Bj Bart Janssen

On image reconstruction from multiscale top points

Image reconstruction from a fiducial collection of scale space interest points and attributes (e.g. in terms of image derivatives) can be used to make the amount of information contained in them explicit. Previous work by various authors includes both linear and non-linear image reconstruction schemes. In this paper, the authors present new results on image reconstruction using a top point representation of an image. A hierarchical ordering of top points based on a stability measure is presented, comparable to feature strength presented in various other works. By taking this into account our results show improved reconstructions from top points compared to previous work. The proposed top point representation is compared with previously proposed representations based on alternative feature sets, such as blobs using two reconstruction schemes (one linear, one non-linear). The stability of the reconstruction from the proposed top point representation under noise is also considered.

Warping a Neuro-Anatomy Atlas on 3D MRI Data with Radial Basis Functions

Navigation for neurosurgical procedures must be highly accurate. Often small structures are hardly seen on pre-operative scans. Fitting a 3D electronic neuro-anatomical atlas on the data assists with the localization of small structures and dim outlines. During surgery also brainshifts occurs. With intra-operative MRI the pre-operative MRI can be warped to the real 3D situation. The paper describes a general 3D landmark-based warping method, based on radial basis functions (thin plate splines) for data of any number of dimensions, including all code in Mathematica.

A Linear Image Reconstruction Framework Based on Sobolev Type Inner Products

Exploration of information content of features that are present in images has led to the development of several reconstruction algorithms. These algorithms aim for a reconstruction from the features that is visually close to the image from which the features are extracted. Degrees of freedom that are not fixed by the constraints are disambiguated with the help of a so-called prior (i.e. a user defined model). We propose a linear reconstruction framework that generalizes a previously proposed scheme. The algorithm greatly reduces the complexity of the reconstruction process compared to non-linear methods. As an example we propose a specific prior and apply it to the reconstruction from singular points. The reconstruction is visually more attractive and has a smaller 핃2-error than the reconstructions obtained by previously proposed linear methods.

Optic flow from multi-scale dynamic anchor point attributes

Optic flow describes the apparent motion that is present in an image sequence. We show the feasibility of obtaining optic flow from dynamic properties of a sparse set of multi-scale anchor points. Singular points of a Gaussian scale space image are identified as feasible anchor point candidates and analytical expressions describing their dynamic properties are presented. Advantages of approaching the optic flow estimation problem using these anchor points are that (i) in these points the notorious aperture problem does not manifest itself, (ii) it combines the strengths of variational and multi-scale methods, (iii) optic flow definition becomes independent of image resolution, (iv) computations of the components of the optic flow field are decoupled and that (v) the feature set inducing the optic flow field is very sparse (typically

Towards a new paradigm for motion extraction

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Coarse-to-Fine Image Reconstruction Based on Weighted Differential Features and Background Gauge Fields

of the number of pixels in a frame). A dense optic flow vector field is obtained through projection into a Sobolev space defined by and consistent with the dynamic constraints in the anchor points. As opposed to classical optic flow estimation schemes the proposed method accounts for an explicit scale component of the vector field, which encodes some dynamic differential flow property.

A variational approach to cardiac motion estimation based on covariant derivatives and multi-scale Helmholtz decomposition

A new multiscale paradigm is proposed for motion extraction. It exploits the fact that certain geometrically meaningful, isolated points in scale space provide unambiguous motion evidence, and the fact that such evidence narrows down the space of admissible motion fields. The paradigm combines the strengths of multiscale and variational frameworks. Besides spatial velocity, two additional degrees of freedom are taken into account, viz. a temporal and an isotropic spatial scale component. The first one is conventionally set to unity (“temporal gauge”), but may in general account for creation or annihilation of structures over time. The second one pertains to changes in the image that can be attributed to a sharpening or blurring of structures over time. This paper serves to introduce the new generalized motion paradigm de-emphasizing performance issues. We focus on the conceptual idea and provide recommendations for future directions.

Linear image reconstruction from a sparse set of α-scale space features by means of inner products of sobolev type

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.

A linear image reconstruction framework based on sobolev type inner products

The investigation and quantification of cardiac motion is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider a new method to track cardiac motion from magnetic resonance (MR) tagged images. Tracking is achieved by following the spatial maxima in scale-space of the MR images over time. Reconstruction of the velocity field is then carried out by minimizing an energy functional which is a Sobolev-norm expressed in covariant derivatives. These covariant derivatives are used to express prior knowledge about the velocity field in the variational framework employed. Furthermore, we propose a multi-scale Helmholtz decomposition algorithm that combines diffusion and Helmholtz decomposition in one non-singular analytic kernel operator in order to decompose the optic flow vector field in a divergence free, and rotation free part. Finally, we combine both the multi-scale Helmholtz decomposition and our vector field reconstruction (based on covariant derivatives) in a single algorithm and show the practical benefit of this approach by an experiment on real cardiac images.

Extraction of Cardiac Motion Using Scale-Space Features Points and Gauged Reconstruction

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.