Tensor Train Decompression for Radiance Field Memory Reduction
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Solution Overview
Problem
Current data compression methods for radiance fields are memory-intensive, sensitive to noise, and limited in their ability to handle large datasets and hierarchical spaces, requiring significant memory storage and being inefficient in on-demand evaluation and parameter updates.
Innovation Solution
A computer-implemented method using block tensor train decomposition that reduces memory storage by forming tensor cores with specific rank axes, allowing for efficient compression and decompression of multi-dimensional arrays through gradient descent optimization, enabling robustness to noise and scalability to arbitrary dimensions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If conventional tensor decomposition methods are used to compress radiance fields, then compression is achieved, but memory storage requirements during compression and decompression remain high
Solution Approach 1:
The patent segments the radiance field data into multiple tensor trains, where each tensor train represents a portion of the scene. This segmentation allows processing and storage of smaller tensor cores independently, reducing peak memory requirements while maintaining overall compression quality through the distributed representation across multiple segmented tensor structures.
2Quantity of substance
If SVD-based tensor train decomposition is used, then low-memory representation is achieved, but the method requires storing the whole data to be represented
Solution Approach 1:
The patent applies preliminary action by performing iterative optimization to compute tensor train decompositions progressively, allowing the system to work with smaller data subsets in each iteration rather than requiring all data to be loaded simultaneously. This enables memory-efficient processing through staged computation where intermediate results are stored and refined over multiple passes.
3Adaptability or versatility
If tensor train decomposition with relaxed rank constraints is used, then vector field storage is enabled, but compression quality degrades with noisy data
Solution Approach 1:
The patent dynamically adjusts tensor train rank parameters based on the specific data characteristics and noise levels encountered. By adaptively modifying rank constraints rather than using fixed relaxed constraints, the system maintains compression quality for vector fields while improving robustness to noise through parameter optimization that balances flexibility and stability.
4Measurement precision
If occupancy mask is stored in uncompressed form, then representation accuracy is improved, but memory storage requirement increases significantly
Solution Approach 1:
The patent merges the occupancy mask representation with the tensor train decomposition structure by encoding the mask information within the tensor cores themselves rather than storing it separately in uncompressed form. This integration allows the occupancy information to be represented efficiently alongside the radiance field data, maintaining representation accuracy while significantly reducing total memory storage requirements.
Data Source
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AI summary
A computer-implemented method for compressing a multi-dimensional array of data comprising a plurality of vector elements having the same number R of scalar elements, the method comprising obtaining (E10) D subsequent tensor cores (C1-CD) forming a Tensor Train Decomposition, said method comprising at least one iteration comprising following steps of: • obtaining (E20) current tensor cores; • obtaining (E30) approximations (A1-AB) of B subsequent vector elements (E1-EB) of said array of data by determining matrix product between sections of said tensor cores at indices indexing said B subsequent vector elements; and • modifying (E40) values of said tensor cores with gradient descent, to minimize an approximation error between said B subsequent vector elements and their obtained approximations, and a step of obtaining (E50) compression of said array of data from the Tensor Train Decomposition formed by the tensor cores modified after the plurality of iterations.