3D Object Rotation Matrix Estimation Without Gram-Schmidt
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Solution Overview
Problem
Existing neural network models struggle with poor performance in rotation estimation due to the need for Gram-Schmidt orthogonalization (GS processing) to convert a 3×2 matrix into a 3×3 rotation matrix, leading to issues like gradient backflow and numerical gradient errors, resulting in inaccurate object model rotation.
Innovation Solution
The method involves obtaining a first matrix from the target object's information, which is then unbiased Gram-Schmidt orthogonalized to obtain a second rotation matrix, allowing direct rotation of the object model without GS processing, thereby improving model performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Gram-Schmidt orthogonalization processing is performed on a 3×2 matrix to obtain a 3×3 rotation matrix, then a rotation matrix can be obtained for object model rotation, but the model training process becomes difficult and performance deteriorates due to gradient backflow and numerical gradient errors
Solution Approach 1:
The patent extracts and removes the Gram-Schmidt orthogonalization processing step from the training pipeline. Instead of requiring the neural network to output a 3×2 matrix that undergoes GS processing, the model directly outputs a 3×3 rotation matrix, eliminating the source of gradient backflow and numerical errors that plagued the training process.
Solution Approach 2:
The patent changes the output parameter structure from a 3×2 matrix to a 3×3 rotation matrix. This parameter change allows the model to directly generate valid rotation matrices without requiring subsequent orthogonalization processing, thereby improving both training stability and rotation estimation accuracy.
2Measurement precision
If Gram-Schmidt orthogonalization processing is used to convert a 3×2 matrix to a 3×3 rotation matrix, then rotation estimation can be completed, but numerical gradient errors occur during training
Solution Approach 1:
The patent removes the Gram-Schmidt orthogonalization processing step that caused numerical gradient errors. By having the neural network directly output a 3×3 rotation matrix, the problematic conversion step is eliminated, ensuring training stability while maintaining rotation estimation precision.
Solution Approach 2:
Instead of generating a 3×2 matrix and then converting it to a 3×3 rotation matrix through GS processing, the patent inverts the approach by having the model directly generate the final 3×3 rotation matrix. This inversion eliminates the intermediate conversion step that introduced numerical errors.
3Productivity
If a 3×2 matrix is output by the neural network model, then the model structure is simpler, but GS processing is required which is not conducive to model training
Solution Approach 1:
The patent changes the output parameter structure from a 3×2 matrix to a 3×3 rotation matrix. Although this increases the output dimension, it eliminates the need for subsequent Gram-Schmidt processing, thereby improving training efficiency and overall productivity.
Data Source
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AI summary
This application discloses an object model rotation method and a related device thereof. A target model provided in the method can accurately complete rotation estimation, to accurately complete rotation of an object model. The method in this application includes: After information about a target object in a first state is obtained, the information may be input into the target model. Next, the information may be processed by using the target model, to obtain a first matrix, where the first matrix is an n-order matrix, and n is a positive integer greater than or equal to 2. Then, the first matrix may be orthogonalized to obtain a second matrix, where the second matrix is an n-order rotation matrix. Finally, a preset n-dimensional model of the target object may be rotated directly based on the second matrix, to obtain a rotated n-dimensional model of the target object. The preset n-dimensional model of the target object indicates the target object in a second state, and the rotated n-dimensional model of the target object indicates the target object in the first state.