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## Study of Binary Partition Tree Pruning Techniques for Polarimetric SAR images

### Citations

625 | Learning to detect natural image boundaries using local brightness, color, and texture cues
- Martin, Fowlkes, et al.
- 2004
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Citation Context ... 3 shows the evaluation of the segmentation results as classically done in the supervised case through Precision and Recall curves. On the left side, the so-called Precision and Recall for boundaries =-=[15]-=- is presented. In this case, each partition is evaluated by considering all pairs of neighboring pixels and by classifying them in either boundary or interior segments. The Precision and the Recall va... |

245 |
A review of target decomposition theorems in radar polarimetry.
- Cloude, Pottier
- 1996
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Citation Context ...ss is known as the 3speckle. Although the speckle represents a true electromagnetic measurement, its complexity is such that it is considered as a random process. Rewriting the S matrix as a vector k =-=[6]-=-: k = [Shh, √ 2Shv, Svv] T (2) k is characterized by a three dimensional zero-mean complex Gaussian pdf: pk(k) = 1 pi3|C| exp(−k HC−1k). (3) Therefore, the distribution of k is completely described by... |

222 | Slic superpixels compared to state-of-the-art superpixel methods
- Achanta, Shaji, et al.
- 2012
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Citation Context ...ted to PolSAR images such as [14, 7] before computing the super-pixel partitions. The best combination found in [17] involves the use of the σ-Lee denoising filter [14] followed by the SLIC algorithm =-=[1]-=- to compute the super-pixel. Only the three 41 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 SourcesSinks1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 SourcesPruningsFig. 1. Illustration of the pruning on a BPT... |

146 | Binary partition tree as an efficient representation for image processing, segmentation and information retrieval,”
- Salembier, Garrido
- 2000
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Citation Context ...the definition of the optimization criterion. Keywords: Binary Partition Tree, PolSAR, graph-cut, pruning, speckle noise, segmentation. 1 Introduction The application of Binary Partition Trees (BPTs) =-=[18]-=- for remote sensing applications such as Polarimetric SAR (PolSAR) [2] and hyperspectral images [20, 21] is currently gaining interest. BPTs are hierarchical region-based representations in which pixe... |

96 |
Intensity and phase statistics of multilook polarimetric and interferometric
- Lee, Hoppel, et al.
- 1994
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Citation Context ...ndicates the number of independent looks or samples employed to estimate C and ki is the i th sample vector. The estimated covariance matrix Z is statistically characterized by a Wishart distribution =-=[12]-=-. 3 BPT creation and processing through graph cut The BPT creation starts by the definition of an initial partition which can be composed of individual pixels as in [2, 3]. While this strategy guarant... |

95 |
Polarimetric Radar Imaging: From Basics to Applications,
- Lee, Pottier
- 2009
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Citation Context ... the early 90’s, multidimensional systems were developed. They provide complex SAR images [S1, S2, . . . , Sm] by introducing some sort of diversity. An important example is Polarimetric SAR (PolSAR) =-=[5, 13]-=- where the diversity is based on considering different polarization states for the transmitted and received electromagnetic waves. This makes SAR data sensitive to the target geometry, including veget... |

31 |
Unsupervised classification of polarimetric synthetic aperture radar images using fuzzy clustering and EM clustering
- Kersten, Lee, et al.
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Citation Context ...e MLE defined by Eq. 5. The distance between neighboring regions, which defines the merging order, relies on the Symmetric revised Wishart dissimilarity [2]. The revised Wishart dissimilarity measure =-=[9]-=- is based on a statistical test assuming that the two regions follow a Wishart pdf and that one pdf is known. Thus, it is not symmetric as it depends on which region pdf is assumed to be known. In ord... |

19 |
Interactions between symmetric cones and information geometrics: Bruhat-tits and Siegel spaces models for high resolution autoregressive Doppler imagery,”
- Barbaresco
- 2009
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Citation Context ...us norm of matrix A with elements [a(k, l)] is: ‖A‖F = √∑ k,l a(k, l) 2. 7Finally, the last pruning criterion relies on a geodesic distance adapted to the cone of positive definite Hermitian matrices =-=[4]-=-. This measure exploits the geometry of the space defined by the covariance matrices and is given by: ‖log ( Z −1/2 R Z I i,jZ −1/2 R ) ‖F , where log(.) represents the matrix logarithm. As previously... |

19 |
Polarisation Applications in Remote Sensing.
- Cloude
- 2010
(Show Context)
Citation Context ... the early 90’s, multidimensional systems were developed. They provide complex SAR images [S1, S2, . . . , Sm] by introducing some sort of diversity. An important example is Polarimetric SAR (PolSAR) =-=[5, 13]-=- where the diversity is based on considering different polarization states for the transmitted and received electromagnetic waves. This makes SAR data sensitive to the target geometry, including veget... |

16 |
Improved sigma filter for speckle filtering of SAR imagery,
- Lee, Wen, et al.
- 2009
(Show Context)
Citation Context ...reation without any significant impact on the quality of the regions and partitions represented by the tree. One of the key point however is to use a denoising filter adapted to PolSAR images such as =-=[14, 7]-=- before computing the super-pixel partitions. The best combination found in [17] involves the use of the σ-Lee denoising filter [14] followed by the SLIC algorithm [1] to compute the super-pixel. Only... |

9 |
Processing multidimensional SAR and hyperspectral images with binary partition tree
- Alonso-Gonzalez, Valero, et al.
- 2012
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Citation Context ...equence in a binary tree structure. Once constructed, BPTs can be used for a large number of tasks including image filtering with connected operators, segmentation, object detection or classification =-=[18, 3]-=-. Many of these tasks involve the extraction of a partition from the BPT through a graph cut. In this paper, we focus on low level PolSAR image processing tasks. We study in particular the interest of... |

9 |
Polarimetric SAR estimation based on non-local means
- Deledalle, Tupin, et al.
- 2010
(Show Context)
Citation Context ...reation without any significant impact on the quality of the regions and partitions represented by the tree. One of the key point however is to use a denoising filter adapted to PolSAR images such as =-=[14, 7]-=- before computing the super-pixel partitions. The best combination found in [17] involves the use of the σ-Lee denoising filter [14] followed by the SLIC algorithm [1] to compute the super-pixel. Only... |

9 | Hyperspectral image representation and processing with binary partition trees
- Valero, Salembier, et al.
- 2013
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Citation Context ...uning, speckle noise, segmentation. 1 Introduction The application of Binary Partition Trees (BPTs) [18] for remote sensing applications such as Polarimetric SAR (PolSAR) [2] and hyperspectral images =-=[20, 21]-=- is currently gaining interest. BPTs are hierarchical region-based representations in which pixels are grouped by similarity. Their construction is often based on an iterative region-merging algorithm... |

7 |
Evaluation and bias removal of multilook effect on entropy/alpha/anisotropy in polarimetric SAR decomposition
- Lee, Ainsworth, et al.
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Citation Context ...represent the 8 classes found in the H/α plane and randomly assigned to each class. Then, single look complex images have been generated from the polarimetric responses using a Cholesky decomposition =-=[11]-=-. Examples of images and their corresponding ground-truth, denoised images and super-pixel partitions are presented in Fig. 2. Thanks to this dataset with ground-truth, we can measure the quality of t... |

6 |
Filtering and segmentation of polarimetric SAR data based on binary partition trees
- Alonso-Gonzalez, Lopez-Martinez, et al.
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Citation Context ...n Tree, PolSAR, graph-cut, pruning, speckle noise, segmentation. 1 Introduction The application of Binary Partition Trees (BPTs) [18] for remote sensing applications such as Polarimetric SAR (PolSAR) =-=[2]-=- and hyperspectral images [20, 21] is currently gaining interest. BPTs are hierarchical region-based representations in which pixels are grouped by similarity. Their construction is often based on an ... |

5 | Hyperspectral image segmentation using a new spectral unmixing-based binary partition tree representation. Image Processing
- Veganzones, Tochon, et al.
- 2014
(Show Context)
Citation Context ...uning, speckle noise, segmentation. 1 Introduction The application of Binary Partition Trees (BPTs) [18] for remote sensing applications such as Polarimetric SAR (PolSAR) [2] and hyperspectral images =-=[20, 21]-=- is currently gaining interest. BPTs are hierarchical region-based representations in which pixels are grouped by similarity. Their construction is often based on an iterative region-merging algorithm... |

4 |
Hierarchy and Optima
- Serra
(Show Context)
Citation Context ...n recently shown that the algorithm identifying optimum partitions as described in section 4 is valid for a larger class of criteria than purely ad11 ditive criteria such as C = ∑ R φR. In particular =-=[19]-=- introduces the notion of h-increasing criterion which is sufficient (and necessary) to guarantee that the search algorithm identifies the optimum partition. Moreover, [10] shows that Minkowski norms:... |

3 | Measures and meta-measures for the supervised evaluation of image segmentation
- Pont-Tuset, Marques
- 2013
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Citation Context ...th the classification resulting from the ground-truth partition. In addition to this boundary-oriented evaluation, a region-oriented evaluation known as the Precision and Recall for objects and parts =-=[16]-=- is presented on the right side of Fig. 3. In this context, regions of the partition are considered as potential candidates to form regions of the ground-truth partition, and are classified as correct... |

2 |
Analysis, evaluation, and comparison of polarimetric SAR speckle filtering techniques
- Foucher, Lopez-Martinez
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Citation Context ...runing strategies for PolSAR images as well as the objective evaluation of the resulting partitions thanks to a set of realistic simulated PolSAR images where the underlying ground truth is available =-=[8]-=-. The paper is organized as follows: Section 2 is a short introduction on PolSAR data. Section 3 discusses the BPT creation and its processing with graph cut. Four pruning criteria useful for segmenta... |

1 | Energetic-Lattice based optimization
- Kiran
- 2014
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Citation Context ...s C = ∑ R φR. In particular [19] introduces the notion of h-increasing criterion which is sufficient (and necessary) to guarantee that the search algorithm identifies the optimum partition. Moreover, =-=[10]-=- shows that Minkowski norms: C = ( ∑ R φ α R) 1 α ,∀α, are h-increasing as well as their combination by addition or supremum. Therefore the same search algorithm can be used for this larger class of c... |

1 |
Low-level processing of PolSAR images with binary partition trees
- Salembier, Foucher, et al.
- 2014
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Citation Context ...nto account the specific nature of PolSAR data and the presence of speckle noise resulting from the coherent integration of the electromagnetic waves. The main contributions of this paper compared to =-=[2, 3, 17]-=- is the proposal of new pruning strategies for PolSAR images as well as the objective evaluation of the resulting partitions thanks to a set of realistic simulated PolSAR images where the underlying g... |