Subset Warping: Rubber Sheeting with Cuts

Image warping, often referred to as "rubber sheeting" represents the deformation of a domain image space into a range image space. In this paper, a technique is described which extends the definition of a rubber-sheet transformation to allow a polygonal region to be warped into one or more subsets of itself, where the subsets may be multiply connected. To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities in the range image, using a technique based on generalized Voronoi diagrams. The concept of medial axis is extended to describe inner and outer medial contours of a polygon. Polygonal regions are decomposed into annular subregions, and path homotopies are introduced to describe the annular subregions. These constructions motivate the definition of a ladder, which guides the construction of grid point pairs necessary to effect the warp itself

Active skeleton for bacteria modeling

The investigation of spatio-temporal dynamics of bacterial cells and their molecular components requires automated image analysis tools to track cell shape properties and molecular component locations inside the cells. In the study of bacteria aging, the molecular components of interest are protein aggregates accumulated near bacteria boundaries. This particular location makes very ambiguous the correspondence between aggregates and cells, since computing accurately bacteria boundaries in phase-contrast time-lapse imaging is a challenging task. This paper proposes an active skeleton formulation for bacteria modeling which provides several advantages: an easy computation of shape properties (perimeter, length, thickness, orientation), an improved boundary accuracy in noisy images, and a natural bacteria-centered coordinate system that permits the intrinsic location of molecular components inside the cell. Starting from an initial skeleton estimate, the medial axis of the bacterium is obtained by minimizing an energy function which incorporates bacteria shape constraints. Experimental results on biological images and comparative evaluation of the performances validate the proposed approach for modeling cigar-shaped bacteria like Escherichia coli. The Image-J plugin of the proposed method can be found online at http://fluobactracker.inrialpes.fr.Comment: Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging and Visualizationto appear i

Image inpainting based on coherence transport with adapted distance functions

We discuss an extension of our method Image Inpainting Based on Coherence Transport. For the latter method the pixels of the inpainting domain have to be serialized into an ordered list. Up till now, to induce the serialization we have used the distance to boundary map. But there are inpainting problems where the distance to boundary serialization causes unsatisfactory inpainting results. In the present work we demonstrate cases where we can resolve the difficulties by employing other distance functions which better suit the problem at hand

Unwind: Interactive Fish Straightening

The ScanAllFish project is a large-scale effort to scan all the world's 33,100 known species of fishes. It has already generated thousands of volumetric CT scans of fish species which are available on open access platforms such as the Open Science Framework. To achieve a scanning rate required for a project of this magnitude, many specimens are grouped together into a single tube and scanned all at once. The resulting data contain many fish which are often bent and twisted to fit into the scanner. Our system, Unwind, is a novel interactive visualization and processing tool which extracts, unbends, and untwists volumetric images of fish with minimal user interaction. Our approach enables scientists to interactively unwarp these volumes to remove the undesired torque and bending using a piecewise-linear skeleton extracted by averaging isosurfaces of a harmonic function connecting the head and tail of each fish. The result is a volumetric dataset of a individual, straight fish in a canonical pose defined by the marine biologist expert user. We have developed Unwind in collaboration with a team of marine biologists: Our system has been deployed in their labs, and is presently being used for dataset construction, biomechanical analysis, and the generation of figures for scientific publication

The three dimensional skeleton: tracing the filamentary structure of the universe

The skeleton formalism aims at extracting and quantifying the filamentary structure of the universe is generalized to 3D density fields; a numerical method for computating a local approximation of the skeleton is presented and validated here on Gaussian random fields. This method manages to trace well the filamentary structure in 3D fields such as given by numerical simulations of the dark matter distribution on large scales and is insensitive to monotonic biasing. Two of its characteristics, namely its length and differential length, are analyzed for Gaussian random fields. Its differential length per unit normalized density contrast scales like the PDF of the underlying density contrast times the total length times a quadratic Edgeworth correction involving the square of the spectral parameter. The total length scales like the inverse square smoothing length, with a scaling factor given by 0.21 (5.28+ n) where n is the power index of the underlying field. This dependency implies that the total length can be used to constrain the shape of the underlying power spectrum, hence the cosmology. Possible applications of the skeleton to galaxy formation and cosmology are discussed. As an illustration, the orientation of the spin of dark halos and the orientation of the flow near the skeleton is computed for dark matter simulations. The flow is laminar along the filaments, while spins of dark halos within 500 kpc of the skeleton are preferentially orthogonal to the direction of the flow at a level of 25%.Comment: 17 pages, 11 figures, submitted to MNRA

Skeleton as a probe of the cosmic web: the 2D case

We discuss the skeleton as a probe of the filamentary structures of a 2D random field. It can be defined for a smooth field as the ensemble of pairs of field lines departing from saddle points, initially aligned with the major axis of local curvature and connecting them to local maxima. This definition is thus non local and makes analytical predictions difficult, so we propose a local approximation: the local skeleton is given by the set of points where the gradient is aligned with the local curvature major axis and where the second component of the local curvature is negative. We perform a statistical analysis of the length of the total local skeleton, chosen for simplicity as the set of all points of space where the gradient is either parallel or orthogonal to the main curvature axis. In all our numerical experiments, which include Gaussian and various non Gaussian realizations such as \chi^2 fields and Zel'dovich maps, the differential length is found within a normalization factor to be very close to the probability distribution function of the smoothed field. This is in fact explicitly demonstrated in the Gaussian case. This result might be discouraging for using the skeleton as a probe of non Gausiannity, but our analyses assume that the total length of the skeleton is a free, adjustable parameter. This total length could in fact be used to constrain cosmological models, in CMB maps but also in 3D galaxy catalogs, where it estimates the total length of filaments in the Universe. Making the link with other works, we also show how the skeleton can be used to study the dynamics of large scale structure.Comment: 15 pages, 11 figures, submitted to MNRA

Role of critical points of the skin friction field in formation of plumes in thermal convection

The dynamics in the thin boundary layers of temperature and velocity is the key to a deeper understanding of turbulent transport of heat and momentum in thermal convection. The velocity gradient at the hot and cold plates of a Rayleigh-B\'{e}nard convection cell forms the two-dimensional skin friction field and is related to the formation of thermal plumes in the respective boundary layers. Our analysis is based on a direct numerical simulation of Rayleigh-B\'{e}nard convection in a closed cylindrical cell of aspect ratio $\Gamma=1$ and focused on the critical points of the skin friction field. We identify triplets of critical points, which are composed of two unstable nodes and a saddle between them, as the characteristic building block of the skin friction field. Isolated triplets as well as networks of triplets are detected. The majority of the ridges of line-like thermal plumes coincide with the unstable manifolds of the saddles. From a dynamical Lagrangian perspective, thermal plumes are formed together with an attractive hyperbolic Lagrangian Coherent Structure of the skin friction field. We also discuss the differences from the skin friction field in turbulent channel flows from the perspective of the Poincar\'{e}-Hopf index theorem for two-dimensional vector fields