Lie Algebra Deep Image Compression
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Solution Overview
Problem
Conventional computer graphics compositing techniques struggle with elements that have varying depth order, particularly volumetric elements like clouds, as they cannot directly compute new pixel values for overlapping regions, leading to suboptimal results.
Innovation Solution
The method involves converting voxel values in a deep image to a Lie algebra using a logarithmic mapping function, applying linear interpolation, and recursively subdividing the image until deviations meet a threshold, allowing for efficient compression and reconstruction of deep images.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional compositing techniques are used, then the processing is simple, but the ability to handle volumetric elements with varying depth order is insufficient
Solution Approach 1:
The patent introduces an intermediary data structure (depth buffer and extended RGBA values) that mediates between the input volumetric elements and the compositing operation. This intermediary structure enables the representation of varying depth order and opacity information, allowing conventional compositing techniques to be extended to handle volumetric elements effectively
Solution Approach 2:
The patent extends the traditional 2D compositing approach by adding depth information as an additional dimension. By representing each pixel with extended RGBA values that include depth ordering information, the system transforms planar compositing into volumetric compositing, enabling proper handling of elements with varying depth order
2Adaptability or versatility
If depth ordering is known a priori, then compositing is straightforward, but elements with varying depth order cannot be handled
Solution Approach 1:
The patent performs preliminary encoding of depth ordering information directly into the pixel data structure before compositing operations. By embedding depth information in the extended RGBA values, the system prepares the data in advance to preserve depth ordering information throughout subsequent processing steps, eliminating the need for a priori depth knowledge
3Productivity
If compression is applied to deep images, then storage efficiency improves, but reconstruction accuracy may be compromised
Solution Approach 1:
The patent extracts and separately stores critical depth ordering information and opacity data from the full voxel representation. By identifying and preserving only the essential information needed for accurate reconstruction, the system achieves effective compression while maintaining reconstruction accuracy for volumetric elements
Solution Approach 2:
The patent transforms the representation parameters of deep image data by converting voxel values to Lie algebra using logarithmic mapping. This parameter transformation enables more efficient compression by exploiting the mathematical properties of the transformed space while preserving the ability to accurately reconstruct the original image through inverse transformation
Data Source
AI summary
Systems, method, and computer program products for compressing a deep image comprising a plurality of voxels by, for each of the plurality of voxels, converting a voxel value to a corresponding value in a Lie algebra based on a logarithmic mapping function, interpolating a first subset of the plurality of values in the Lie algebra using a linear interpolation function applied to a first endpoint and a second endpoint of a first voxel column of the deep image, and upon determining that a deviation of the interpolation of each value in the first subset of the plurality of values does not exceed a threshold, storing an indication of the first endpoint, the second endpoint, and the respective values in the Lie algebra corresponding to the first and second endpoints.