Curve Fitting via Iterative Digital Filtering and Polygon Transformation
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Solution Overview
Problem
Existing curve fitting methods, particularly those using polynomial splines, often require laborious interactive improvements to achieve acceptable fitting quality, especially when dealing with noisy data points, and do not effectively integrate digital filtering into the curve generation process.
Innovation Solution
A system and method that iteratively performs global filtering and piecewise transformation on an upsampled polygonal representation of data points, using a cycle of filtering and reshaping to converge on a fitting curve, with stability conditions to ensure convergence and adjustability of filtering parameters for spectral content control.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Extent of automation
If polynomial splines are used for curve fitting, then the curve can be generated automatically, but laborious interactive improvements are required to achieve acceptable fitting quality
Solution Approach 1:
The patent merges digital filtering operations directly into the curve generation process, combining what were previously separate steps (filtering as preprocessing, curve fitting as separate operation) into a unified iterative process where filtering and piecewise transformation occur simultaneously until convergence
Solution Approach 2:
The patent implements an iterative feedback loop where the filtered polygon is used to generate a new interpolation polygon, which is then filtered again, continuously refining the result until convergence criteria are met, thereby automatically improving fitting quality without manual intervention
2Shape
If digital filtering is applied to noisy data points, then the curve smoothness is improved, but the fitting accuracy to original data points may deteriorate
Solution Approach 1:
The patent uses a dynamic iterative process where the filtering strength and transformation parameters are adjusted based on convergence criteria and stability conditions, allowing the system to adaptively balance smoothness and accuracy by controlling the number of iterations and filter application intensity
Solution Approach 2:
The patent changes filtering parameters such as filter type, filter strength, and sampling density dynamically during the iterative process, using stability conditions to determine when to stop filtering and when to continue, thereby optimizing the balance between smoothness and fidelity to original data
3Ease of operation
If interactive manipulation of control polygon is used, then the curve can be adjusted manually, but the process becomes less automated and more time-consuming
Solution Approach 1:
The patent implements self-service automation where the system automatically performs the curve optimization process by iteratively applying filtering and transformation operations until convergence, eliminating the need for manual user intervention to adjust control points while maintaining ease of use through automatic parameter optimization
Data Source
AI summary
In one embodiment, a method for curve generation includes forming an initial interpolation polygon using samples within input data as interpolation knots, and upsampling the interpolation polygon by inserting extra samples in each segment between interpolation knots. A filter is then passed throughout a sequence of samples representing the upsampled interpolation polygon. Next, the interpolation polygon is substituted with the filtered polygon converted into a next interpolation polygon using segment-by-segment transformations, where segments of the filtered polygon are delimited by consecutive samples corresponding to interpolation knots, and each segment is transformed to fit between respective interpolation knots. Further, the passing of the filter and the substitution of the current interpolation polygon are repeated until a predefined condition is satisfied, to provide fitting curves.