Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Evolutionary fronts for topology-independent shape modeling and recovery
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Robust computation of optical flow in a multi-scale differential framework
International Journal of Computer Vision
International Journal of Computer Vision
Computer Vision and Image Understanding - Special issue on empirical evaluation of computer vision algorithms
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods
International Journal of Computer Vision
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal on Scientific Computing
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Building Blocks for Computer Vision with Stochastic Partial Differential Equations
International Journal of Computer Vision
Mumford-Shah regularizer with spatial coherence
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
IEEE Transactions on Image Processing
An estimation theoretical approach to Ambrosio-tortorelli image segmentation
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
From a modified ambrosio-tortorelli to a randomized part hierarchy tree
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Fast parameter sensitivity analysis of PDE-based image processing methods
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
International Journal of Computer Vision
Segmentation of Stochastic Images using Level Set Propagation with Uncertain Speed
Journal of Mathematical Imaging and Vision
From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree
Journal of Mathematical Imaging and Vision
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We present an extension of the classical Ambrosio-Tortorelli approximation of the Mumford-Shah approach for the segmentation of images with uncertain gray values resulting from measurement errors and noise. Our approach yields a reliable precision estimate for the segmentation result, and it allows to quantify the robustness of edges in noisy images and under gray value uncertainty. We develop an ansatz space for such images by identifying gray values with random variables. The use of these stochastic images in the minimization of energies of Ambrosio-Tortorelli type leads to stochastic partial differential equations for the stochastic smoothed image and a stochastic phase field for the edge set. For their discretization we utilize the generalized polynomial chaos expansion and the generalized spectral decomposition (GSD) method. We demonstrate the performance of the method on artificial data as well as real medical ultrasound data.