Sub-pixel Displacement Detection via Second Order Taylor Expansion

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Solution Overview

Problem

Conventional methods for detecting sub-pixel displacement are prone to errors, especially with larger displacements, and are sensitive to noise, limiting their accuracy and ability to detect tiny movements.

Innovation Solution

A method and apparatus that utilize interpolation to increase the searching area and resolution, employing a two-stage searching process to capture and compare array images, forming reference and comparison images, and calculating displacement with sub-pixel accuracy.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Device complexity

If the first order Taylor Expansion model is used for displacement detection, then the detection process is simple, but the accuracy deteriorates for larger displacements due to omitted higher order terms

Engineering Contradiction:

Improvedetection process complexityVSAvoiddisplacement detection accuracy

Core Design Contradiction:

Device complexityVSMeasurement precision

Solution Approach 1:

The patent changes the mathematical model from first order Taylor Expansion to second order Taylor Expansion, altering the parameter of polynomial order to improve accuracy while maintaining computational feasibility

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent performs preliminary action by capturing multiple images at different time points and pre-calculating the expansion terms before final displacement computation, reducing the impact of higher order terms on accuracy

Inventive Principle:

Principle #10Preliminary action

2Ease of operation

If partial derivatives are used in displacement detection, then the detection method is straightforward, but the results become sensitive to noise

Engineering Contradiction:

Improvedetection method simplicityVSAvoidnoise sensitivity

Core Design Contradiction:

Ease of operationVSReliability

Solution Approach 1:

The patent merges multiple image data and combines multiple calculation terms in the second order Taylor Expansion model to average out noise effects, reducing overall noise sensitivity while maintaining operational simplicity

Inventive Principle:

Principle #5Merging (Combining)

3Area of stationary object

If conventional correlation method is used with pixel-level resolution, then the searching area is limited to one pixel, but tiny movements smaller than one pixel cannot be detected

Engineering Contradiction:

Improvesearching areaVSAvoidtiny movement detection capability

Core Design Contradiction:

Area of stationary objectVSMeasurement precision

Solution Approach 1:

The patent extends the search from discrete pixel locations to continuous sub-pixel positions by introducing fractional pixel offsets in the Taylor Expansion model, effectively adding a dimensional precision beyond the pixel grid

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

Solution Approach 2:

The patent changes the displacement parameter from integer pixel values to real-valued sub-pixel measurements, enabling detection of movements smaller than one pixel width through the mathematical framework of second order expansion

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS8090221B2Method and apparatus for detecting displacement with sub-pixel accuracy

Publication Date: 2012.01.03 SAMSUNG ELECTRONICS CO LTD

AI summary

A method for detecting displacement with sub-pixel accuracy includes the steps of: capturing a first array image and a second array image; interpolating the first array image to form a reference image; interpolating the second array image to form a comparison image; comparing the reference image with the comparison image so as to obtain a displacement. The present invention also provides an apparatus for detecting displacement with sub-pixel accuracy.