Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
Ten lectures on wavelets
A Fast Poisson Solver of Arbitrary Order Accuracy in Rectangular Regions
SIAM Journal on Scientific Computing
The Topological Structure of Scale-Space Images
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Advanced Engineering Mathematics: Maple Computer Guide
Advanced Engineering Mathematics: Maple Computer Guide
International Journal of Computer Vision
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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
A Linear Image Reconstruction Framework Based on Sobolev Type Inner Products
International Journal of Computer Vision
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
α scale spaces on a bounded domain
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
IEEE Transactions on Information Theory
Improvement of DCT-Based Compression Algorithms Using Poisson's Equation
IEEE Transactions on Image Processing
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The reconstruction problem is usually formulated as a variational problem in which one searches for that image that minimizes a so called prior (image model) while insisting on certain image features to be preserved. When the prior can be described by a norm induced by some inner product on a Hilbert space, the exact solution to the variational problem can be found by orthogonal projection. In previous work we considered the image as compactly supported in $\mathbb{L}_{2}(\mathbb{R}^{2})$ and we used Sobolev norms on the unbounded domain including a smoothing parameter 驴0 to tune the smoothness of the reconstructed image. Due to the assumption of compact support of the original image, components of the reconstructed image near the image boundary are too much penalized. Therefore, in this work we minimize Sobolev norms only on the actual image domain, yielding much better reconstructions (especially for 驴驴0). As an example we apply our method to the reconstruction of singular points that are present in the scale space representation of an image.