Response Function Determination via Rank Minimization

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Solution Overview

Problem

Existing technologies lack a unified framework for determining the response function of devices, particularly in scenarios where input data is unavailable or limited, leading to issues in computer vision applications due to assumed linear relationships between sensor irradiance and recorded intensity.

Innovation Solution

Transforming the problem of determining the response function into a rank minimization problem, where input data is arranged into a matrix form to find an inverse function that minimizes the rank, allowing for the recovery of the response function based on properties like monotonicity and continuity.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If ad-hoc algorithms are used to determine response function, then specific calibration tasks can be performed, but no unified framework is provided and reliability is insufficient

Engineering Contradiction:

Improveunified frameworkVSAvoidresponse function determination accuracy

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The patent applies universality by formulating response function determination as a rank minimization problem that can handle multiple calibration scenarios (known irradiance, unknown irradiance, single image, multiple images) within a single unified framework, eliminating the need for separate ad-hoc algorithms for each case

Inventive Principle:

Principle #6Universality (Multi-functionality)

2Device complexity

If linear relationship between sensor irradiance and recorded intensity is assumed, then computation is simplified, but measurement precision deteriorates due to unaccounted nonlinearity

Engineering Contradiction:

Improvecomputation complexityVSAvoidirradiance reconstruction accuracy

Core Design Contradiction:

Device complexityVSMeasurement precision

Solution Approach 1:

The patent inverts the approach by not assuming linearity and instead seeking a nonlinear response function through rank minimization. The inverse function is determined by minimizing the rank of the transformed observation matrix, which naturally captures nonlinear relationships without requiring explicit linear assumptions

Inventive Principle:

Principle #13The other way round (Inversion)

3Measurement precision

If rank minimization framework is applied, then measurement precision and reliability are improved, but device complexity increases due to matrix operations

Engineering Contradiction:

Improveresponse function determination accuracyVSAvoidalgorithm complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent changes the parameter space by transforming the response function determination problem into a rank minimization problem in matrix space. By working with matrix rank instead of direct function fitting, the method achieves higher precision while the complexity is managed through standard linear algebra operations rather than complex optimization procedures

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS8928781B2Response function determination by rank minimization

Publication Date: 2015.01.06 MICROSOFT TECHNOLOGY LICENSING LLC

AI summary

A response function of a device may be determined using rank minimization to transform a problem of determining a response function of the device into a framework of a rank minimization problem. A function is identified that minimizes a rank of an observation matrix which includes data of observations obtained by the device. This transformation may be used to determine a response function of the device under various conditions and to determine response functions of different devices in a unified framework.