International Journal of Computer Vision
Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in 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
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
The monogenic scale space on a bounded domain and its applications
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Image reconstruction from multiscale critical points
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Stability of top-points in scale space
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
A linear image reconstruction framework based on sobolev type inner products
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
On image reconstruction from multiscale top points
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
A Linear Image Reconstruction Framework Based on Sobolev Type Inner Products
International Journal of 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
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Inner products of Sobolev type are extremely useful for image reconstruction of images from a sparse set of α-scale space features. The common (non)-linear reconstruction frameworks, follow an Euler Lagrange minimization. If the Lagrangian (prior) is a norm induced by an inner product of a Hilbert space, this Euler Lagrange minimization boils down to a simple orthogonal projection within the corresponding Hilbert space. This basic observation has been overlooked in image analysis for the cases where the Lagrangian equals a norm of Sobolev type, resulting in iterative (non-linear) numerical methods, where already an exact solution with non-iterative linear algorithm is at hand. Therefore we provide a general theory on linear image reconstructions and metameric classes of images. By applying this theory we obtain visually more attractive reconstructions than the previously proposed linear methods and we find connected curves in the metameric class of images, determined by a fixed set of linear features, with a monotonic increase of smoothness. Although the theory can be applied to any linear feature reconstruction or principle component analysis, we mainly focus on reconstructions from so-called topological features (such as top-points and grey-value flux) in scale space, obtained from geometrical observations in the deep structure of a scale space.