Diffeomorphic Point Matching

Guo, Hongyu; Rangarajan, A.; Joshi, Shantanu H.

doi:10.1007/0-387-28831-7_13

Cited by 22 publications

(17 citation statements)

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“…In the first, also called (exact/inexact) diffeomorphic point matching [24,18], one has landmark pairs {(x i , y i )} Npts i=1 and seeks T : Ω → Ω such that {T (x i ) ≈ y i } Npts i=1 . We note that for n = 1, by Corollary 1, our ability to easily solve this problem using CPAB transformations means we can solve a monotonic regression problem, as we demonstrate in Fig.…”

Section: Applications and Resultsmentioning

confidence: 99%

“…Our work is influenced by the impressive works initiated by Grenander and continued in the geometryoriented subcommunities of computer vision and medical imaging. Due to space limits, we mention only a few: [15,16,8,24,42,4,1,18,17,43,30,45,9]. However, rather than focusing on complicated, possibly ∞-dimensional spaces (whose both representations and asso- Table 1:…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Highly-Expressive Spaces of Well-Behaved Transformations: Keeping it Simple

Freifeld

Hauberg

Batmanghelich

et al. 2015

2015 IEEE International Conference on Computer Vision (ICCV)

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show abstract

Section: Applications and Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Highly-Expressive Spaces of Well-Behaved Transformations: Keeping it Simple

Freifeld

Hauberg

Batmanghelich

et al. 2015

2015 IEEE International Conference on Computer Vision (ICCV)

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show abstract

“…In the first, also called (exact/inexact) diffeomorphic point matching [10], [14], one has a set of landmark pairs,

{false(x_{i}, y_{i} false)}_{i = 1}^{N_{pts}}

and seeks T : Ω → Ω such that

{T false(x_{i} false) \approx y_{i}}_{i = 1}^{N_{pts}}

. We observe that for n = 1, by Corollary 1, our ability to easily solve this problem using CPAB transformations lets us solve a monotonic regression problem, as Fig.…”

Section: Methodsmentioning

confidence: 99%

“…Our work is influenced by many impressive works in this field, primarily in the geometry-oriented areas of computer vision and medical imaging. Due to space limits, we can mention only a few: [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. Most of these works are based on complicated, usually ∞-dimensional, spaces, and the associated representations and computations are, in practice, discretized and/or otherwise approximated.…”

Section: Related Workmentioning

confidence: 99%

Transformations Based on Continuous Piecewise-Affine Velocity Fields

Freifeld

Hauberg²,

Batmanghelich

et al. 2017

IEEE Trans. Pattern Anal. Mach. Intell.

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We propose novel finite-dimensional spaces of well-behaved ℝn → ℝn transformations. The latter are obtained by (fast and highly-accurate) integration of continuous piecewise-affine velocity fields. The proposed method is simple yet highly expressive, effortlessly handles optional constraints (e.g., volume preservation and/or boundary conditions), and supports convenient modeling choices such as smoothing priors and coarse-to-fine analysis. Importantly, the proposed approach, partly due to its rapid likelihood evaluations and partly due to its other properties, facilitates tractable inference over rich transformation spaces, including using Markov-Chain Monte-Carlo methods. Its applications include, but are not limited to: monotonic regression (more generally, optimization over monotonic functions); modeling cumulative distribution functions or histograms; time-warping; image warping; image registration; real-time diffeomorphic image editing; data augmentation for image classifiers. Our GPU-based code is publicly available.

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“…An entirely different approach could be to perform diffeomorphic point matching [2,9,12,13] for obtaining a invertible mean displacement. This will be addressed in future work.…”

Section: Smooth Mean Displacementmentioning

confidence: 99%

Variational Image Registration Using Inhomogeneous Regularization

et al. 2014

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We present a generalization of the convolutionbased variational image registration approach, in which different regularizers can be implemented by conveniently exchanging the convolution kernel, even if it is nonseparable or nonstationary. Nonseparable kernels pose a challenge because they cannot be efficiently implemented by separate 1D convolutions. We propose to use a low-rank tensor decomposition to efficiently approximate nonseparable convolution. Nonstationary kernels pose an even greater challenge because the convolution kernel depends on, and needs to be evaluated for, every point in the image. We propose to pre-compute the local kernels and efficiently store them in memory using the Tucker tensor decomposition model. In our experiments we use the nonseparable exponential kernel and a nonstationary landmark kernel. The exponential kernel replicates desirable properties of elastic image registration, while the landmark kernel incorporates local prior knowledge about corresponding points in the images. We examine the trade-off between the computational resources needed and the approximation accuracy of the tensor decomposition methods. Furthermore, we obtain very smooth displacement fields even in the presence of large landmark displacements.

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Diffeomorphic Point Matching

Cited by 22 publications

References 0 publications

Highly-Expressive Spaces of Well-Behaved Transformations: Keeping it Simple

Highly-Expressive Spaces of Well-Behaved Transformations: Keeping it Simple

Transformations Based on Continuous Piecewise-Affine Velocity Fields

Variational Image Registration Using Inhomogeneous Regularization

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