3D Mesh Compression via Geometry Image Grid Resizing
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing mesh simplification methods, such as those described by Wang et al., suffer from non-smooth transformations and artifacts during large reductions, leading to reduced compression ratios and disregard for the final simplified mesh's boundary regularity.
Innovation Solution
A computer-implemented method that parameterizes a 3D mesh into a 2D plane, converts it into a Geometry Image, defines a grid of cells, computes cell relevance, and applies transformations to resize cells iteratively until a compression criterion is met, using free-form deformation splines to ensure smooth and regular reduction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of substance
If content-aware image resizing algorithms are used to reduce mesh size, then compression ratio is improved, but visible artifacts and spurious vertices are created in the mesh
Solution Approach 1:
The patent changes the parameter of transformation smoothness from non-smooth (prior art) to smooth (invention), specifically by using C1-continuous transformations instead of non-smooth deformations. This resolves the contradiction by maintaining mesh smoothness while achieving compression through the smooth transformation approach.
Solution Approach 2:
The patent creates a Geometry Image as a 2D representation copy of the 3D mesh, performs resizing operations on this copy, and then reconstructs the mesh from the resized copy. This copying approach allows compression to be applied to the mesh representation without directly deforming the original mesh structure, thereby avoiding artifacts.
2Loss of substance
If large reduction of the mesh is performed, then compression ratio is improved, but non-smooth transformations create local maxima in derivatives making further compression difficult
Solution Approach 1:
The patent ensures continuous smooth transformations throughout the compression process, avoiding discontinuities and local maxima in derivatives. By maintaining C1-continuity, the transformation remains smooth and differentiable, allowing compression to proceed efficiently without creating obstacles for further compression operations.
Solution Approach 2:
The patent changes the transformation parameter from non-smooth to smooth (C1-continuous), which fundamentally alters the compression process. This parameter change ensures that even large reductions maintain smoothness, preventing the creation of local maxima that would hinder further compression and maintaining high productivity throughout the process.
3Manufacturing precision
If boundary regularity of the geometry image is preserved, then image quality is maintained, but the final simplified mesh may not achieve optimal compression
Solution Approach 1:
The patent inverts the traditional approach by not preserving boundary regularity of the Geometry Image during resizing. Instead of constraining the boundaries to remain regular, the method allows boundaries to be transformed freely according to the smooth transformation field, achieving better compression ratios while maintaining overall mesh quality through the smoothness of the transformation itself.
Data Source
Figure 1
Figure 2~3
Figure 4~5
AI summary
The invention notably relates to a computer-implemented method for compressing a three-dimensional modeled object. The method comprises providing a mesh of a three-dimensional modeled object, parameterizing (u,v) the mesh on a two-dimensional plane, converting the parameterized mesh into an image I, defining a grid of cells from the image I, each cell being defined by a set of control points, computing a relevance of each cell of the grid, determining at least one cell having a relevance lower than a pre-determined threshold, resizing the at least one determined cell and computing a resulting grid, computing a transformation for each pixel of the image from the resulting grid, and applying the computed transformation to the image I.