Deep Neural Network Geometric Model Fitting
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Solution Overview
Problem
Conventional geometric model fitting methods, such as RANSAC, face challenges in high-dimensional problems due to the exponential rise in the probability of sampling outliers, leading to impracticality and instability, especially in NP-hard maximum consensus problems.
Innovation Solution
The proposed solution employs a learning-based pipeline architecture that uses deep neural networks to generate and update model weights, avoiding random sampling and reducing dependence on the number of data points, thereby enabling more robust and accurate geometric model fitting.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If conventional geometric model fitting methods like RANSAC are used, then the fitting process can be implemented with simple algorithms, but the probability of sampling outliers rises exponentially in high-dimensional problems leading to impracticality and instability
Solution Approach 1:
The patent replaces the mechanical random sampling process of RANSAC with a learned sampling strategy implemented through deep neural networks. The network learns optimal sampling distributions from data, substituting the brute-force mechanical sampling approach with an intelligent, adaptive system that achieves reliable fitting in high-dimensional spaces without exponential complexity growth.
Solution Approach 2:
The patent transforms the fixed sampling probability parameters of RANSAC into learned parameters through deep neural networks. By changing from static sampling probabilities to dynamic, data-driven sampling distributions, the system adapts to high-dimensional problem characteristics and maintains reliability without suffering from exponential complexity increases.
2Manufacturing precision
If the minimum number of data points required to define the model increases, then the model can capture more complex geometric structures, but the probability of sampling at least one outlier data point rises exponentially
Solution Approach 1:
The patent performs preliminary learning of data distributions and outlier patterns before actual model fitting. The deep neural network is pre-trained to recognize complex geometric structures and identify potential outliers, enabling the system to handle high-dimensional models without exponentially increased outlier sampling probability by preparing optimal sampling strategies in advance.
Solution Approach 2:
The patent introduces deep neural networks as an intermediary between raw data and geometric model fitting. This intermediary layer learns to filter, weight, and prioritize data points, reducing the effective outlier sampling probability even when complex high-dimensional models require more data points, thereby maintaining both accuracy and reliability.
3Measurement precision
If global optimization of the maximum consensus problem is performed, then the most accurate geometric model can be obtained, but the computational time becomes impractically slow
Solution Approach 1:
The patent performs preliminary optimization through deep neural network training that learns the optimal solution path and weighting schemes before actual model fitting. This preliminary action captures the essence of global optimization in the network weights, enabling fast approximate solutions that approach global optimization accuracy without the impractical computational time of exhaustive global optimization.
Solution Approach 2:
The patent applies partial optimization through learned weighting schemes that focus computational effort on the most critical data points and dimensions. Rather than performing complete global optimization on all data, the neural network identifies and optimizes the most influential subsets, achieving near-global-optimization accuracy with significantly reduced computational time.
Data Source
AI summary
Systems, apparatuses and methods may provide for technology that generates, by a first neural network, an initial set of model weights based on input data and iteratively generates, by a second neural network, an updated set of model weights based on residual data associated with the initial set of model weights and the input data. Additionally, the technology may output a geometric model of the input data based on the updated set of model weights. In one example, the first neural network and the second neural network reduce the dependence of the geometric model on the number of data points in the input data.