Surface Similarity Determination via Variable Curvature Embedding

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Solution Overview

Problem

Current methods for determining similarity between surfaces, especially non-planar surfaces, face challenges due to metric distortions introduced by embedding into high-dimensional spaces, limiting the accuracy of surface matching in applications like face recognition and security systems.

Innovation Solution

A method and apparatus that calculate an extremal value of an objective function describing the embedding of a probe surface into an embedding space with non-constant sectional curvature, allowing for similarity determination between non-planar probe and model surfaces represented by point-clouds, using techniques like multiresolution optimization and geodesic distance calculations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If surfaces are embedded into high-dimensional spaces for similarity determination, then surface matching capability is improved, but metric distortions are introduced that reduce accuracy

Engineering Contradiction:

Improvesurface matching capabilityVSAvoidsimilarity determination accuracy

Core Design Contradiction:

Adaptability or versatilityVSMeasurement precision

Solution Approach 1:

The patent changes the mathematical parameters of the embedding space from constant curvature (Euclidean) to variable curvature (Riemannian) to better represent the intrinsic geometry of surfaces, thereby reducing metric distortions while maintaining matching capability

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent introduces a Riemannian manifold as an intermediary structure between the probe surface and model surface, using geodesic distances on this manifold to compute similarity measures that avoid the metric distortions of direct high-dimensional embedding

Inventive Principle:

Principle #24Intermediary (Mediator)

2Reliability

If 3D surface geometry information is used for recognition, then robustness to illumination and viewpoint is improved, but computational complexity increases

Engineering Contradiction:

Improverecognition robustnessVSAvoidcomputation power requirements

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent extracts the essential geometric information by computing geodesic distances on the surface manifold, which capture intrinsic geometry while filtering out extrinsic factors like viewpoint and illumination, thereby reducing computational requirements compared to full 3D processing

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent transforms 3D surface data into a 2D manifold representation with variable curvature, reducing the dimensionality and complexity of computations while preserving the essential geometric features needed for robust recognition

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

Data Source

PatentUS8280150B2Method and apparatus for determining similarity between surfaces

Publication Date: 2012.10.02 INTEL BENELUX

AI summary

A method for determining similarity between a non-planar probe surface and a non-planar model surface is disclosed. The method comprises calculating an extremal value of an objective function describing embedding of the probe surface into an embedding space having a non-constant sectional curvature; and determining similarity between the probe surface and the model surface based on the extremal value.