Trajectory-Based Morphological Operators: A Model for Efficient Image Processing

Mathematical morphology has been an area of intensive research over the last few years. Although many remarkable advances have been achieved throughout these years, there is still a great interest in accelerating morphological operations in order for them to be implemented in real-time systems. In this work, we present a new model for computing mathematical morphology operations, the so-called morphological trajectory model (MTM), in which a morphological filter will be divided into a sequence of basic operations. Then, a trajectory-based morphological operation (such as dilation, and erosion) is defined as the set of points resulting from the ordered application of the instant basic operations. The MTM approach allows working with different structuring elements, such as disks, and from the experiments, it can be extracted that our method is independent of the structuring element size and can be easily applied to industrial systems and high-resolution images.

A new boundary-based morphological model

Mathematical morphology addresses the problem of describing shapes in an n-dimensional space using the concepts of set theory. A series of standardized morphological operations are defined, and they are applied to the shapes to transform them using another shape called the structuring element. In an industrial environment, the process of manufacturing a piece is based on the manipulation of a primitive object via contact with a tool that transforms the object progressively to obtain the desired design. The analogy with the morphological operation of erosion is obvious. Nevertheless, few references about the relation between the morphological operations and the process of design and manufacturing can be found. The non-deterministic nature of classic mathematical morphology makes it very difficult to adapt their basic operations to the dynamics of concepts such as the ordered trajectory. A new geometric model is presented, inspired by the classic morphological paradigm, which can define objects and apply morphological operations that transform these objects. The model specializes in classic morphological operations, providing them with the determinism inherent in dynamic processes that require an order of application, as is the case for designing and manufacturing objects in professional computer-aided design and manufacturing (CAD/CAM) environments. The operators are boundary-based so that only the points in the frontier are handled. As a consequence, the process is more efficient and more suitable for use in CAD/CAM systems.

Constraining the GRB-Magnetar Model by Means of the Galactic Pulsar Population

A large fraction of Gamma-ray bursts (GRBs) displays an X-ray plateau phase within <105 s from the prompt emission, proposed to be powered by the spin-down energy of a rapidly spinning newly born magnetar. In this work we use the properties of the Galactic neutron star population to constrain the GRB-magnetar scenario. We re-analyze the X-ray plateaus of all Swift GRBs with known redshift, between 2005 January and 2014 August. From the derived initial magnetic field distribution for the possible magnetars left behind by the GRBs, we study the evolution and properties of a simulated GRB-magnetar population using numerical simulations of magnetic field evolution, coupled with Monte Carlo simulations of Pulsar Population Synthesis in our Galaxy. We find that if the GRB X-ray plateaus are powered by the rotational energy of a newly formed magnetar, the current observational properties of the Galactic magnetar population are not compatible with being formed within the GRB scenario (regardless of the GRB type or rate at z = 0). Direct consequences would be that we should allow the existence of magnetars and "super-magnetars" having different progenitors, and that Type Ib/c SNe related to Long GRBs form systematically neutron stars with higher initial magnetic fields. We put an upper limit of ≤16 "super-magnetars" formed by a GRB in our Galaxy in the past Myr (at 99% c.l.). This limit is somewhat smaller than what is roughly expected from Long GRB rates, although the very large uncertainties do not allow us to draw strong conclusion in this respect.

A hydrological–economic model for sustainable groundwater use in sparse-data drylands: Application to the Amtoudi Oasis in southern Morocco, northern Sahara

A hydrological–economic model is introduced to describe the dynamics of groundwater-dependent economics (agriculture and tourism) for sustainable use in sparse-data drylands. The Amtoudi Oasis, a remote area in southern Morocco, in the northern Sahara attractive for tourism and with evidence of groundwater degradation, was chosen to show the model operation. Governing system variables were identified and put into action through System Dynamics (SD) modeling causal diagrams to program basic formulations into a model having two modules coupled by the nexus ‘pumping’: (1) the hydrological module represents the net groundwater balance (G) dynamics; and (2) the economic module reproduces the variation in the consumers of water, both the population and tourists. The model was operated under similar influx of tourists and different scenarios of water availability, such as the wet 2009–2010 and the average 2010–2011 hydrological years. The rise in international tourism is identified as the main driving force reducing emigration and introducing new social habits in the population, in particular concerning water consumption. Urban water allotment (PU) was doubled for less than a 100-inhabitant net increase in recent decades. The water allocation for agriculture (PI), the largest consumer of water, had remained constant for decades. Despite that the 2-year monitoring period is not long enough to draw long-term conclusions, groundwater imbalance was reflected by net aquifer recharge (R) less than PI + PU (G < 0) in the average year 2010–2011, with net lateral inflow from adjacent Cambrian formations being the largest recharge component. R is expected to be much less than PI + PU in recurrent dry spells. Some low-technology actions are tentatively proposed to mitigate groundwater degradation, such as: wastewater capture, treatment, and reuse for irrigation; storm-water harvesting for irrigation; and active maintenance of the irrigation system to improve its efficiency.