Hyperbolic Image Convolution With Hierarchical Pixel Weighting
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Solution Overview
Problem
Existing data learning methods in hyperbolic space are limited to fields with hierarchical data structures, such as knowledge graphs and synonym hierarchies, and have low usability in the computer vision field.
Innovation Solution
An image convolution method that embeds image feature vectors into hyperbolic feature vectors, allocates hierarchical weights based on geodesic distances, and applies these weights to improve learning efficiency and accuracy in spatial propagation neural networks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Stability of the object's composition
If data learning methods in hyperbolic space are applied to computer vision fields, then hierarchical relationship formation is improved, but usability is reduced due to limitation to fields with hierarchical data structures
Solution Approach 1:
The patent applies hyperbolic space data learning methods to computer vision image processing, extending the applicability beyond hierarchical data structures to general image feature extraction and convolution operations, thereby achieving multi-functionality and versatility in different application domains
2Measurement precision
If hierarchical weights are allocated to all pixels in hyperbolic feature vectors, then learning accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent allocates hierarchical weights to pixels based on their local importance and affinity in the hyperbolic feature space, rather than uniform treatment of all pixels. This local differentiation approach improves learning accuracy for critical regions while reducing unnecessary computational overhead in less important areas
3Adaptability or versatility
If image feature vectors are embedded into hyperbolic space, then hierarchical property utilization is improved, but embedding complexity increases
Solution Approach 1:
The patent performs preliminary embedding of image feature vectors intohyperbolic space before convolution operations, transforming Euclidean space features intohyperbolic space representations that capture hierarchical relationships. This preliminary transformation enables subsequent efficient hierarchical processing and weight allocation
Data Source
AI summary
A method for performing image convolution by considering a hierarchical relationship of hyperbolic feature vectors in a hyperbolic space is provided. The method includes steps of embedding an image feature vector on a Euclidean space into a hyperbolic feature vector on a hyperbolic space, allocating a hierarchical weight on the hyperbolic feature vector based on a hierarchical property of the hyperbolic feature vector, and convolutioning the hyperbolic feature vector by applying the hierarchical weight.