Local Regression Shaping Matrix for Color Transformation Accuracy
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Solution Overview
Problem
Existing local linear regression methods in color imaging applications, such as printer and scanner characterization, face challenges in accurately approximating complex non-linear transforms due to the intuitive choice of weighting functions, which can lead to large regression errors, especially with sparse training data, and fail to optimize the shape and orientation of neighborhoods for improved accuracy.
Innovation Solution
The introduction of a shaping matrix in the weight function to optimize the shape and orientation of neighborhoods, allowing for the use of an iterative alternating least squares algorithm to jointly minimize the cost function and derive the regression and shaping parameters, ensuring optimal local transforms and reducing regression errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If intuitive weight functions are used in local regression, then the implementation is simple, but the regression accuracy deteriorates with sparse training data
Solution Approach 1:
The patent changes the parameters of the weight function by introducing a shaping matrix that modifies the distance metric. Instead of using a simple Euclidean distance, the patent transforms the distance calculation to account for the local geometry of the training data, thereby improving regression accuracy while maintaining implementation feasibility through parameter optimization.
Solution Approach 2:
The patent performs preliminary computation of the shaping matrix during the training phase by analyzing the covariance structure of the training data. This preliminary action prepares the optimal weight function parameters in advance, so that during actual regression tasks, the improved accuracy is achieved without adding significant computational overhead.
2Device complexity
If a single global fit is used for color transformation, then the model is simple, but the accuracy deteriorates for complex non-linear transforms
Solution Approach 1:
The patent segments the global color transformation problem into multiple local linear regression problems. By dividing the input space into local neighborhoods and fitting separate linear models to each region, the patent captures complex non-linear transformations through composition of simple local fits, thereby improving accuracy without requiring a single complex global model.
Solution Approach 2:
The patent applies local quality by allowing different linear transformation parameters in different regions of the color space. Each local neighborhood has its own optimized regression parameters, enabling the model to adapt to local variations in the non-linear transformation, thus achieving high accuracy for complex color mappings while keeping each local model simple.
3Productivity
If the neighborhood shape is not optimized, then the computation is faster, but the regression error increases for sparse training data
Solution Approach 1:
The patent computes the optimal neighborhood shape parameters (shaping matrix) in advance during the training phase by analyzing the data distribution. This preliminary computation stores the optimized geometric parameters, so that during actual regression operations, the system can quickly apply the pre-determined optimal neighborhood shapes without performing complex optimization, thus maintaining both speed and accuracy.
Solution Approach 2:
The patent optimizes the geometric parameters of the neighborhood by transforming the standard spherical neighborhood into an ellipsoidal shape based on the local data covariance. This parameter change adapts the neighborhood geometry to the actual data distribution, improving regression accuracy for sparse data while the optimized parameters enable efficient computation during inference.
Data Source
AI summary
This disclosure provides methods, apparatus and systems for performing image processing regression for approximating multidimensional color transformation. According to an exemplary method, a shaping matrix is selected to minimize a cost function associated with a local linear regression representation of the color transformation. In addition, an alternating least squares algorithm is utilized to jointly optimize regression and shaping parameters.