3D Surface Reconstruction Using Laplacian Coordinates for Detail Preservation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing 3D reconstruction methods struggle to accurately capture intricate details on surfaces, particularly those affected by deformation, such as wrinkles on clothed humans, due to the introduction of noise when using chamfer distance as a loss function and the smoothing effect of regularization functions.
Innovation Solution
A method and apparatus utilizing Laplacian coordinates to represent and modify 3D meshes, incorporating a 3D surface function optimization and Laplacian coordinate integration to enhance detail representation, especially for surfaces with pose-dependent changes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If regularization function is used to remove noise during optimization, then surface smoothness is improved, but surface details are lost
Solution Approach 1:
The patent changes the coordinate system parameter from absolute coordinates to Laplacian coordinates. This parameter change allows the optimization process to work in a different mathematical space where regularization can be applied without the same detrimental smoothing effect on surface details, thereby resolving the contradiction between surface smoothness and detail accuracy
Solution Approach 2:
The patent introduces Laplacian coordinates as an intermediary representation between the input point cloud and the final 3D model. This intermediary coordinate system acts as a mediator that preserves surface details while allowing noise removal through regularization, thus resolving the contradiction between smoothness and detail preservation
2Measurement precision
If chamfer distance is used as loss function for optimization, then point cloud alignment is improved, but noise is introduced in reconstructed values
Solution Approach 1:
The patent changes the optimization parameter space by using Laplacian coordinates instead of absolute coordinates. This parameter transformation allows the chamfer distance loss function to align point clouds more effectively without introducing the same level of noise in the reconstructed values, thereby resolving the contradiction between alignment accuracy and reconstruction quality
3Shape
If traditional absolute coordinate-based methods are used for 3D reconstruction, then overall shape reconstruction is achieved, but intricate surface details are missed
Solution Approach 1:
The patent fundamentally changes the coordinate parameter from absolute coordinates to Laplacian coordinates. This parameter change enables the reconstruction system to capture intricate surface details while maintaining overall shape accuracy, as Laplacian coordinates inherently encode local geometric information that is lost in absolute coordinate systems
Solution Approach 2:
The patent transitions from a standard 3D absolute coordinate system to a Laplacian coordinate system that incorporates additional dimensional information about local surface geometry. This dimensional transformation allows the system to represent both global shape and local surface details simultaneously, resolving the contradiction between overall shape reconstruction and surface detail capture
Data Source
AI summary
A detailed 3-dimensional (3D) object reconstruction method, executed by a computing device, may comprise: obtaining Laplacian coordinates with local details and direction and size information for of curvatures on a 3D surface defined by an input point cloud; and converting the Laplacian coordinates to absolute coordinates using a mesh for the 3D surface and Laplacian coordinates for each vertex of the mesh and a Laplace-Beltrami operator.