Fast Global Minimization of the Active Contour/Snake Model

The active contour/snake model is one of the most successful variational models in image segmentation. It consists of evolving a contour in images toward the boundaries of objects. Its success is based on strong mathematical properties and efficient numerical schemes based on the level set method. The only drawback of this model is the existence of local minima in the active contour energy, which makes the initial guess critical to get satisfactory results. In this paper, we propose to solve this problem by determining a global minimum of the active contour model. Our approach is based on the unification of image segmentation and image denoising tasks into a global minimization framework. More precisely, we propose to unify three well-known image variational models, namely the snake model, the Rudin–Osher–Fatemi denoising model and the Mumford–Shah segmentation model. We will establish theorems with proofs to determine the existence of a global minimum of the active contour model. From a numerical point of view, we propose a new practical way to solve the active contour propagation problem toward object boundaries through a dual formulation of the minimization problem. The dual formulation, easy to implement, allows us a fast global minimization of the snake energy. It avoids the usual drawback in the level set approach that consists of initializing the active contour in a distance function and re-initializing it periodically during the evolution, which is time-consuming. We apply our segmentation algorithms on synthetic and real-world images, such as texture images and medical images, to emphasize the performances of our model compared with other segmentation models. Research supported by NIH U54RR021813, NSF DMS-0312222, NSF ACI-0321917 and NSF DMI-0327077.     

Off-line/on-line signatures revisited: a general unifying paradigm, efficient threshold variants and experimental results

The notion of off-line/on-line digital signature scheme was introduced by Even, Goldreich and Micali. Informally such signatures schemes are used to reduce the time required to compute a signature using some kind of preprocessing. Even, Goldreich and Micali show how to realize off-line/on-line digital signature schemes by combining regular digital signatures with efficient one-time signatures. Later, Shamir and Tauman presented an alternative construction (which produces shorter signatures) obtained by combining regular signatures with chameleon hash functions. In this paper, we study off-line/on-line digital signature schemes both from a theoretic and a practical perspective. More precisely, our contribution is threefold. First, we unify the Shamir–Tauman and Even et al. approaches by showing that they can be seen as different instantiations of the same paradigm. We do this by showing that the one-time signatures needed in the Even et al. approach only need to satisfy a weak notion of security. We then show that chameleon hashing is basically a one-time signature which satisfies such a weaker security notion. As a by-product of this result, we study the relationship between one-time signatures and chameleon hashing, and we prove that a special type of chameleon hashing (which we call double-trapdoor) is actually a fully secure one-time signature. Next, we consider the task of building, in a generic fashion, threshold variants of known schemes: Crutchfield et al. proposed a generic way to construct a threshold off-line/on-line signature scheme given a threshold regular one. They applied known threshold techniques to the Shamir–Tauman construction using a specific chameleon hash function. Their solution introduces additional computational assumptions which turn out to be implied by the so-called one-more discrete logarithm assumption. Here, we propose two generic constructions that can be based on any threshold signature scheme, combined with a specific (double-trapdoor) chameleon hash function. Our constructions are efficient and can be proven secure in the standard model using only the traditional discrete logarithm assumption. Finally, we ran experimental tests to measure the difference between the real efficiency of the two known constructions for non-threshold off-line/on-line signatures. Interestingly, we show that, using some optimizations, the two approaches are comparable in efficiency and signature length.     

Visual Lisp/CLOS programming in OpenMusic

OpenMusic (OM) is a visual programming language developed on top of Common Lisp and CLOS, in which most of the functional and object-oriented programming concepts can be implemented and carried out graphically. Although this visual language was designed for musical applications, the focus in this paper is to describe and study OM as a complete general-purpose programming environment.     

Tailoring of elastomeric grafted coating via sol–gel chemistry of crosslinked polymethylhydrosiloxane

Thin coating of crosslinked polymethylhydrosiloxane are grafted on silica using sol–gel process that leads to polymer layers tailored in term of thickness and elasticity. The degree of crosslinking is tuned by sol–gel polycondensation of a mixture of methyldiethoxysilane(DH) HSi(CH₃)(OCH₂CH₃)₂ and triethoxysilane (TH) HSi(OCH₂CH₃)₃, yielding triethoxysilane‐based networks. Samples with well‐defined thicknesses from nanometer to micrometer range are prepared by sol–gel dip‐coating method on silicon surface. Homogeneous or gradient‐thickness coating can be produced in this way. It results in surface‐attached networks bearing Si? H functionalities covalently anchored to the substrate. Powdered gels of DH/TH composition from 50/50 to 95/5 (mol %) were also prepared for a comparison purpose. The structure of the gels was investigated by NMR and FTIR, showing that DH/TH mixtures react totally to yield homogeneous matrix. The surface‐attached polymer films are very stable and present high hydrophobicity as evidenced by contact angle measurements. Their surface and mechanical properties have been qualitatively studied using the atomic force microscopy. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 1504–1516, 2007     

Hydration of tricalcium silicate (C3S) at high temperature and high pressure

Hydration products of tricalcium silicate (C₃S) are the calcium silicate hydrates (C-S-H) and Portlandite. Silica fume, added to anhydrous cement in industrial formulations reacts with Portlandite and leads to C-S-H different from the previous one. C₃S hydration with and without silica fume has been studied under high pressure (1000 bar) and high temperature (160°C) by numerous techniques (²⁹Si and ¹H NMR, XRD, Thermal analysis, SEM) for different hydration times. In these conditions, high temperature more stable crystalline phases are formed and their kinetics of formation is dependent on pressure. Besides, electrical conductivity measurement on hydrating cement under pressure have been carried out in order to evidence the great dependence of hydration kinetics with pressure. This study proposes a practical phase diagram which allows on a thermodynamical base to understand the change of equilibrium temperature with pressure. The kinetics of reaction has been studied and mechanisms of reaction proposed to explain the results.     

Degenerative mineralization in the fibrous capsule of silicone breast implants

The formation of a fibrous capsule made of long collagen fibers surrounding breast implants represents an unavoidable phenomenon as the patients reaction to the presence of a foreign body. Depending upon the size and shape of the implants and the chemicals percolating through the shell, this fibrous capsule is continuously remodeled. The compaction of the foreign debris in the vicinity of the silicone shell is followed by the loss of cellular activity, shrinkage and necrosis. Calcification is the ultimate step. These phenomena were illustrated in the analysis of 18 explanted breast prostheses after 20 or more years of implantation. The degenerative mineralization was shown in scanning electron microscopy and light microscopy. The minerals proved to be bone-like hydroxyapatite by X-ray diffraction and Solid State NMR analysis. Whatever the characteristics of any sophisticated new model of breast implant, phenomenon of mineralization might be minimized but it is very unlikely that it would be totally eliminated.     

Local Histogram Based Segmentation Using the Wasserstein Distance

We propose and analyze a nonparametric region-based active contour model for segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel intensity is independently identically distributed. Our proposed energy functional consists of a geometric regularization term that penalizes the length of the partition boundaries and a region-based image term that uses histograms of pixel intensity to distinguish different regions. More specifically, the region data encourages segmentation so that local histograms within each region are approximately homogeneous. An advantage of using local histograms in the data term is that histogram differentiation is not required to solve the energy minimization problem. We use Wasserstein distance with exponent 1 to determine the dissimilarity between two histograms. The Wasserstein distance is a metric and is able to faithfully measure the distance between two histograms, compared to many pointwise distances. Moreover, it is insensitive to oscillations, and therefore our model is robust to noise. A fast global minimization method based on (Chan et al. in SIAM J. Appl. Math. 66(5):1632–1648, 2006; Bresson et al. in J. Math. Imaging Vis. 28(2):151–167, 2007) is employed to solve the proposed model. The advantages of using this method are two-fold. First, the computational time is less than that of the method by gradient descent of the associated Euler-Lagrange equation (Chan et al. in Proc. of SSVM, pp. 697–708, 2007). Second, it is able to find a global minimizer. Finally, we propose a variant of our model that is able to properly segment a cluttered scene with local illumination changes. This research is supported by ONR grant N00014-09-1-0105 and NSF grant DMS-0610079.     

Multiscale Active Contours

We propose a new multiscale image segmentation model, based on the active contour/snake model and the Polyakov action. The concept of scale, general issue in physics and signal processing, is introduced in the active contour model, which is a well-known image segmentation model that consists of evolving a contour in images toward the boundaries of objects. The Polyakov action, introduced in image processing by Sochen-Kimmel-Malladi in Sochen et al. (1998), provides an efficient mathematical framework to define a multiscale segmentation model because it generalizes the concept of harmonic maps embedded in higher-dimensional Riemannian manifolds such as multiscale images. Our multiscale segmentation model, unlike classical multiscale segmentations which work scale by scale to speed up the segmentation process, uses all scales simultaneously, i.e. the whole scale space, to introduce the geometry of multiscale images in the segmentation process. The extracted multiscale structures will be useful to efficiently improve the robustness and the performance of standard shape analysis techniques such as shape recognition and shape registration. Another advantage of our method is to use not only the Gaussian scale space but also many other multiscale spaces such as the Perona-Malik scale space, the curvature scale space or the Beltrami scale space. Finally, this multiscale segmentation technique is coupled with a multiscale edge detecting function based on the gradient vector flow model, which is able to extract convex and concave object boundaries independent of the initial condition. We apply our multiscale segmentation model on a synthetic image and a medical image.     

A Variational Model for Object Segmentation Using Boundary Information and Shape Prior Driven by the Mumford-Shah Functional

In this paper, we propose a new variational model to segment an object belonging to a given shape space using the active contour method, a geometric shape prior and the Mumford-Shah functional. The core of our model is an energy functional composed by three complementary terms. The first one is based on a shape model which constrains the active contour to get a shape of interest. The second term detects object boundaries from image gradients. And the third term drives globally the shape prior and the active contour towards a homogeneous intensity region. The segmentation of the object of interest is given by the minimum of our energy functional. This minimum is computed with the calculus of variations and the gradient descent method that provide a system of evolution equations solved with the well-known level set method. We also prove the existence of this minimum in the space of functions with bounded variation. Applications of the proposed model are presented on synthetic and medical images.     

Tricalcium silicate (C3S) hydration under high pressure at ambient and high temperature (200 °C)

The hydration of a tricalcium silicate paste at ambient temperature and at 200 °C under high pressure (up to 1000 bar) has been studied. Two high pressure cells have been used, one allows in-situ electrical conductivity measurements during hydration under high pressure. The hydration products were characterized by thermal analysis, X-ray diffraction and ²⁹Si NMR measurements. The pressure has a large kinetic effect on the hydration of a C₃S paste at room temperature. The pressure was seen to affect drastically the hydration of a C₃S paste at 200 °C and this study evidences the competition between the different high temperature phases during the hydration.