Learning spatial relationships in hand-drawn patterns using fuzzy mathematical morphology

International audienceWe introduce in this work a new approach for learning spatial relationships between elements of hand-drawn patterns with the help of fuzzy mathematical morphology operators. Relying on mathematical morphology allows to take into account the actual shapes of hand-drawn patterns when modeling their spatial relationships, and thus to cope with the variability of handwriting signal. Extension of mathematical morphology to the fuzzy set framework further allows to handle imprecision of handwriting and to deal with the ambiguity of spatial relationships. The novelty lies in the generative aspect of the models we propose, in the sense that they can exhibit the region of space where the learnt relation is satisfied with respect to a reference object, and can thus be used for driving structural analysis of complex patterns. Experiments over on-line handwritten data show their performance, and prove their ability to deal with variability of handwriting and reasoning under imprecision

Global morphogenetic flow is accurately predicted by the spatial distribution of myosin motors.

During embryogenesis tissue layers undergo morphogenetic flow rearranging and folding into specific shapes. While developmental biology has identified key genes and local cellular processes, global coordination of tissue remodeling at the organ scale remains unclear. Here, we combine in toto light-sheet microscopy of the Drosophila embryo with quantitative analysis and physical modeling to relate cellular flow with the patterns of force generation during the gastrulation process. We find that the complex spatio-temporal flow pattern can be predicted from the measured meso-scale myosin density and anisotropy using a simple, effective viscous model of the tissue, achieving close to 90% accuracy with one time dependent and two constant parameters. Our analysis uncovers the importance of a) spatial modulation of myosin distribution on the scale of the embryo and b) the non-locality of its effect due to mechanical interaction of cells, demonstrating the need for the global perspective in the study of morphogenetic flow

Image Ellipticity from Atmospheric Aberrations

We investigate the ellipticity of the point-spread function (PSF) produced by imaging an unresolved source with a telescope, subject to the effects of atmospheric turbulence. It is important to quantify these effects in order to understand the errors in shape measurements of astronomical objects, such as those used to study weak gravitational lensing of field galaxies. The PSF modeling involves either a Fourier transform of the phase information in the pupil plane or a ray-tracing approach, which has the advantage of requiring fewer computations than the Fourier transform. Using a standard method, involving the Gaussian weighted second moments of intensity, we then calculate the ellipticity of the PSF patterns. We find significant ellipticity for the instantaneous patterns (up to more than 10%). Longer exposures, which we approximate by combining multiple (N) images from uncorrelated atmospheric realizations, yield progressively lower ellipticity (as 1 / sqrt(N)). We also verify that the measured ellipticity does not depend on the sampling interval in the pupil plane using the Fourier method. However, we find that the results using the ray-tracing technique do depend on the pupil sampling interval, representing a gradual breakdown of the geometric approximation at high spatial frequencies. Therefore, ray tracing is generally not an accurate method of modeling PSF ellipticity induced by atmospheric turbulence unless some additional procedure is implemented to correctly account for the effects of high spatial frequency aberrations. The Fourier method, however, can be used directly to accurately model PSF ellipticity, which can give insights into errors in the statistics of field galaxy shapes used in studies of weak gravitational lensing.Comment: 9 pages, 5 color figures (some reduced in size). Accepted for publication in the Astrophysical Journa

gMotion: A spatio-temporal grammar for the procedural generation of motion graphics

Creating by hand compelling 2D animations that choreograph several groups of shapes requires a large number of manual edits. We present a method to procedurally generate motion graphics with timeslice grammars. Timeslice grammars are to time what split grammars are to space. We use this grammar to formally model motion graphics, manipulating them in both temporal and spatial components. We are able to combine both these aspects by representing animations as sets of affine transformations sampled uniformly in both space and time. Rules and operators in the grammar manipulate all spatio-temporal matrices as a whole, allowing us to expressively construct animation with few rules. The grammar animates shapes, which are represented as highly tessellated polygons, by applying the affine transforms to each shape vertex given the vertex position and the animation time. We introduce a small set of operators showing how we can produce 2D animations of geometric objects, by combining the expressive power of the grammar model, the composability of the operators with themselves, and the capabilities that derive from using a unified spatio-temporal representation for animation data. Throughout the paper, we show how timeslice grammars can produce a wide variety of animations that would take artists hours of tedious and time-consuming work. In particular, in cases where change of shapes is very common, our grammar can add motion detail to large collections of shapes with greater control over per-shape animations along with a compact rules structure

The effects of landscape modifications on the long-term persistence of animal populations

Background: The effects of landscape modifications on the long-term persistence of wild animal populations is of crucial importance to wildlife managers and conservation biologists, but obtaining experimental evidence using real landscapes is usually impossible. To circumvent this problem we used individual-based models (IBMs) of interacting animals in experimental modifications of a real Danish landscape. The models incorporate as much as possible of the behaviour and ecology of four species with contrasting life-history characteristics: skylark (Alauda arvensis), vole (Microtus agrestis), a ground beetle (Bembidion lampros) and a linyphiid spider (Erigone atra). This allows us to quantify the population implications of experimental modifications of landscape configuration and composition. Methodology/Principal Findings: Starting with a real agricultural landscape, we progressively reduced landscape complexity by (i) homogenizing habitat patch shapes, (ii) randomizing the locations of the patches, and (iii) randomizing the size of the patches. The first two steps increased landscape fragmentation. We assessed the effects of these manipulations on the long-term persistence of animal populations by measuring equilibrium population sizes and time to recovery after disturbance. Patch rearrangement and the presence of corridors had a large effect on the population dynamics of species whose local success depends on the surrounding terrain. Landscape modifications that reduced population sizes increased recovery times in the short-dispersing species, making small populations vulnerable to increasing disturbance. The species that were most strongly affected by large disturbances fluctuated little in population sizes in years when no perturbations took place. Significance: Traditional approaches to the management and conservation of populations use either classical methods of population analysis, which fail to adequately account for the spatial configurations of landscapes, or landscape ecology, which accounts for landscape structure but has difficulty predicting the dynamics of populations living in them. Here we show how realistic and replicable individual-based models can bridge the gap between non-spatial population theory and non-dynamic landscape ecology. A major strength of the approach is its ability to identify population vulnerabilities not detected by standard population viability analyses

Turing Patterns and Biological Explanation

Turing patterns are a class of minimal mathematical models that have been used to discover and conceptualize certain abstract features of early biological development. This paper examines a range of these minimal models in order to articulate and elaborate a philosophical analysis of their epistemic uses. It is argued that minimal mathematical models aid in structuring the epistemic practices of biology by providing precise descriptions of the quantitative relations between various features of the complex systems, generating novel predictions that can be compared with experimental data, promoting theory exploration, and acting as constitutive parts of empirically adequate explanations of naturally occurring phenomena, such as biological pattern formation. Focusing on the roles that minimal model explanations play in science motivates the adoption of a broader diachronic view of scientific explanation