Optical Flow on Evolving Surfaces with an Application to the Analysis of 4D Microscopy Data

Kirisits, Clemens; Lang, Lukas F.; Scherzer, Otmar

doi:10.1007/978-3-642-38267-3_21

Cited by 13 publications

(36 citation statements)

References 16 publications

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“…Using the approach proposed in this paper, a regularization functional based on the covariant derivatives of the vector field can be constructed. We refer to Kirisits et al (2013), where a similar approach was employed to approximate the optical flow of an image on a moving surface. More generally, we plan to use the results presented in this paper to formulate regularization methods based on coefficient norms for the derivatives.…”

Section: Resultsmentioning

confidence: 99%

Derivatives of isogeometric functions on n-dimensional rational patches in Rd

Takacs

Jüttler

Scherzer

2014

Computer Aided Geometric Design

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Section: Resultsmentioning

confidence: 99%

Derivatives of isogeometric functions on n-dimensional rational patches in Rd

Takacs

Jüttler

Scherzer

2014

Computer Aided Geometric Design

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“…Typically, this constraint is termed brightness constancy assumption and is the basis for many motion estimation methods. In order to linearise (32) by differentiation with respect to time, one may consider temporal derivatives along trajectories, see [33,35]. To this end, we define the time derivative off along a trajectory ψ :…”

Section: Conservation Of Brightnessmentioning

confidence: 99%

“…A major gain of this approach is that it can also reduce the computational effort during analysis of the recorded material, see e.g. [33,34,35,37,47]. In addition, introducing a geometric representation of the specimen allows to compute accurate measurements, such as distances, on curved surfaces rather than in-possibly distorting-projections.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Framework for Efficient Motion Estimation on Evolving Sphere-Like Surfaces Based on Brightness and Mass Conservation Laws

Lang¹

2019

SIAM J. Imaging Sci.

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In this work we consider brightness and mass conservation laws for motion estimation on evolving Riemannian 2-manifolds that allow for a radial parametrisation from the 2-sphere. While conservation of brightness constitutes the foundation for optical flow methods and has been generalised to said scenario, we formulate in this article the principle of mass conservation for time-varying surfaces which are embedded in Euclidean 3-space and derive a generalised continuity equation. The main motivation for this work is efficient cell motion estimation in time-lapse (4D) volumetric fluorescence microscopy images of a living zebrafish embryo. Increasing spatial and temporal resolution of modern microscopes require efficient analysis of such data. With this application in mind we address this need and follow an emerging paradigm in this field: dimensional reduction. In light of the ill-posedness of considered conservation laws we employ Tikhonov regularisation and propose the use of spatially varying regularisation functionals that recover motion only in regions with cells. For the efficient numerical solution we devise a Galerkin method based on compactly supported (tangent) vectorial basis functions. Furthermore, for the fast and accurate estimation of the evolving sphere-like surface from scattered data we utilise surface interpolation with spatio-temporal regularisation. We present numerical results based on aforementioned zebrafish microscopy data featuring fluorescently labelled cells.

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“…In the following we will look for solutions that additionally satisfy a regularity constraint in time t. For the optical flow in the plane R 2 , this method has been introduced in [42]. Spatio-temporal regularization of the optical flow on moving manifolds, has also been considered in [24], but with a different regularity term than the one we will construct in the following. In order to construct the regularity term, we consider the product manifold…”

Section: Regularization In Time and Spacementioning

confidence: 99%

Optical Flow on Moving Manifolds

Bauer¹,

Grasmair²,

Kirisits³

2015

SIAM J. Imaging Sci.

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Abstract. Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying image domain. To that end we construct a Riemannian metric that describes the deformation and structure of this evolving surface. The resulting functional can be seen as natural geometric generalization of previous work by Weickert and Schnörr (2001) and Lefèvre and Baillet (2008) for static image domains. In this work we show the existence and wellposedness of the corresponding optical flow problem and derive necessary and sufficient optimality conditions. We demonstrate the functionality of our approach in a series of experiments using both synthetic and real data.

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Optical Flow on Evolving Surfaces with an Application to the Analysis of 4D Microscopy Data

Cited by 13 publications

References 16 publications

Derivatives of isogeometric functions on n-dimensional rational patches in Rd

Derivatives of isogeometric functions on n-dimensional rational patches in Rd

A Numerical Framework for Efficient Motion Estimation on Evolving Sphere-Like Surfaces Based on Brightness and Mass Conservation Laws

Optical Flow on Moving Manifolds

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