Spatial Statistics of Visual Keypoints for Texture Recognition

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On the Minimization of Convex Functionals of Probability Distributions Under Band Constraints

The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality conditions as well as a bound on the optimality gap of feasible candidate solutions are derived. Based on these results, two numerical algorithms are proposed that iteratively solve the system of optimality conditions on a grid of discrete points. Both algorithms use a block coordinate descent strategy and terminate once the optimality gap falls below the desired tolerance. While the first algorithm is conceptually simpler and more efficient, it is not guaranteed to converge for objective functions that are not strictly convex. This shortcoming is overcome in the second algorithm, which uses an additional outer proximal iteration, and, which is proven to converge under mild assumptions. Two examples are given to demonstrate the theoretical usefulness of the optimality conditions as well as the high efficiency and accuracy of the proposed numerical algorithms.Comment: 13 pages, 5 figures, 2 tables, published in the IEEE Transactions on Signal Processing. In previous versions, the example in Section VI.B contained some mistakes and inaccuracies, which have been fixed in this versio

Acoustic seafloor classification using the Weyl transform of multibeam echosounder backscatter mosaic

The use of multibeam echosounder systems (MBES) for detailed seafloor mapping is increasing at a fast pace. Due to their design, enabling continuous high-density measurements and the coregistration of seafloor’s depth and reflectivity, MBES has become a fundamental instrument in the advancing field of acoustic seafloor classification (ASC). With these data becoming available, recent seafloor mapping research focuses on the interpretation of the hydroacoustic data and automated predictive modeling of seafloor composition. While a methodological consensus on which seafloor sediment classification algorithm and routine does not exist in the scientific community, it is expected that progress will occur through the refinement of each stage of the ASC pipeline: ranging from the data acquisition to the modeling phase. This research focuses on the stage of the feature extraction; the stage wherein the spatial variables used for the classification are, in this case, derived from the MBES backscatter data. This contribution explored the sediment classification potential of a textural feature based on the recently introduced Weyl transform of 300 kHz MBES backscatter imagery acquired over a nearshore study site in Belgian Waters. The goodness of the Weyl transform textural feature for seafloor sediment classification was assessed in terms of cluster separation of Folk’s sedimentological categories (4-class scheme). Class separation potential was quantified at multiple spatial scales by cluster silhouette coefficients. Weyl features derived from MBES backscatter data were found to exhibit superior thematic class separation compared to other well-established textural features, namely: (1) First-order Statistics, (2) Gray Level Co-occurrence Matrices (GLCM), (3) Wavelet Transform and (4) Local Binary Pattern (LBP). Finally, by employing a Random Forest (RF) categorical classifier, the value of the proposed textural feature for seafloor sediment mapping was confirmed in terms of global and by-class classification accuracies, highest for models based on the backscatter Weyl features. Further tests on different backscatter datasets and sediment classification schemes are required to further elucidate the use of the Weyl transform of MBES backscatter imagery in the context of seafloor mapping

RV SONNE Fahrtbericht / Cruise Report SO226 - CHRIMP CHatham RIse Methane Pockmarks, 07.01. - 06.02.2013 / Auckland – Lyttelton, 07.02. – 01.03.2013 / Lyttelton - Wellington

[Davy et al., 2010a] reported on pockmark observations along the Chatham Rise, offshore New Zealand’s South Island. The observed structures fall into three categories: features of approx. 150 m diameter are found in water depths of 500 m – 700 m, depressions with diameters of up to 5 km and the largest structures with diameters of up to 11 km were observed in water depth of 800 - 1100 m. Seismic sections across the pockmarks were available at only a few locations and mainly consisted of Parasound data. Multiple layers of small pockmarks could be correlated with sediment interfaces of increased amplitudes that correspond to the transitions between glacial maxima and minima. Consequently [Davy et al., 2010a] assumed that sealevel lowstands during glacial maxima caused the dissolution of gas hydrates and hence triggered the formation of pockmarks. Project SO226 CHRIMP aimed to test this hypothesis with an extended data base. Additional bathymetric coverage revealed multiple occurrences of large and medium size structures. Three working areas were selected along the Chatham Rise each representing one of the three types / sizes of seafloor depression. Area one was chosen to be centred around 178°40’E with the largest pockmark structure of up to 15 km diameter. From the extended bathymetric coverage a south-west to north-east oriented alignment of three similar structures was observed. Seismic sections show a highly variable sedimentation. Inside the structures all sediments had been fully eroded to a surface that can be mapped throughout the entire region. All observed pockmarks show a radial eroded rim to the South-West with a base that corresponds to the above mentioned erosional surface. Near vertical faults and blanking patterns are found underneath the eroded rim of the structures. Shallow bright spots with negative polarity are interpreted as indicators for free gas. Nevertheless no signs were found for active fluid venting above the structure or in the surrounding. The second area centred around 177°05’E hosts medium-size pockmarks. Five depressions were mapped, but some of them might be formed by overlapping pockmarks. Partly resedimented the structures show an eroded southern part with a sharp radial rim. Indifferent from area one a roughly 250 m wide blanking zone was found underneath one of the pockmarks. The area is imaged right above a conical shaped upward extension of a deeper sediment interface. From the 3D data the interface shows a rough topography. The conical structure and the blanking area are interpreted as an ancient feeder channel. This chimney terminates at an erosional interface, which forms the base of the seafloor depression. Multiple events of erosion, sedimentation and slumping have been identified above the erosional surface. Again water column imaging and geochemical analyses do not show indications for active methane venting within this area. The third working area was chosen to be centred 174°35’E where a large zone of small pockmarks was known from earlier mapping. A 2D seismic profile confirms the existence of stacked pockmark layers. The wide funnel shaped opening of the buried pockmarks terminates at distinguished sediment interfaces that show an increased reflection amplitude. This corresponds to the interpretation of [Davy et al., 2010a]. At greater depth the horizontal layering of the sediments is not interrupted. As with the previous two working areas there is no sign of a BSR and active methane venting could not be confirmed by water column imaging or geochemical analyses. In summary all three areas do show images of gas migration pathways of various sizes within the deeper sediments. Nevertheless active venting of fluids could not be confirmed. Therefore other models need to be developed to explain todays still sharp defined rims of the pockmark-like seafloor depressions