Interactions between Symmetric Cone and Information Geometries: Bruhat-Tits and Siegel Spaces Models for High Resolution Autoregressive Doppler Imagery

Barbaresco, Frédéric

doi:10.1007/978-3-642-00826-9_6

Cited by 75 publications

(87 citation statements)

References 19 publications

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“…The superiority of the geodesic distance highlights the importance of considering the covariance matrices in the space of Hermitian definite positive matrices which is not a Euclidean space but a Riemannian manifold. Note that this issue has already been observed and discussed in several references such as [16], [23], [24].…”

Section: B Evaluation Of Pruning Approachesmentioning

confidence: 53%

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Optimum Graph Cuts for Pruning Binary Partition Trees of Polarimetric SAR Images

Salembier

Foucher

2016

IEEE Trans. Geosci. Remote Sensing

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Abstract-This paper investigates several optimum graph-cuts techniques for pruning Binary Partition Trees (BPTs) and their usefulness for low-level processing of Polarimetric SAR (PolSAR) images. BPTs group pixels to form homogeneous regions, which are hierarchically structured by inclusion in a binary tree. They provide multiple resolutions of description and easy access to subsets of regions. Once constructed, BPTs can be used for a large number of applications. Many of these applications consist in populating the tree with a specific feature and in applying a graph-cut called pruning to extract a partition of the space. In this paper, different pruning examples involving the optimization of a global criterion are discussed and analyzed in the context of PolSAR images for segmentation. Through objective evaluation of the resulting partitions by means of Precision and Recall for boundaries curves, the best pruning technique is identified and the influence of the tree construction on the performances is assessed.

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Section: B Evaluation Of Pruning Approachesmentioning

confidence: 53%

“…5. The distance between neighboring regions defining the merging order can be measured by the geodesic similarity adapted to the cone of positive definite Hermitian matrices [16]:…”

Section: Cutmentioning

confidence: 99%

Optimum Graph Cuts for Pruning Binary Partition Trees of Polarimetric SAR Images

Salembier

Foucher

2016

IEEE Trans. Geosci. Remote Sensing

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“…The shortest path between two points on this manifold can be computed by the geodesic distance d G (Equation (8), where || · || F is the Frobenius norm, [33]). Another example is the log-Euclidean distance d LE (Equation (9), [34]), which is less computationally expensive but still invariant with respect to similarity transformations:…”

Section: Polarimetric Distancesmentioning

confidence: 99%

Classification of PolSAR Images by Stacked Random Forests

Hänsch

Hellwich

2018

IJGI

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This paper proposes the use of Stacked Random Forests (SRF) for the classification of Polarimetric Synthetic Aperture Radar images. SRF apply several Random Forest instances in a sequence where each individual uses the class estimate of its predecessor as an additional feature. To this aim, the internal node tests are designed to work not only directly on the complex-valued image data, but also on spatially varying probability distributions and thus allow a seamless integration of RFs within the stacking framework. Experimental results show that the classification performance is consistently improved by the proposed approach, i.e., the achieved accuracy is increased by 4% and 7% for one fully-and one dual-polarimetric dataset. This increase only comes at the cost of a linear increased training and prediction time, which is rather limited as the method converges quickly.

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“…From now on, we regard T n as a Riemannian manifold whose metric, which is introduced in [8] by the Hessian of the Kähler potential…”

Section: Riemannian Geometry Of Toeplitz Covariance Matricesmentioning

confidence: 99%

Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computation

Arnaudon

Barbaresco

Yang

2012

Matrix Information Geometry

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This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local medians are given. In order to compute medians in practical cases, we propose a subgradient algorithm and prove its convergence. After that, Fréchet medians are considered. We prove their statistical consistency and give some quantitative estimations of their robustness with the aid of upper curvature bounds. We also show that, in compact Riemannian manifolds, the Fréchet medians of generic data points are always unique. Stochastic and deterministic algorithms are proposed for computing Riemannian p-means. The rate of convergence and error estimates of these algorithms are also obtained. Finally, we apply the medians and the Riemannian geometry of Toeplitz covariance matrices to radar target detection.

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Interactions between Symmetric Cone and Information Geometries: Bruhat-Tits and Siegel Spaces Models for High Resolution Autoregressive Doppler Imagery

Cited by 75 publications

References 19 publications

Optimum Graph Cuts for Pruning Binary Partition Trees of Polarimetric SAR Images

Optimum Graph Cuts for Pruning Binary Partition Trees of Polarimetric SAR Images

Classification of PolSAR Images by Stacked Random Forests

Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computation

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