In order to define a metric on jet space, linear scalespace is considered from a statistical standpoint. Given a scale sigma, the scalespace solution can be interpreted as maximizing a certain Gaussian posterior pro...
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ISBN:
(纸本)9783540728221
In order to define a metric on jet space, linear scalespace is considered from a statistical standpoint. Given a scale sigma, the scalespace solution can be interpreted as maximizing a certain Gaussian posterior probability, related to a particular Tikhonov regularization. The Gaussian prior, which governs this solution, in fact induces a Mahalanobis distance on the space of functions. This metric on the function space gives, in a rather precise way, rise to a metric on n-jets. The latter, in turn, can be employed to define a norm on jet space, as the metric is translation invariant and homogeneous. Recently, [1] derived a metric on jet space and our results reinforce his findings, while providing a totally different approach to defining a scalespace jet metric.
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.
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.
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.
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.
Extracting regions that are noticeably different from their surroundings, so called salient regions, is a topic of considerable interest for image retrieval. There are many current techniques but it has been shown tha...
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ISBN:
(纸本)9783540728221
Extracting regions that are noticeably different from their surroundings, so called salient regions, is a topic of considerable interest for image retrieval. There are many current techniques but it has been shown that SIFT and MSER regions are among the best. The SIFT methods have their basis in linear scale-space but less well known is that MSERs are based on a non-linear scale-space. We demonstrate the connection between MSERs and morphological scale-space. Using this connection, MSERs can be enhanced to form a saliency tree which we evaluate via its effectiveness at a standard image retrieval task. The tree out-performs scale-saliency methods. We also examine the robustness of the tree using another standard task in which patches are compared across images transformations such as illuminant change, perspective transformation and so on. The saliency tree is one of the best performing methods.
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 paper we present a variational, spatiotemporal video super resolution scheme that produces not just one but n high resolution video frames from an n frame low resolution video sequence. We use a generic prior ...
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ISBN:
(纸本)9783540728221
In this paper we present a variational, spatiotemporal video super resolution scheme that produces not just one but n high resolution video frames from an n frame low resolution video sequence. We use a generic prior and the output is artifact-free, sharp and superior in quality to state of the art home cinema video processors. Unlike many other super resolution schemes, ours does not limit itself to just translational or affine motion;or to certain subclasses of image content to optimize the output quality. We present a link between image reconstruction and super resolution and formulate our super resolution constraint with arbitrary up-scaling factors in space from that.
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.
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 standard scale-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.
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