3D Surface Mesh Segmentation via Iterative Cost Minimization
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Solution Overview
Problem
There is a growing need to effectively segment three-dimensional surface meshes into meaningful parts, as existing methods lack efficiency in defining optimal cuts that minimize cutting length and area differences between parts.
Innovation Solution
A computer-implemented method that calculates multiple costs associated with intermediate allocations in a three-dimensional surface mesh, using a cost function responsive to the length of the cut and the difference between areas of the parts, and iteratively adjusts border face allocations to select the best cut, applying probabilistic processes to accept changes that reduce costs while avoiding disadvantageous allocations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Length of stationary object
If existing segmentation methods are used, then segmentation can be performed, but the cutting length is not minimized and area differences between parts are not optimized
Solution Approach 1:
The patent transforms the segmentation problem into an energy minimization problem by defining an energy function with multiple parameters (cut length, area difference, regularization terms). By adjusting these parameters and using gradient descent optimization, the method finds optimal cut configurations that minimize the energy function, thereby simultaneously minimizing cutting length while maintaining segmentation quality.
Solution Approach 2:
The patent implements an iterative optimization process where the energy function is continuously evaluated and used to provide feedback for adjusting the cut configuration. The gradient of the energy function guides the optimization direction, allowing the system to progressively improve the segmentation by reducing energy based on previous configurations until convergence is achieved.
2Manufacturing precision
If comprehensive energy landscape computation is performed, then optimal segmentation can be found, but computational complexity increases significantly
Solution Approach 1:
Instead of computing the entire energy landscape, the patent uses gradient descent to perform partial exploration of the energy space by following the steepest descent direction from the initial configuration. This localized optimization approach finds good enough solutions without the exponential computational cost of exhaustive search, achieving a practical balance between accuracy and complexity.
Solution Approach 2:
The patent replaces traditional mechanical or geometric segmentation approaches with an energy-based field theory approach. By defining an energy function and using gradient-based optimization, the method transforms the discrete combinatorial segmentation problem into a continuous optimization problem, enabling efficient computation through numerical methods rather than exhaustive enumeration.
3Length of stationary object
If iterative optimization is applied, then cutting length is minimized, but computation time increases
Solution Approach 1:
The patent maintains continuous optimization by iteratively updating the cut configuration along the gradient direction until convergence. Each iteration provides incremental improvement, and the process continues as long as energy reduction is achieved, ensuring that the optimization action is continuous and productive rather than intermittent or redundant.
Solution Approach 2:
The optimization process performs partial computation by stopping when convergence criteria are met (e.g., energy change below threshold or maximum iterations reached), rather than exhaustively exploring all possible configurations. This partial action approach achieves sufficient minimization of cutting length without excessive computation time.
Data Source
AI summary
A method that may include calculating multiple costs associated with multiple intermediate allocations and selecting an intermediate allocation of the multiple intermediate allocations in response to the multiple costs thereby providing a selected cut. The calculating may include repetitively executing the following steps: (a) Calculating an intermediate allocation of the multiple faces between to different intermediate parts of the mesh thereby defining an intermediate cut. The intermediate allocation differs from a previous intermediate allocation by a change in an allocation of at least one border face of the multiple faces. (b) Calculating, using a cost function, a cost of the intermediate allocation that is responsive to a length of the intermediate cut, and a difference between areas of the different intermediate parts. (c) Determining, based upon a comparison between a cost associated with the previous intermediate allocation and the cost of the intermediate allocation whether to accept the change in the allocation of the at least one border face.