3D Geometry Descriptors via Trace Transform and FFT
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Solution Overview
Problem
Current digital processing of 3D geometries becomes computationally complex due to increased resolution and detail, requiring more efficient methods for descriptor-based tasks like search, recognition, and classification that are robust against spatial and photometrical transformations.
Innovation Solution
A computer-implemented method using the Trace Transform and FFT to generate geometry descriptors that are invariant to spatial and photometrical transformations, with low computational burden, allowing for accurate representation and comparison of 3D geometry regions despite changes in position or orientation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the resolution of 3D geometries is increased to improve detail and resemblance to reality, then the quality of representation is improved, but the computational complexity of digital processing increases
Solution Approach 1:
The patent extracts only the essential geometric features by computing trace transforms that capture the shape characteristics of 3D geometries. Instead of processing all vertices and polygons, the method extracts a condensed representation through trace computation, reducing the data volume while preserving the essential geometric information needed for recognition and classification tasks.
Solution Approach 2:
The patent transforms the geometric representation from vertex-based coordinates to frequency-domain parameters through Fourier transform. This parameter transformation converts spatial domain data into frequency domain descriptors, changing the representation form to achieve computational efficiency while maintaining the ability to represent high-resolution geometries accurately.
2Device complexity
If traditional descriptor methods are used to represent 3D geometries, then the representation is simple, but the descriptors are not robust against spatial and photometrical transformations
Solution Approach 1:
The patent extends the descriptor representation into the frequency domain by applying Fourier transform to the trace data. This dimensional transformation from spatial to frequency domain creates descriptors that are inherently more robust to spatial transformations. The frequency domain representation captures invariant properties that remain consistent under rotation, translation, and scaling operations.
Solution Approach 2:
The patent replaces traditional geometric comparison methods with a frequency-domain analysis approach. Instead of directly comparing vertex coordinates or surface geometries, the method uses Fourier transform to convert geometric data into frequency spectra, substituting mechanical geometric operations with spectral analysis that naturally provides transformation invariance.
Data Source
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AI summary
A computer-implemented method for providing one or more descriptors of a 3D geometry, the method comprising: determining a first key point in the 3D geometry; selecting a plurality of points in a vicinity of the first key point; computing a normal of the first key point and a normal of each point of a plurality of points; computing an angle of each normal of the plurality of points with respect to the normal of the first key point; providing a first matrix comprising the angles computed; applying a Trace Transform to the first matrix thereby providing a second matrix; and applying an FFT to the second matrix thereby providing a descriptor.