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Hyperbolic geometry has recently garnered considerable attention in machine learning due to its ability to embed hierarchical graph structures with low distortions for further downstream processing. This paper introduces a simple framework to detect local outliers for datasets grounded in hyperbolic 2-space, which is referred to as Hyperbolic Local Outlier Probability (HLoOP). Within a Euclidean space, well-known techniques for local outlier detection are based on the Local Outlier Factor (LOF) and its variant, the LoOP (Local Outlier Probability), which incorporates probabilistic concepts to model the outlier level of a data vector. The proposed HLoOP combines the notion of finding nearest neighbors, density-based outlier scoring with a probabilistic, statistically oriented approach. Therefore, the method computes the Riemmanian distance of a data point to its nearest neighbors following a Gaussian probability density function expressed in a hyperbolic space. This is achieved by defining a Gaussian cumulative distribution in this space. The proposed HLoOP algorithm is tested on the WordNet dataset and desmonstrated promising results. The code and data will be made available upon request for reproducibility.

Abstract This work proposes a marginalised particle filter with variational inference for non‐linear state‐space models (SSMs) with Gaussian mixture noise. A latent variable indicating the component of the Gaussian mixture considered at each time instant is introduced to specify the measurement mode of the SSM. The resulting joint posterior distribution of the state vector, the mode variable and the parameters of the Gaussian mixture noise is marginalised with respect to the noise variables. The marginalised posterior distribution of the state and mode is then approximated by using an appropriate marginalised particle filter. The noise parameters conditionally on each particle system of the state and mode variable are finally updated by using variational Bayesian inference. A simulation study is conducted to compare the proposed method with state‐of‐the‐art approaches in the context of positioning in urban canyons using global navigation satellite systems.

Non-line-of-sight imaging is typically limited by loss of directional information due to diffuse reflections scattering light in all directions. Here, the authors see around corners by using vertical edges and temporal response to pulsed light to obtain angular and longitudinal resolution, respectively.

This paper develops a Rao-Blackwellized particle filter with variational inference for jointly estimating state and time-varying parameters in non-linear state-space models (SSM) with non-Gaussian measurement noise. Depending on the availability of the conjugate prior for the unknown parameters, the joint posterior distribution of the state and unknown parameters is approximated by using an auxiliary particle filter with a probabilistic changepoint model. The distribution of the SSM parameters conditionally on each particle is then updated by using variational Bayesian inference. Experiments are first conducted on a modified nonlinear benchmark model to compare the performance of the proposed approach with other state-of-the-art approaches. Finally, in the context of GNSS multipath mitigation, the proposed approach is evaluated based on data obtained from a measurement campaign conducted in a street urban canyon.

The use of single-photon data has been limited by time-consuming reconstruction algorithms. Here, the authors combine statistical models and computational tools known from computer graphics and show real-time reconstruction of moving scenes.

This paper studies the detection of anomalous crop development at the parcel-level based on an unsupervised outlier detection technique. The experimental validation is conducted on rapeseed and wheat parcels located in Beauce (France). The proposed methodology consists of four sequential steps: (1) preprocessing of synthetic aperture radar (SAR) and multispectral images acquired using Sentinel-1 and Sentinel-2 satellites, (2) extraction of SAR and multispectral pixel-level features, (3) computation of parcel-level features using zonal statistics and (4) outlier detection. The different types of anomalies that can affect the studied crops are analyzed and described. The different factors that can influence the outlier detection results are investigated with a particular attention devoted to the synergy between Sentinel-1 and Sentinel-2 data. Overall, the best performance is obtained when using jointly a selection of Sentinel-1 and Sentinel-2 features with the isolation forest algorithm. The selected features are co-polarized (VV) and cross-polarized (VH) backscattering coefficients for Sentinel-1 and five Vegetation Indexes for Sentinel-2 (among us, the Normalized Difference Vegetation Index and two variants of the Normalized Difference Water). When using these features with an outlier ratio of 10%, the percentage of detected true positives (i.e., crop anomalies) is equal to 94.1% for rapeseed parcels and 95.5% for wheat parcels.

A statistical model for detecting changes in remote sensing images has recently been proposed in (Prendes et al., 2014a,b). This model is sufficiently general to be used for homogeneous images acquired by the same kind of sensors (e.g., two optical images from Pléiades satellites, possibly with different acquisition conditions), and for heterogeneous images acquired by different sensors (e.g., an optical image acquired from a Pléiades satellite and a synthetic aperture radar (SAR) image acquired from a TerraSAR-X satellite). This model assumes that each pixel is distributed according to a mixture of distributions depending on the noise properties and on the sensor intensity responses to the actual scene. The parameters of the resulting statistical model can be estimated by using the classical expectation-maximization (EM) algorithm. The estimated parameters are finally used to learn the relationships between the images of interest, via a manifold learning strategy. These relationships are relevant for many image processing applications, particularly those requiring a similarity measure (e.g., image change detection and image registration). The main objective of this paper is to evaluate the performance of a change detection method based on this manifold learning strategy initially introduced in (Prendes et al., 2014a,b). This performance is evaluated by using results obtained with pairs of real optical images acquired from Pléiades satellites and pairs of optical and SAR images.

This paper derives new closed-form expressions for the masses of negative multinomial distributions. These masses can be maximized to determine the maximum likelihood estimator of its unknown parameters. An application to polarimetric image processing is investigated. We study the maximum likelihood estimators of the polarization degree of polarimetric images using different combinations of images.