Orthorectification of Skin Nevi Images by Means of 3D Model of the Human Body

Melanoma is the most lethal form of skin cancer, and develops from mutation of pigment-producing cells. As it becomes malignant, it usually grows in size, changes proportions, and develops an irregular border. We introduce a system for early detection of such changes, which enables whole-body screening, especially useful in patients with atypical mole syndrome. The paper proposes a procedure to build a 3D model of the patient, relate the high-resolution skin images with the model, and orthorectify these images to enable detection of size and shape changes in nevi. The novelty is in the application of image encoding indices and barycentric coordinates of the mesh triangles. The proposed procedure was validated with a set of markers of a specified geometry. The markers were attached to the body of a volunteer and analyzed by the system. The results of quantitative comparison of original and corrected images confirm that the orthorectification allows for more accurate estimation of size and proportions of skin nevi.

Visualizing temperature-dependent phase stability in high entropy alloys

High entropy alloys (HEAs) contain near equimolar amounts of five or more elements and are a compelling space for materials design. In the design of HEAs, great emphasis is placed on identifying thermodynamic conditions for single-phase and multi-phase stability regions, but this process is hindered by the difficulty of navigating stability relationships in high-component spaces. Traditional phase diagrams use barycentric coordinates to represent composition axes, which require (N – 1) spatial dimensions to represent an N-component system, meaning that HEA systems with N > 4 components cannot be readily visualized. Here, we propose forgoing barycentric composition axes in favor of two energy axes: a formation-energy axis and a ‘reaction energy’ axis. These Inverse Hull Webs offer an information-dense 2D representation that successfully captures complex phase stability relationships in N ≥ 5 component systems. We use our proposed diagrams to visualize the transition of HEA solid-solutions from high-temperature stability to metastability upon quenching, and identify important thermodynamic features that are correlated with the persistence or decomposition of metastable HEAs.

Improved Well-Control Progressive Optimization with Generalized Barycentric Coordinates and Manifold Mapping

Summary Well-control management is nowadays frequently approached by means of mathematical optimization. However, in many practical situations the optimization algorithms used are still computationally expensive. In this paper, we present progressive optimization (PO), a simulator-nonintrusivefour-stage methodology to accelerate optimal search substantially in well-controlapplications. The first stage of PO comprises a global exploration of the search space using design of experiments (DOEs). Thereafter, in the second stage, a fast-to-evaluate proxy model is constructed with the points considered in the experimental design. This proxy is based on generalized barycentric coordinates (GBCs), a generalization of the concept of barycentric coordinates used within a triangle. GBCs can be especially suited to problems in which nonlinearities are not strong, as is the case often for well-control optimization. This fact is supported by the good performance in these types of optimization problems of techniques that rely strongly on linearity assumptions, such as trajectory piecewise linearization, a procedure that is not always applicable due to its simulator-intrusive nature. In the third stage, the precision of the proxy model is iteratively improved and the enhanced surrogate model is reoptimized by means of manifold mapping (MM), a method that combines models with different levels of accuracy. MM has solid theoretical foundations and leads to efficient optimization schemes in multiple engineering disciplines. The final and fourth stage aims at additional improvement, resorting to direct optimization of the best solution from the previous stages. Nonlinear (operational) constraints are handled in PO with the filter method. The optimal search may be finalized earlier than at the fourth stage whenever the solution obtained is of satisfactory quality. PO is tested on two waterflooding problems built upon a synthetic model previously studied in well-control optimization literature. In these problems, which have 120 and 40 well controls and include nonlinear constraints, we observe for PO reductions in computational cost, for solutions of comparable quality, of approximately 30% and 50% with respect to Hooke-Jeeves direct search (HJDS), which, in turn, outperforms particle swarm optimization (PSO). HJDS and PSO are simulator-nonintrusive algorithms that usually perform well in optimization for oilfield operations. The novel concepts of GBC and MM within the framework of the PO paradigm can be extremely helpful for practitioners to efficiently deal with optimized well-control management. Savings of 50% in computing cost may be translated in practice into days of computations for just a single field and optimization run.

On the Geometric Description of Nonlinear Elasticity via an Energy Approach Using Barycentric Coordinates

The deformation of a solid due to changing boundary conditions is described by a deformation gradient in Euclidean space. If the deformation process is reversible (conservative), the work done by the changing boundary conditions is stored as potential (elastic) energy, a function of the deformation gradient invariants. Based on this, in the present work we built a “discrete energy model” that uses maps between nodal positions of a discrete mesh linked with the invariants of the deformation gradient via standard barycentric coordinates. A special derivation is provided for domains tessellated by tetrahedrons, where the energy functionals are constrained by prescribed boundary conditions via Lagrange multipliers. The analysis of these domains is performed via energy minimisation, where the constraints are eliminated via pre-multiplication of the discrete equations by a discrete null-space matrix of the constraint gradients. Numerical examples are provided to verify the accuracy of the proposed technique. The standard barycentric coordinate system in this work is restricted to three-dimensional (3-D) convex polytopes. We show that for an explicit energy expression, applicable also to non-convex polytopes, the general barycentric coordinates constitute fundamental tools. We define, in addition, the discrete energy via a gradient for general polytopes, which is a natural extension of the definition for discrete domains tessellated by tetrahedra. We, finally, prove that the resulting expressions can consistently describe the deformation of solids.

A Polygonal Finite Element Method for Stokes Equations

In this paper, we extend the Bernardi-Raugel element [1] to convex polygonal meshes by using the generalized barycentric coordinates. Comparing to traditional discretizations defined on triangular and rectangular meshes, polygonal meshes can be more flexible when dealing with complicated domains or domains with curved boundaries. Theoretical analysis of the new element follows the standard mixed finite element theory for Stokes equations, i.e., we shall prove the discrete inf-sup condition (LBB condition) by constructing a Fortin operator. Because there is no scaling argument on polygonal meshes and the generalized barycentric coordinates are in general not polynomials, special treatments are required in the analysis. We prove that the extended Bernardi-Raugel element has optimal convergence rates. Supporting numerical results are also presented.

Computer-Aided Assessment of Displacement and Reduction of Distal Radius Fractures

This study aims to investigate displacements and reductions of distal radius fractures using measurement indices based on the computer-aided three-dimensional (3D) radius shape model. Fifty-two distal radius fracture patients who underwent osteosynthesis were evaluated with pre- and post-operative distal radius 3D images. In the 3D images, three reference points, i.e., the radial styloid process (1), sigmoid notch volar, and dorsal edge (2) (3) were marked. The three-dimensional coordinates of each reference point and the barycentric coordinates of the plane connecting the three reference points were evaluated. The distance and direction moved, due to the reductions for each reference point, were (1) 12.1 ± 8.1 mm in the ulnar-palmar-distal direction, (2) 7.5 ± 4.1 mm in the ulnar-palmar-proximal direction, and (3) 8.2 ± 4.7 mm in the ulnar-palmar-distal direction relative to the preoperative position. The barycentric coordinate moved 8.4 ± 5.3 mm in the ulnar-palmar-distal direction compared to the preoperative position. This analyzing method will be helpful to understand the three-dimensional direction and the extent of displacements in distal radius fractures.