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2_IGARSS2011_BPT_v2.pdf

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  • 1. Binary Partition Tree as a Polarimetric SAR Data Representation in the Space-Time Domain AUTHORS: ALBERTO ALONSO-GONZÁLEZ CARLOS LÓPEZ-MARTÍNEZ PHILIPPE SALEMBIER UNIVERSITAT POLITÈCNICA DE CATALUNYA ESCOLA TÈCNICA SUPERIOR D’ENGINYERIA DE TELECOMUNICACIÓ DE BARCELONAJuly, 2011 DEPARTAMENT DE TEORIA DEL SENYAL I COMUNICACIONS REMOTE SENSING LABORATORY
  • 2. OUTLINEBinary Partition TreeBPT-based processing schemeBPT pruning for PolSAR speckle filteringSpace-time BPTBPT pruning for Space-Time PolSAR specklefilteringConclusions Remote Sensing Lab. 2 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 3. BINARY PARTITION TREEBPT is a region-based and multi-scale data representation ● Each node of the tree represents a connected region of the data Region model ● Hierarchical structure: each node represents the region generated by merging of its two son nodes  The leaves of the tree represent single pixels  The root node represents the whole dataset ● Between the leaves and the root there are a wide number of nodes representing homogeneous regions of the image at different detail levels The BPT can be considered as a data abstraction Motivation: Due to its multi-scale nature, the BPT contains a lot of useful information about the image structure that may be exploited for different applications Remote Sensing Lab. 3 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 4. BPT CONSTRUCTION PROCESSBPT construction: iterative algorithm in a bottom-up approach Each iteration the two most similar neighboring regions are merged Starting from the pixels, as the leaves of the tree, to the root node, representing the whole datasetRegion Model: Estimated covariance matrix Z over all the pixels of the region: N 1 H Z =〈k k 〉= N ∑ kikH i i=1To guide the BPT construction process the similarity between regions has tobe evaluated Dissimilarity measure: Evaluates the similarity of two regions. Measure in the region model space. The dissimilarity measure is the keystone of the construction process Remote Sensing Lab. 4 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 5. DISSIMILARITY MEASURES IDissimilarity measures are based in two region features: ● Polarimetric information (3 by 3 covariance matrix) ● Region size information (number of pixels of each region)Revised Wishart dissimilarity: Based on the Wishart pdf Full matrix: d sw  A , B = tr  Z −1 Z B tr  Z −1 Z A  ⋅ n An B  A B   N Z A Z B Diagonal: d dw  A , B = ∑ ii Z A ZB ii ⋅n A n B  i=1 ii iiGeodesic dissimilarity: Adapted to the hermitian positive definite matrix conegeometry Full matrix: ∥ d sg  A , B = log  Z Z B  −1 A ∥ F ln 2 n A nB n A nB        N ZA 2 nA nB d dg  A , B= ∑ ln 2 Diagonal: ln ii i=1 ZB n An B ii   N N N 2 H ∥A∥ = F ∑ ∑ ∣aij∣ = tr  A i=1 j =1 A= ∑ 2 i=1 i Remote Sensing Lab. 5 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 6. DISSIMILARITY MEASURES IIWard relative dissimilarity: based on the increment of the Error Sum ofSquares (ESS) 2 2 d wr  A , B =n A⋅ N H  Z A − Z AB  N AB∥ n B⋅ N H  Z B −Z AB  N AB∥ ∥ AB F ∥ AB F  Z A11  0 0 n A⋅Z A n B⋅Z B where: N A= 0 Z A22 0 Z AB = n An B 0 0 Z A33Diagonal relative normalized dissimilarity: based on the normalizeddifference of the matrix diagonal vector 1/ 2   N 2 Z A −Z B d dn  A , B = ∑ ii Z A Z B ii  n A n B  i=1 ii iiDiagonal relative dissimilarity: based on the sum of the relative errorsrespect to both regions 1/2   N 2 ZA −ZB Z B −Z A d dr  A , B= ∑ ii ZB ii  ii ZA ii  n An B  i =1 ii ii Remote Sensing Lab. 6 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 7. BPT-BASED PROCESSING SCHEME The BPT data abstraction may be exploited for different applications ➔ To exploit the BPT structure a tree pruning process is proposed ➔ The most useful or interesting regions from the tree are selected Data Results BPT Construction BPT Pruning BPT Application independent Application dependent➔ The BPT construction process can be considered application independent since it only exploits the internal relationships within the data➔ The BPT pruning process is application dependent since it searches for interesting regions within the tree for a particular purpose Remote Sensing Lab. 7 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 8. BPT-BASED SPECKLE FILTERINGA region homogeneity measure has to be defined for the BPT pruning  Measure of the error committed when representing a region by its estimated covariance matrix nX 1 2 ➔ Region homogeneity:  X = 2 ∑∥ X i− Z X ∥ n X ∥Z X ∥ i =1 This measure can be interpreted as the relative MSE of the region X ➔ A pruning threshold  p is defined over this error BPT pruning for filtering: Top-down approach, selecting the first nodes that fulfill  X  p Alberto Alonso, Carlos López-Martínez and Philippe Salembier, “Filtering and Segmentation of Polarimetric SAR Data With Binary Partition Trees,” IGARSS 2010 Alberto Alonso, Carlos López-Martínez and Philippe Salembier, “Filtering and Segmentation of Polarimetric BPT Pruning SAR Data Based on Binary Partition Trees,” accepted IEEE TGRS Remote Sensing Lab. 8 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 9. RESULTS WITH REAL DATAESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999 Spatial resolution: Original image Data courtesy of DLR 1.5m x 1.5m |Shh+Svv| |Shv+Svh| |Shh-Svv| Remote Sensing Lab. 9 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 10. RESULTS WITH REAL DATAESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999 d sw  p=−2 dB Data courtesy of DLR Region homogeneity based pruning Remote Sensing Lab. 10 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 11. RESULTS WITH REAL DATAESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999 d sw  p=−1 dB Data courtesy of DLR Region homogeneity based pruning Remote Sensing Lab. 11 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 12. RESULTS WITH REAL DATAESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999 d sw  p=0 dB Data courtesy of DLR Region homogeneity based pruning Remote Sensing Lab. 12 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 13. SMALL DETAILS PRESERVATION Original BPT: d sw ,  p=−2 dBBPT: d sw ,  p=−1 dB BPT: d sw ,  p=0 dB IDAN Boxcar 7x7 |Shh+Svv|, |Shv+Svh|, |Shh-Svv| Remote Sensing Lab. 13 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 14. SPACE-TIME BPTThe BPT representation can be extended to series of co-registered images |Shh+Svv| |Shv+Svh| |Shh-Svv|RADARSAT-2, C-band, Fine Quad-Pol, Flevoland, Netherlands, Beam FQ13➔ The dataset contains 8 images from April 14th, 2009 to September 29th, 2009, with an acquisition every 24 days➔ The full dataset contains 4000 x 2000 x 8 pixelsData courtesy of ESA Remote Sensing Lab. 14 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 15. SPACE-TIME BPTTo generate a space-time BPT representation the following elements have tobe defined A new pixel connectivity in the space-time domain: 10-connectivity: Each pixel (blue) has 10 neighbors (red) A region model. As for a single PolSAR image, the estimated covariance matrix Z will be employed A dissimilarity measure on the region model space. Since the region model is the same, previously defined dissimilarity measures will be employed Assuming the same data behavior in space and time dimensions Remote Sensing Lab. 15 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 16. SPACE-TIME BPT EXPLOITATIONThe same tree pruning strategies can be employed over the space-time BPTrepresentation PolSAR image Results Space- BPT Pruning time BPT dataset BPT Construction Application dependent Application independent In fact, since the application dependent part is based on the BPT, not in the data itself, the BPT allows the generalization of the application rationale For the filtering application this rationale can be expressed as: “extract the biggest homogeneous regions of the image” Remote Sensing Lab. 16 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 17. SPACE-TIME FILTERINGResults of space-time BPT filtering over the first acquisition: d sg ,  p =−5 dB d sg ,  p =−3 dB d sg ,  p =−5 dB d sg ,  p =−3 dB Space-time BPT filtering Single image BPT filtering➔ On space-time BPT filtering the region models are estimated employing samples of different acquisitions |Shh+Svv|, |Shv+Svh|, |Shh-Svv| Remote Sensing Lab. 17 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 18. SPACE-TIME FILTERINGThe average region depth in the temporal dimension in the first slice: Pruning factor Regions at 1st acquisition Average region depth -5 dB 359371 2,067 -4 dB 223969 2,652 -3 dB 127957 4,068 -2 dB 52077 6,727 -1 dB 14660 7,758 0 dB 4666 7,921 d sgAt  p=−3 dB 4 times more samples may be attained by the space-time BPTfiltering application with respect to a single PolSAR image filtering➔ The polarimetric information temporal evolution is preserved by the 3D BPT Remote Sensing Lab. 18 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 19. TEMPORAL EVOLUTIONTemporal evolution of the filtered dataset in Pauli and H/A/Alpha parameters Acquisition number: |Shh+Svv|, |Shv+Svh|, |Shh-Svv| 1 2 3 4 5 6 7 8Entropy H d sg ,  p =−3 dB 0 1 Remote Sensing Lab. 19 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 20. TEMPORAL EVOLUTIONTemporal evolution of the filtered dataset in Pauli and H/A/Alpha parameters 0 1 Acquisition number: Anisotropy A 1 2 3 4 5 6 7 8 Alpha 0º d sg ,  p =−3 dB 90º Remote Sensing Lab. 20 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 21. TEMPORAL CHANGE DETECTIONAnalyzing the temporal contours of the space-time BPT homogeneousregions, a map can be generated representing the number of changes: 7 0 d sg  p=−5 dB  p=−3 dB  p=−1 dB Remote Sensing Lab. 21 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 22. TEMPORAL CHANGE DETECTIONDetail of an urban area: Original Changes detected 7 |Shh+Svv| |Shv+Svh| |Shh-Svv| 0  p=−5 dB d sg➔ Some small blue dots can be seen, corresponding to stable human-made structures within the urban areas Remote Sensing Lab. 22 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 23. TEMPORAL CHANGE DETECTIONValues for stable regions in the temporal dimensions: 7 0 d sg ,  p =−5 dB Remote Sensing Lab. 23 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 24. VESSEL DETECTIONDetail of a 270 by 270 pixel sea area, original Pauli images: Acquisition number: |Shh+Svv|, |Shv+Svh|, |Shh-Svv| 1 2 3 4 5 6 7 8 ML 3x3 has been applied over plots d dw ,  p =−1 dB➔ The sea area is filtered as one region in the temporal dimension but small details as the vessels are preserved also in this dimension Remote Sensing Lab. 24 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya
  • 25. CONCLUSIONS The BPT constructed with the proposed algorithm and dissimilarity measures has proven to be a useful region-based and multi-scale data representation The BPT exploitation can be addressed as a tree pruning process, allowing the generalization of the application rationale The proposed BPT-based speckle filtering technique does not introduce bias or distortion and has a good spatial resolution preservation, being a very promising technique for PolSAR data processing. When employing a full- matrix dissimilarity measure the whole process is sensitive to all the polarimetric information The BPT structure has been extended to the time domain. Over this domain the same speckle filtering application can be exploited and the temporal contours have been analyzed as a temporal change detection application However, it has some drawbacks: the BPT construction is more complex and requires more computational resources than other simpler filtering strategies Remote Sensing Lab. 25 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya