Name
Title | ||
|---|---|---|
Linear image reconstruction from a sparse set of α-scale space features by means of inner products of sobolev type |
Abstract | ||
|---|---|---|
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.
|
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/11577812_9 | DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision |
Keywords | DocType | Volume |
linear reconstruction framework,linear method,sobolev type,metameric class,inner product,scale space feature,linear feature reconstruction,euler lagrange minimization,linear feature,linear image reconstruction,scale space,image analysis,image reconstruction,sobolev space,numerical method,principle component analysis,orthogonal projection,exact solution,tikhonov regularization,hilbert space | Conference | 3753 |
ISSN | ISBN | Citations |
0302-9743 | 3-540-29836-3 | 1 |
PageRank | References | Authors |
0.36 | 9 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Remco Duits | 1 | 380 | 33.83 |
| Bart Janssen | 2 | 24 | 2.56 |
| Frans Kanters | 3 | 53 | 4.17 |
| L. M. J. Florack | 4 | 1212 | 210.47 |