We present a hierarchical clustering method for a dataset based on the deep structure of the probability density function (PDF) of the data in the scalespace. The data clusters correspond to the modes of the PDF, and...
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ISBN:
(纸本)9783540728221
We present a hierarchical clustering method for a dataset based on the deep structure of the probability density function (PDF) of the data in the scalespace. The data clusters correspond to the modes of the PDF, and their hierarchy is determined by regarding the nonparametric estimation of the PDF with the Gaussian kernel as a scale-space representation. It is shown that the number of clusters is statistically deterministic above a certain critical scale, even though the positions of the data points are stochastic. Such a critical scale is estimated by analysing the distribution of cluster lifetime in the scalespace, and statistically valid clusters are detected above the critical scale. This cluster validation using the critical scale can be recursively employed according to the hierarchy of the clusters.
This paper investigates the scale selection problem for vector-valued nonlinear diffusion scale-spaces. We present a new approach for the localization scale selection, which aims at maximizing the image content's ...
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ISBN:
(纸本)9783540728221
This paper investigates the scale selection problem for vector-valued nonlinear diffusion scale-spaces. We present a new approach for the localization scale selection, which aims at maximizing the image content's presence by finding the scale having a maximum correlation with the noise-free image. For scale-space discretization, we propose to address an adaptation of the optimal diffusion stopping time criterion introduced by Mrazek and Navara [1], in such a way that it identifies multiple scales of importance.
In this paper, a new method of content identification using topological invariants is proposed. First, we show a Reeb-graph of topological invariants of images in a scale-space. Different from well-known scale-space t...
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ISBN:
(纸本)9783540728221
In this paper, a new method of content identification using topological invariants is proposed. First, we show a Reeb-graph of topological invariants of images in a scale-space. Different from well-known scale-space trees of salient or critical points based on catastrophe or singularity theory, we use topologically stable blobs or primary sketches with nonzero lifetimes in scale and nonzero areas at each scale. The continuum of such blobs as a 3D manifold is featured by trees of topological invariants of the image called a Reeb graph. We show that this Reeb-graph representation is more robust against deformation attacks and perturbation such as numerical errors than traditional scale-space trees. A fast matching algorithm for the graphs is also presented.
In this work we study the relation between the Gabor-Morlet wavelet transform and scale-space theory. It is shown that the usual wavelet transform is a projection of scale-space on a specific frequency component. This...
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ISBN:
(纸本)9783540728221
In this work we study the relation between the Gabor-Morlet wavelet transform and scale-space theory. It is shown that the usual wavelet transform is a projection of scale-space on a specific frequency component. This result is then generalized to the full two-dimensional affine group. A close relation between this generalized wavelet transform and a family of scale-spaces of images that are related by SL(2) is established. Using frame theory we show that sampling from different images in this family;and from different scales enables a complete reconstruction of the image.
In this paper, we propose a variational model for curve matching based on Kullback-Leibler(KL) divergence. This framework accomplishes the difficult task of finding correspondences for a group of curves simultaneously...
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ISBN:
(纸本)9783540728221
In this paper, we propose a variational model for curve matching based on Kullback-Leibler(KL) divergence. This framework accomplishes the difficult task of finding correspondences for a group of curves simultaneously in a symmetric and transitive fashion. Moreover the distance in the energy functional has the metric property. We also introduce a location weighted model to handle noise, distortion and occlusion. Numerical results indicate the effective of this framework. The existence of this model is also provided.
Inverse scalespacemethods are derived as asymptotic limits of iterative regularization methods. They have proven to be efficient methods for denoising of gray valued images and for the evaluation of unbounded operat...
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ISBN:
(纸本)9783540728221
Inverse scalespacemethods are derived as asymptotic limits of iterative regularization methods. They have proven to be efficient methods for denoising of gray valued images and for the evaluation of unbounded operators. In the beginning, inverse scalespacemethods have been derived from iterative regularization methods with squared Hilbert norm regularization terms, and later this concept was generalized to Bregman distance regularization (replacing the squared regularization norms);therefore allowing for instance to consider iterative total variation regularization. We have proven recently existence of a solution of the associated inverse total variation flow equation. In this paper we generalize these results and prove existence of solutions of inverse flow equations derived from iterative regularization with general convex regularization functionals. We present some applications to filtering of color data and for the stable evaluation of the diZenzo edge detector.
A variational formulation of an image analysis problem has the nice feature that it is often easier to predict the effect of minimizing a certain energy functional than to interpret the corresponding Euler-Lagrange eq...
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ISBN:
(纸本)9783540728221
A variational formulation of an image analysis problem has the nice feature that it is often easier to predict the effect of minimizing a certain energy functional than to interpret the corresponding Euler-Lagrange equations. For example, the equations of motion for an active contour usually contains a mean curvature term, which we know will regularizes the contour because mean curvature is the first variation of curve length, and shorter curves are typically smoother than longer ones. In some applications it may be worth considering Gaussian curvature as a regularizing term instead of mean curvature. The present paper provides a variational principle for this: We show that Gaussian curvature of a regular surface in three-dimensional Euclidean space is the first variation of an energy functional defined on the surface. Some properties of the corresponding motion by Gaussian curvature are pointed out, and a simple example is given, where minimization of this functional yields a nontrivial solution.
A family of spatio-temporal scale-spaces suitable for a moving observer is developed. The scale-spaces are required to be time causal for being usable for real time measurements, and to be "velocity adapted"...
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ISBN:
(纸本)9783540728221
A family of spatio-temporal scale-spaces suitable for a moving observer is developed. The scale-spaces are required to be time causal for being usable for real time measurements, and to be "velocity adapted";i.e. to have Galilean covariance to avoid favoring any particular motion. Furthermore standardscale-space axioms: linearity, positivity, continuity, translation invariance, scaling covariance in space and time, rotational invariance in space and recursivity are used. An infinitesimal criterion for scale-spaces is developed, which simplifies calculations and makes it possible to define scalespaces on bounded regions. We show that there are no temporally causal Galilean scale-spaces that are semigroups acting on space and time, but that there are such scale-spaces that are semigroups acting on space and memory (where the memory is the scale-space). The temporally causal scale-space is a time-recursive process using current input and the scale-space as state, i.e. there is no need for storing earlier input. The diffusion equation acting on the memory with the input signal as boundary condition, is a member of this family of scalespaces and is special in the sense that its generator is local.
We propose a variational approach for multi-valued velocity field estimation in transparent sequences. Starting from existing local motion estimators, we show a variational model for integrating in space and time thes...
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ISBN:
(纸本)9783540728221
We propose a variational approach for multi-valued velocity field estimation in transparent sequences. Starting from existing local motion estimators, we show a variational model for integrating in space and time these local estimations to obtain a robust estimation of the multi-valued velocity field. With this approach, we can indeed estimate some multi-valued velocity fields which are not necessarily piecewise constant on a layer: Each layer can evolve according to non-parametric optical flow. We show how our approach outperforms some existing approaches, and we illustrate its capabilities on several challenging synthetic/real sequences.
Level set methods have been proven to be efficient tools for tracing interface problems. Recently;some variants of the Osher- Sethian level set methods, which are called the Piecewise Constant Level Set methods (PCLSM...
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ISBN:
(纸本)9783540728221
Level set methods have been proven to be efficient tools for tracing interface problems. Recently;some variants of the Osher- Sethian level set methods, which are called the Piecewise Constant Level Set methods (PCLSM), have been proposed for some interface problems. The methods need to minimize a smooth cost functional under some special constraints. In this paper a PCLSM for 3D image segmentation is tested. The algorithm uses the gradient descent method combined with a Quasi-Newton method to minimize an augmented Lagrangian functional. Experiments for medical image segmentation are shown on synthetic three dimensional MR brain images. The efficiency of the algorithm and the quality of the obtained images are demonstrated.
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