Fitted Function Residual Error Visualization via Color Codes
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Solution Overview
Problem
Existing methods for displaying residual errors of fitted functions in multi-dimensional spaces require observers to view multiple graphs simultaneously, making it difficult to accurately assess the quality of the fit, especially in two-dimensional and three-dimensional fits due to perspective rendering.
Innovation Solution
Assigning visual codes to the fitted function based on residual errors, allowing the function to be displayed with integrated visual representations that convey residual information, eliminating the need for a separate residuals graph, using optical densities, colors, or hues to differentiate and quantify error severity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If separate residual error graphs are used to display fit quality, then detailed assessment of local deviations is improved, but the complexity of the display increases and legibility deteriorates due to requiring simultaneous viewing of multiple graphs
Solution Approach 1:
The patent combines the display of the fitted function and residual errors into a single graph by integrating visual codes directly onto the function representation. This merging eliminates the need for separate residual graphs while preserving the ability to assess fit quality, thereby reducing display complexity and improving legibility.
Solution Approach 2:
The patent employs color-coded visual indicators (visual codes) that change based on residual error values. These color variations are superimposed on the fitted function graph, allowing observers to perceive residual error information through color intensity or hue variations without requiring separate graphs, thus maintaining assessment accuracy while simplifying the display.
2Adaptability or versatility
If perspective rendering is used for two-dimensional fits, then the display of multi-dimensional functions is improved, but the visual assignment of residual errors becomes particularly difficult and inaccurate
Solution Approach 1:
The patent applies local quality by assigning visual codes to specific regions or points on the fitted function graph based on their local residual error characteristics. Each location on the graph receives a visual code that reflects the residual error at that particular point, allowing accurate local assessment even in multi-dimensional perspective representations.
3Loss of information
If two graphs are displayed simultaneously for one-dimensional and two-dimensional fits, then comprehensive fit information is provided, but the space requirements increase and the display becomes less legible
Solution Approach 1:
The patent merges the information from what would traditionally require two separate graphs into a single integrated display. By encoding residual error information directly onto the fitted function graph through visual codes, the patent eliminates the need for additional graph space while maintaining complete fit assessment information.
Data Source
AI summary
The invention is directed to a method and an arrangement for displaying residual errors of a function which is fitted to a set of points. In the prior art, the residual errors are displayed in a separate graph apart from the function graph so that it is difficult for an observer to discern the quality of the fit of the function to the data points. An improved method and an improved arrangement make it possible to visually assess the quality of the fit in a simple, accurate manner. According to the invention, visual codes are assigned to the fitted function or to the data points of the point set piecewise or pointwise depending on the residual errors, and the fitted function is displayed graphically at an interface, wherein the fitted function is displayed piecewise or pointwise in the form of the assigned visual codes. The invention is preferably used for raster image spectroscopy with laser scanning microscopes.