Tchebichef Moment Shape Descriptor for Partial Point Clouds
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Solution Overview
Problem
Existing 3D shape descriptors are ineffective for feature extraction and recognition from low-resolution, partial point cloud data generated by mobile and standoff sensors due to their dependency on dense and smooth full-body scans, which are often degenerated by self-occlusions and viewing angle variations.
Innovation Solution
A multi-scale 3D shape descriptor based on discrete orthogonal Tchebichef moments (TMSD) is developed, combined with a voxelization scheme for translation, scale, and resolution invariance, allowing for effective characterization of low-resolution partial point clouds.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing 3D shape descriptors are used for feature extraction from point cloud data, then they work well for dense full-body scans, but they fail for low-resolution partial point clouds from mobile sensors
Solution Approach 1:
The patent transforms the point cloud data into a different parameter space by computing Tchebichef moments, which are algebraic invariants that capture shape characteristics. This parameter transformation allows the descriptor to work reliably on partial point clouds by focusing on global shape properties rather than local surface details that are lost in low-resolution data.
Solution Approach 2:
The patent introduces Tchebichef moments as an intermediary representation between the raw point cloud data and the final shape descriptor. These moments serve as a bridge that converts geometric information into a form that is both compact and robust to partial observations, enabling reliable feature extraction from degraded data.
2Reliability
If voxelization scheme is applied to achieve translation, scale, and resolution invariance, then the descriptor becomes more robust, but the computational complexity increases
Solution Approach 1:
The patent applies voxelization as a preliminary processing step before computing Tchebichef moments. By pre-processing the point cloud into a voxel grid representation, the method establishes translation, scale, and resolution invariance early in the pipeline, which simplifies subsequent moment computation and reduces the overall computational burden despite the initial voxelization cost.
Solution Approach 2:
The patent segments the continuous point cloud space into discrete voxel cells, creating a grid-based representation. This segmentation transforms the continuous geometric problem into a discrete one, making the computation of Tchebichef moments more efficient and enabling invariance properties without requiring complex continuous transformations.
3Loss of information
If Tchebichef moments are computed for multi-scale characterization, then the descriptor captures more shape details, but the processing time increases
Solution Approach 1:
The patent computes Tchebichef moments at multiple scales by periodically applying the moment computation to voxel grids at different resolution levels. This multi-scale periodic computation captures shape details at various levels of abstraction, allowing the descriptor to retain comprehensive shape information while maintaining efficient processing through the regular structure of the Tchebichef moment algorithm.
Data Source
AI summary
A process and apparatus are provided to characterize low-resolution partial point clouds for object recognition or query. A partial point cloud representation of an object is received. Zero and first order geometric moments of the partial point cloud are computed. A location of a center of a point cloud mass is computed using the geometric moments. A cubic bounding box is generated centered at the location of the mass center of the point cloud, with one side of the box bounding the point cloud at its longest semi-axis. The bounding box is divided into a three dimensional grid. A normalized voxel mass distribution is generated over the three dimensional grid. Tchebichef moments of different orders are calculated with respect to the voxel mass distribution in the grid. Low-order moments are collected to form TMSDs. Similarity is compared between the TMSD of the point cloud with TMSDs of other point clouds.