theor ..."
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Cited by 108 (13 self)
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We propose an efficient nonparametric diffeomorphic image registration algorithm based on Thirion’s demons algorithm. In the first part of this paper, we show that Thirion’s demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theoretical roots to the different variants of Thirion’s demons algorithm. This analysis predicts a theoretical advantage for the symmetric forces variant of the demons algorithm. We show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, we adapt the optimization procedure underlying the demons algorithm to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of displacement fields by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the gold standard, available in controlled experiments, in terms of Jacobians.
Optimization algorithms exploiting unitary constraints
 IEEE Trans. Signal Processing
, 2002
"... Abstract—This paper presents novel algorithms that iteratively converge to a local minimum of a realvalued function ( ) subject to the constraint that the columns of the complexvalued matrix are mutually orthogonal and have unit norm. The algorithms are derived by reformulating the constrained ..."
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Cited by 103 (13 self)
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Abstract—This paper presents novel algorithms that iteratively converge to a local minimum of a realvalued function ( ) subject to the constraint that the columns of the complexvalued matrix are mutually orthogonal and have unit norm. The algorithms are derived by reformulating the constrained optimization problem as an unconstrained one on a suitable manifold. This significantly reduces the dimensionality of the optimization problem. Pertinent features of the proposed framework are illustrated by using the framework to derive an algorithm for computing the eigenvector associated with either the largest or the smallest eigenvalue of a Hermitian matrix. Index Terms—Constrained optimization, eigenvalue problems, optimization on manifolds, orthogonal constraints. I.
Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
 Acta Appl. Math
"... Abstract. We give simple formulas for the canonical metric, gradient, Lie ..."
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Cited by 95 (22 self)
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Abstract. We give simple formulas for the canonical metric, gradient, Lie
Scale DriftAware Large Scale Monocular SLAM
"... Abstract—State of the art visual SLAM systems have recently been presented which are capable of accurate, largescale and realtime performance, but most of these require stereo vision. Important application areas in robotics and beyond open up if similar performance can be demonstrated using monocu ..."
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Cited by 65 (4 self)
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Abstract—State of the art visual SLAM systems have recently been presented which are capable of accurate, largescale and realtime performance, but most of these require stereo vision. Important application areas in robotics and beyond open up if similar performance can be demonstrated using monocular vision, since a single camera will always be cheaper, more compact and easier to calibrate than a multicamera rig. With high quality estimation, a single camera moving through a static scene of course effectively provides its own stereo geometry via frames distributed over time. However, a classic issue with monocular visual SLAM is that due to the purely projective nature of a single camera, motion estimates and map structure can only be recovered up to scale. Without the known intercamera distance of a stereo rig to serve as an anchor, the scale of locally constructed map portions and the corresponding motion estimates is therefore liable to drift over time. In this paper we describe a new near realtime visual SLAM system which adopts the continuous keyframe optimisation approach of the best current stereo systems, but accounts for the additional challenges presented by monocular input. In particular, we present a new posegraph optimisation technique which allows for the efficient correction of rotation, translation and scale drift at loop closures. Especially, we describe the Lie group of similarity transformations and its relation to the corresponding Lie algebra. We also present in detail the system’s new image processing frontend which is able accurately to track hundreds of features per frame, and a filterbased approach for feature initialisation within keyframebased SLAM. Our approach is proven via largescale simulation and realworld experiments where a camera completes large looped trajectories. I.
Nonparametric Diffeomorphic Image Registration with Demons Algorithm
, 2007
"... We propose a nonparametric diffeomorphic image registration algorithm based on Thirion’s demons algorithm. The demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. The main idea of our algorithm is to adapt this procedure to a space of diffeomorphi ..."
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Cited by 48 (9 self)
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We propose a nonparametric diffeomorphic image registration algorithm based on Thirion’s demons algorithm. The demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. The main idea of our algorithm is to adapt this procedure to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of free form deformations by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the true ones in terms of Jacobians.
Insight into efficient image registration techniques and the demons algorithm
 IN: PROC. IPMI’07
, 2007
"... As image registration becomes more and more central to many biomedical imaging applications, the efficiency of the algorithms becomes a key issue. Image registration is classically performed by optimizing a similarity criterion over a given spatial transformation space. Even if this problem is cons ..."
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Cited by 21 (6 self)
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As image registration becomes more and more central to many biomedical imaging applications, the efficiency of the algorithms becomes a key issue. Image registration is classically performed by optimizing a similarity criterion over a given spatial transformation space. Even if this problem is considered as almost solved for linear registration, we show in this paper that some tools that have recently been developed in the field of visionbased robot control can outperform classical solutions. The adequacy of these tools for linear image registration leads us to revisit nonlinear registration and allows us to provide interesting theoretical roots to the different variants of Thirion’s demons algorithm. This analysis predicts a theoretical advantage to the symmetric forces variant of the demons algorithm. We show that, on controlled experiments, this advantage is confirmed, and yields a faster convergence.
Visual tracking via geometric particle filtering on the affine group with optimal importance functions
 in Proc. IEEE CVPR
, 2009
"... We propose a geometric method for visual tracking, in which the 2D affine motion of a given object template is estimated in a video sequence by means of coordinateinvariant particle filtering on the 2D affine group Aff(2). Tracking performance is further enhanced through a geometrically defined ..."
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Cited by 18 (3 self)
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We propose a geometric method for visual tracking, in which the 2D affine motion of a given object template is estimated in a video sequence by means of coordinateinvariant particle filtering on the 2D affine group Aff(2). Tracking performance is further enhanced through a geometrically defined optimal importance function, obtained explicitly via Taylor expansion of a principal component analysis based measurement function on Aff(2). The efficiency of our approach to tracking is demonstrated via comparative experiments. 1.
A Geometrical Study of Matching Pursuit parametrization
"... This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) g ..."
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Cited by 13 (2 self)
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This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) geometry can be applied. The main contribution of this paper is twofold. First, we prove that if a discrete dictionary reaches a minimal density criterion, then the corresponding discrete MP (dMP) is equivalent in terms of convergence to a weakened hypothetical continuous MP. Interestingly, the corresponding weakness factor depends on a density measure of the discrete dictionary. Second, we show that the insertion of a simple geometric gradient ascent optimization on the atom dMP selection maintains the previous comparison but with a weakness factor at least two times closer to unity than without optimization. Finally, we present numerical experiments confirming our theoretical predictions for decomposition of signals and images on regular discretizations of dictionary parametrizations.
T.: An ITK Implementation of the Symmetric LogDomain Diffeomorphic Demons Algorithm
 Insight Journal
, 2009
"... This article provides an implementation of the symmetric logdomain diffeomorphic image registration algorithm, or symmetric demons algorithm for short. It generalizes Thirion’s demons and the diffeomorphic demons algorithm. The main practical advantages of the symmetric demons with respect to the o ..."
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Cited by 11 (0 self)
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This article provides an implementation of the symmetric logdomain diffeomorphic image registration algorithm, or symmetric demons algorithm for short. It generalizes Thirion’s demons and the diffeomorphic demons algorithm. The main practical advantages of the symmetric demons with respect to the other demons variants is that is provides the inverse of the spatial transformation at no additional computational cost and ensures that the registration of image A to image B provides the inverse of the registration from image B to image A. The algorithm works completely in the logdomain, i.e. it uses a stationaryvelocityfieldtoencodethespatialtransformationasitsexponential. WithintheInsightToolkit (ITK), the classical demons algorithm is implemented as part of the finite difference solver framework. Our code reuses and extends this generic framework. The source code is composed of a set of reusable ITK filters and classes together with their unit tests. We also provide a small example program that allowstheusertocomparethedifferentvariantsofthedemonsalgorithm. Thispapergivesanoverviewof thealgorithm,anoverviewofitsimplementationandasmalluserguidetoeasetheuseoftheregistration