Modelling potential movement in constrained travel environments using rough space-time prisms

The widespread adoption of location-aware technologies (LATs) has afforded analysts new opportunities for efficiently collecting trajectory data of moving individuals. These technologies enable measuring trajectories as a finite sample set of time-stamped locations. The uncertainty related to both finite sampling and measurement errors makes it often difficult to reconstruct and represent a trajectory followed by an individual in space-time. Time geography offers an interesting framework to deal with the potential path of an individual in between two sample locations. Although this potential path may be easily delineated for travels along networks, this will be less straightforward for more nonnetwork-constrained environments. Current models, however, have mostly concentrated on network environments on the one hand and do not account for the spatiotemporal uncertainties of input data on the other hand. This article simultaneously addresses both issues by developing a novel methodology to capture potential movement between uncertain space-time points in obstacle-constrained travel environments

Constraining the History of the Sagittarius Dwarf Galaxy Using Observations of its Tidal Debris

We present a comparison of semi-analytic models of the phase-space structure of tidal debris with observations of stars associated with the Sagittarius dwarf galaxy (Sgr). We find that many features in the data can be explained by these models. The properties of stars 10-15 degrees away from the center of Sgr --- in particular, the orientation of material perpendicular to Sgr's orbit (c.f. Alard 1996) and the kink in the velocity gradient (Ibata et al 1997) --- are consistent with those expected for unbound material stripped during the most recent pericentric passage ~50 Myrs ago. The break in the slope of the surface density seen by Mateo, Olszewski & Morrison (1998) at ~ b=-35 can be understood as marking the end of this material. However, the detections beyond this point are unlikely to represent debris in a trailing streamer, torn from Sgr during the immediately preceding passage ~0.7 Gyrs ago, but are more plausibly explained by a leading streamer of material that was lost more that 1 Gyr ago and has wrapped all the way around the Galaxy. The observations reported in Majewski et al (1999) also support this hypothesis. We determine debris models with these properties on orbits that are consistent with the currently known positions and velocities of Sgr in Galactic potentials with halo components that have circular velocities v_circ=140-200 km/s. The best match to the data is obtained in models where Sgr currently has a mass of ~10^9 M_sun and has orbited the Galaxy for at least the last 1 Gyr, during which time it has reduced its mass by a factor of 2-3, or luminosity by an amount equivalent to ~10% of the total luminosity of the Galactic halo. These numbers suggest that Sgr is rapidly disrupting and unlikely to survive beyond a few more pericentric passages.Comment: 19 pages, 5 figures, accepted to Astronomical Journa

An Adaptive Semi-Parametric and Context-Based Approach to Unsupervised Change Detection in Multitemporal Remote-Sensing Images

In this paper, a novel automatic approach to the unsupervised identification of changes in multitemporal remote-sensing images is proposed. This approach, unlike classical ones, is based on the formulation of the unsupervised change-detection problem in terms of the Bayesian decision theory. In this context, an adaptive semi-parametric technique for the unsupervised estimation of the statistical terms associated with the gray levels of changed and unchanged pixels in a difference image is presented. Such a technique exploits the effectivenesses of two theoretically well-founded estimation procedures: the reduced Parzen estimate (RPE) procedure and the expectation-maximization (EM) algorithm. Then, thanks to the resulting estimates and to a Markov Random Field (MRF) approach used to model the spatial-contextual information contained in the multitemporal images considered, a change detection map is generated. The adaptive semi-parametric nature of the proposed technique allows its application to different kinds of remote-sensing images. Experimental results, obtained on two sets of multitemporal remote-sensing images acquired by two different sensors, confirm the validity of the proposed approach

Characterization and mapping of surface physical properties of Mars from CRISM multi-angular data: application to Gusev Crater and Meridiani Planum

The analysis of the surface texture from the particle (grain size, shape and internal structure) to its organization (surface roughness) provides information on the geological processes. CRISM multi-angular observations (varied emission angles) allow to characterize the surface scattering behavior which depends on the composition but also the material physical properties (e.g., grain size, shape, internal structure, the surface roughness). After an atmospheric correction by the Multi-angle Approach for Retrieval of the Surface Reflectance from CRISM Observations, the surface reflectances at different geometries are analyzed by inverting the Hapke photometric model depending on the single scattering albedo, the 2-term phase function, the macroscopic roughness and the 2-term opposition effects. Surface photometric maps are created to observe the spatial variations of surface scattering properties as a function of geological units at the CRISM spatial resolution (200m/pixel). An application at the Mars Exploration Rover (MER) landing sites located at Gusev Crater and Meridiani Planum where orbital and in situ observations are available, is presented. Complementary orbital observations (e.g. CRISM spectra, THermal EMission Imaging System, High Resolution Imaging Science Experiment images) are used for interpreting the estimated Hapke photometric parameters in terms of physical properties. The in situ observations are used as ground truth to validate the interpretations. Varied scattering properties are observed inside a CRISM observation (5x10km) suggesting that the surfaces are controlled by local geological processes (e.g. volcanic resurfacing, aeolian and impact processes) rather than regional or global. Consistent results with the in situ observations are observed thus validating the approach and the use of photometry for the characterization of Martian surface physical properties