Color Model Inversion via Adaptive Seed Selection
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Solution Overview
Problem
Convergence issues in inverting color device models, particularly due to piecewise linear and bounded device color spaces, lead to inefficiencies in existing iterative algorithms like the local Newton method, which fail to guarantee convergence and are computationally expensive when trying to find solutions far from the initial estimate.
Innovation Solution
A method that restarts the local iterative root finding process with adaptive seeds, using a seed matrix to select a reasonably good initial seed and generating additional seeds through perturbation, allowing for faster and more robust convergence without relying on expensive computational steps.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If the local Newton algorithm is used to invert the color device model, then the computational speed is fast, but the convergence is not guaranteed when the initial estimate is far from the true solution
Solution Approach 1:
The patent applies preliminary action by generating a seed matrix before the inversion process and selecting an appropriate seed based on the input color value. This pre-computation of multiple candidate seeds ensures that at least one seed will be close to the true solution, guaranteeing convergence while maintaining the speed advantage of the local Newton algorithm.
Solution Approach 2:
The patent changes the parameter of the initial estimate by selecting from multiple seeds in the seed matrix rather than using a fixed or single initial estimate. The seed selection process adapts the initial parameter based on the input color value, ensuring the algorithm starts from a favorable position for convergence.
2Ease of manufacture
If the forward model is constructed using tetrahedral interpolation, then the model is piecewise linear and computationally efficient, but the derivative is discontinuous on the facets creating a barrier for iteration
Solution Approach 1:
The patent applies local quality by identifying which tetrahedron contains the current iterate and using only the seeds from that local region in the seed matrix. This localizes the seed selection to the relevant neighborhood, ensuring the initial estimate is close to the solution while maintaining compatibility with the piecewise linear model structure.
Solution Approach 2:
The seed matrix acts as an intermediary between the piecewise linear forward model and the Newton algorithm. It provides a set of pre-computed candidate points that bridge the discontinuity issue, allowing the algorithm to jump over the barriers created by facet discontinuities while maintaining convergence.
3Manufacturing precision
If the device color space is bounded by 0 and 1 in each channel, then the model reflects physical constraints, but the assumption of unbounded independent variables in the Newton algorithm is violated
Solution Approach 1:
The patent applies local quality by generating the seed matrix locally within the bounded color space and selecting seeds that satisfy the boundary constraints. This ensures the algorithm operates within the physical constraints of the device color space while maintaining the mathematical validity of the Newton algorithm.
Solution Approach 2:
The patent changes the parameter handling by working with transformed coordinates or constrained seeds that respect the bounded nature of the color space. This allows the Newton algorithm to operate on parameters that effectively handle the boundaries, resolving the contradiction between physical constraints and algorithmic assumptions.
Data Source
AI summary
A method and apparatus for inverting a color device model. A systematic color device model inversion process restarts a local iterative root finding process with new seeds that are adaptive to the last found solution. Because of the relative simplicity of the logic used, it is more robust and makes less assumptions about the smoothness of the forward model. It is also computationally inexpensive, because a reasonably good seed is chosen from the seed matrix using a fast calculation of distance, instead of running each seed in the seed matrix through the iterative root finding process. In the worst case, including the initial run, N+1 runs of the local iterative root finding process are needed to invert an input point, with N being the number of additional, a posteriori seeds generated.