Multi-Dimensional Data Filtering With Lower-Dimensional Transforms
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Solution Overview
Problem
Existing methods for processing multi-dimensional data objects fail to effectively address the need for improved data processing of multi-dimensional data objects with filtering functions that achieve high-quality filtering of the multi-dimensional data object in all dimensions of the data object while, at the same time, keeping memory consumption and processor load at levels significantly (at least more than one order of magnitude) below the levels required for multi-dimensional filtering with filters having the same dimensionality as the multi-dimensional data object.
Innovation Solution
A computer-implemented method that uses lower-dimensional filter functions to process n-dimensional data objects, applying invertible integral transformations and weight functions to reduce artefacts, allowing for high-quality filtering with reduced memory consumption and processor load.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If n-dimensional filters are used to filter n-dimensional data objects, then filtering quality in all dimensions is improved, but memory consumption and processor load increase significantly
Solution Approach 1:
The patent segments the n-dimensional filtering operation into multiple lower-dimensional filtering steps. Instead of applying a single n-dimensional filter, the method applies a series of (n-1)-dimensional filters sequentially, each operating on a reduced dimensionality subset of the data. This segmentation reduces the memory footprint of each filtering operation while collectively achieving comprehensive n-dimensional filtering coverage.
Solution Approach 2:
The patent transforms the filtering problem from n-dimensional space to (n-1)-dimensional space by applying lower-dimensional filters. Each filter operates in a subspace of dimension n-1, and through multiple such filters applied in sequence, the equivalent effect of an n-dimensional filter is achieved. This dimensionality reduction is the core mechanism for reducing memory consumption while maintaining filtering quality.
2Measurement precision
If n-dimensional filters are used to filter n-dimensional data objects, then filtering quality in all dimensions is improved, but processor load increases significantly
Solution Approach 1:
The patent divides the computationally intensive n-dimensional filtering task into multiple smaller (n-1)-dimensional filtering operations. Each lower-dimensional filter requires fewer computational resources and can be processed more efficiently. The segmented approach allows for better utilization of processing resources and reduces the peak processor load compared to a single monolithic n-dimensional filter operation.
Solution Approach 2:
By reducing the dimensionality of each filtering operation from n to n-1, the patent significantly reduces the computational complexity of each individual filter application. The overall filtering quality is maintained through the application of multiple such reduced-dimensionality filters, each contributing to the suppression of noise and artifacts from different directional perspectives in the n-dimensional data space.
3Quantity of substance
If lower-dimensional filters are used to filter n-dimensional data objects, then memory consumption and processor load are reduced, but filtering quality deteriorates due to loss of higher dimension information
Solution Approach 1:
The patent merges the results of multiple (n-1)-dimensional filtering operations to achieve the equivalent effect of n-dimensional filtering. By combining several lower-dimensional filters that each capture different aspects of the data structure, the method recovers and utilizes information that would otherwise be lost in a single lower-dimensional approach, thereby restoring filtering quality across all n dimensions.
Solution Approach 2:
The patent employs a feedback mechanism where the output of one lower-dimensional filter becomes the input for subsequent filters. This iterative process allows information to be progressively refined and combined across multiple filtering passes, ensuring that higher-dimensional information is not permanently lost but rather reconstructed and utilized through the feedback loop of sequential filtering operations.
Data Source
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AI summary
A computer-implemented method, computer program product and computer system (100) for processing an n-dimensional data object (202) of a metrological investigation received from a data source (200). A plurality of k filtered objects (FO1 to FOB) is calculated by filtering the n-dimensional data object with k filter functions (F1 to F3), wherein each filter function, in the space of the data object, is missing at least one of the n dimensions (x, y, z) of the data object (202) such that none of the n dimensions of the data object is missing in all filter functions. The k filtered objects are transformed by an invertible integral transformation (130) into k transformed filtered objects (TFOL to TFO3) followed by point-wise weighting of each of the k transformed filtered objects with a respective weight function (WF1 to WF3) resulting in k weighted transformed filtered objects (WTFO1 to WTFO3). The k weighted transformed filtered objects are combined into a combined transformed filtered object (CTFO). The combined filtered object is transformed, by applying the inverse (160) of the invertible integral transformation, into a weighted-filtered n-dimensional data object (202wf).