Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
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
Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models
Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal on Scientific Computing
Random Walks for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A sensitivity analysis method and its application in physics-based nonrigid motion modeling
Image and Vision Computing
Building Blocks for Computer Vision with Stochastic Partial Differential Equations
International Journal of Computer Vision
UPRE method for total variation parameter selection
Signal Processing
Ambrosio-tortorelli segmentation of stochastic images
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Automatic parameter selection for denoising algorithms using a no-reference measure of image content
IEEE Transactions on Image Processing
International Journal of Computer Vision
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We present a fast parameter sensitivity analysis by combining recent developments from uncertainty quantification with image processing operators. The approach is not based on a sampling strategy, instead we combine the polynomial chaos expansion and stochastic finite elements with PDE-based image processing operators. With our approach and a moderate number of parameters in the models the full sensitivity analysis is obtained at the cost of a few Monte Carlo runs. To demonstrate the efficiency and simplicity of the approach we show a parameter sensitivity analysis for Perona-Malik diffusion, random walker and Ambrosio-Tortorelli segmentation, and discontinuity-preserving optical flow computation.