The Topological Structure of Scale-Space Images
Journal of Mathematical Imaging and Vision
A multigrid tutorial: second edition
A multigrid tutorial: second edition
International Journal of Computer Vision
What Do Features Tell about Images?
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
A Linear Image Reconstruction Framework Based on Sobolev Type Inner Products
International Journal of Computer Vision
Image Compression with Anisotropic Diffusion
Journal of Mathematical Imaging and Vision
Linear image reconstruction by Sobolev norms on the bounded domain
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Towards a new paradigm for motion extraction
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
Optic flow from multi-scale dynamic anchor point attributes
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
A pyramid approach to subpixel registration based on intensity
IEEE Transactions on Image Processing
B-Spline Image Model for Energy Minimization-Based Optical Flow Estimation
IEEE Transactions on Image Processing
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We propose an iterative approximate reconstruction method where we minimize the difference between reconstructions from subsets of multi scale measurements. To this end we interpret images not as scalar-valued functions but as sections through a fibered space. Information from previous reconstructions, which can be obtained at a coarser scale than the current one, is propagated by means of covariant derivatives on a vector bundle. The gauge field that is used to define the covariant derivatives is defined by the previously reconstructed image. An advantage of using covariant derivatives in the variational formulation of the reconstruction method is that with the number of iterations the accuracy of the approximation increases. The presented reconstruction method allows for a reconstruction at a resolution of choice, which can also be used to speed up the approximation at a finer level. An application of our method to reconstruction from a sparse set of differential features of a scale space representation of an image allows for a weighting of the features based on the sensitivity of those features to noise. To demonstrate the method we apply it to the reconstruction from singular points of a scale space representation of an image.