A Low Distortion Mesh Parameterization Mapping Method Based on Proxy Function and Combined Newton

To address the issues of low efficiencies and serious mapping distortions in current mesh parameterization methods, we present a low distortion mesh parameterization mapping method based on proxy function and combined Newton’s method in this paper. First, the proposed method calculates visual blind areas and distortion prone areas of a 3D mesh model, and generates a model slit. Afterwards, the method performs the Tutte mapping on the cut three-dimensional mesh model, measures the mapping distortion of the model, and outputs a distortion metric function and distortion values. Finally, the method sets iteration parameters, establishes a reference mesh, and finds the optimal coordinate points to get a convergent mesh model. When calculating mapping distortions, Dirichlet energy function is used to measure the isometric mapping distortion, and MIPS energy function is used to measure the conformal mapping distortion. To find the minimum value of the mapping distortion metric function, we use an optimal solution method combining proxy functions and combined Newton’s method. The experimental data show that the proposed method has high execution efficiency, fast descending speed of mapping distortion energy and stable optimal value convergence quality. When a texture mapping is performed, the texture is evenly colored, close laid and uniformly lined, which meets the standards in practical applications.

Quasi-Isometric Mesh Parameterization Using Heat-Based Geodesics and Poisson Surface Fills

In the context of CAD, CAM, CAE, and reverse engineering, the problem of mesh parameterization is a central process. Mesh parameterization implies the computation of a bijective map ϕ from the original mesh M ∈ R 3 to the planar domain ϕ ( M ) ∈ R 2 . The mapping may preserve angles, areas, or distances. Distance-preserving parameterizations (i.e., isometries) are obviously attractive. However, geodesic-based isometries present limitations when the mesh has concave or disconnected boundary (i.e., holes). Recent advances in computing geodesic maps using the heat equation in 2-manifolds motivate us to revisit mesh parameterization with geodesic maps. We devise a Poisson surface underlying, extending, and filling the holes of the mesh M. We compute a near-isometric mapping for quasi-developable meshes by using geodesic maps based on heat propagation. Our method: (1) Precomputes a set of temperature maps (heat kernels) on the mesh; (2) estimates the geodesic distances along the piecewise linear surface by using the temperature maps; and (3) uses multidimensional scaling (MDS) to acquire the 2D coordinates that minimize the difference between geodesic distances on M and Euclidean distances on R 2 . This novel heat-geodesic parameterization is successfully tested with several concave and/or punctured surfaces, obtaining bijective low-distortion parameterizations. Failures are registered in nonsegmented, highly nondevelopable meshes (such as seam meshes). These cases are the goal of future endeavors.

HIGH QUALITY TEXTURE MAPPING PROCESS AIMED AT THE OPTIMIZATION OF 3D STRUCTURED LIGHT MODELS

<p><strong>Abstract.</strong> This article presents the evaluation of a pipeline to develop a high-quality texture mapping implementation which makes it possible to carry out a semantic high-quality 3D textured model. Due to geometric errors such as camera parameters or limited image resolution or varying environmental parameters, the calculation of a surface texture from 2D images could present several color errors. And, sometimes, it needs adjustments to the RGB or lightness information on a defined part of the texture. The texture mapping procedure is composed of mesh parameterization, mesh partitioning, mesh segmentation unwraps, UV map and projection of island, UV layout optimization, mesh packing and mesh baking. The study focuses attention to the mesh partitioning that essentially assigns a weight to each mesh, which reveals a mesh’s weight calculated by considering the flatness and distance of the mesh with respect to a chart. The 3D texture mapping has been developed in <i>Blender</i> and implemented in <i>Python</i>. In this paper we present a flowchart that resumes the procedure which aims to achieve a high-quality mesh and texture 3D model starting from the 3D <i>Spider</i> acquire, integrated with the <i>SfM</i> texture and using the texture mapping to reduce the color errors according to a semantic interpretation.</p>

A High-Resolution Texture Mapping Technique for 3D Textured Model

We proposed a texture mapping technique that comprises mesh partitioning, mesh parameterization and packing, texture transferring, and texture correction and optimization for generating a high-quality texture map of a three-dimensional (3D) model for applications in e-commerce presentations. The main problems in texture mapping are that the texture resolution is generally worse than in the original images and considerable photo inconsistency exists at the transition of different image sources. To improve the texture resolution, we employed an oriented boundary box method for placing mesh islands on the parametric (UV) map. We also provided a texture size that can keep the texture resolution of the 3D textured model similar to that of the object images. To improve the photo inconsistency problem, we employed a method to detect and overcome the missing color that might exist on a texture map. We also proposed a blending process to minimize the transition error caused by different image sources. Thus, a high-quality 3D textured model can be obtained by applying this series of processes for presentations in e-commerce.

Weighted area/angle distortion minimization for Mesh Parameterization

Purpose Mesh Parameterization is central to reverse engineering, tool path planning, etc. This work synthesizes parameterizations with un-constrained borders, overall minimum angle plus area distortion. This study aims to present an assessment of the sensitivity of the minimized distortion with respect to weighed area and angle distortions. Design/methodology/approach A Mesh Parameterization which does not constrain borders is implemented by performing: isometry maps for each triangle to the plane Z = 0; an affine transform within the plane Z = 0 to glue the triangles back together; and a Levenberg–Marquardt minimization algorithm of a nonlinear F penalty function that modifies the parameters of the first two transformations to discourage triangle flips, angle or area distortions. F is a convex weighed combination of area distortion (weight: α with 0 ≤ α ≤ 1) and angle distortion (weight: 1 − α). Findings The present study parameterization algorithm has linear complexity [𝒪(n), n = number of mesh vertices]. The sensitivity analysis permits a fine-tuning of the weight parameter which achieves overall bijective parameterizations in the studied cases. No theoretical guarantee is given in this manuscript for the bijectivity. This algorithm has equal or superior performance compared with the ABF, LSCM and ARAP algorithms for the Ball, Cow and Gargoyle data sets. Additional correct results of this algorithm alone are presented for the Foot, Fandisk and Sliced-Glove data sets. Originality/value The devised free boundary nonlinear Mesh Parameterization method does not require a valid initial parameterization and produces locally bijective parameterizations in all of our tests. A formal sensitivity analysis shows that the resulting parameterization is more stable, i.e. the UV mapping changes very little when the algorithm tries to preserve angles than when it tries to preserve areas. The algorithm presented in this study belongs to the class that parameterizes meshes with holes. This study presents the results of a complexity analysis comparing the present study algorithm with 12 competing ones.