Sub-sample Motion Estimation via Quadratic Fitting Segmentation
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Solution Overview
Problem
Current motion estimation techniques in signal processing, such as cross-correlation and spline-based methods, face limitations in accurately estimating sub-sample displacements without incurring significant computational costs, leading to systematic errors and high bias, especially in multidimensional applications like medical imaging and ultrasound.
Innovation Solution
The method processes discrete data samples to form a piecewise continuous representation using non-separable multidimensional splines, computes an error function to minimize discrepancies between datasets, and determines alterations that optimize this error, allowing for precise estimation of sub-sample displacements with reduced computational burden.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If cross-correlation and pattern matching techniques are applied to sampled data, then motion estimation can be performed, but the estimation is limited to multiples of the sample distance and cannot achieve sub-sample precision
Solution Approach 1:
The patent segments the continuous motion estimation problem into discrete steps: first performing cross-correlation at sample intervals to identify candidate displacement ranges, then applying quadratic fitting within those narrowed ranges to achieve sub-sample precision. This segmentation allows the algorithm to obtain accurate results without searching the entire possible displacement space, reducing computational complexity while maintaining high precision.
Solution Approach 2:
The patent applies partial action by using quadratic fitting only in the specific displacement ranges identified by cross-correlation, rather than applying complex fitting methods across the entire search space. This selective application of refined estimation techniques achieves sub-sample precision where needed while avoiding unnecessary computational overhead in regions where coarse estimation suffices.
2Measurement precision
If interpolation is applied to increase sampling rate, then sub-sample motion estimation becomes possible, but computational cost increases dramatically
Solution Approach 1:
The patent divides the computational task into two phases: a coarse phase using cross-correlation at the original sampling rate to identify candidate displacement intervals, and a fine phase using quadratic fitting only within those identified intervals. This segmentation avoids the need to interpolate the entire dataset at higher sampling rates, thereby maintaining computational efficiency while achieving sub-sample precision in the final estimation.
Solution Approach 2:
The patent performs preliminary cross-correlation analysis at the original sampling rate to pre-identify the relevant displacement search ranges before applying the more computationally intensive quadratic fitting method. This preliminary action narrows down the search space, allowing subsequent sub-sample estimation to be performed efficiently only where necessary, rather than processing the entire data range at high computational cost.
3Measurement precision
If spline-based image registration is applied, then continuous displacement estimation is achieved, but the use of separable spline models limits accuracy and increases computational burden
Solution Approach 1:
The patent segments the displacement estimation into a coarse grid-based cross-correlation step and a refined quadratic fitting step, avoiding the need to implement complex separable spline models across the entire image. This segmentation achieves continuous displacement estimation through simpler mathematical operations, reducing computational burden while maintaining accuracy.
Solution Approach 2:
The patent replaces the mechanical complexity of separable spline model computations with a more efficient mathematical approach: quadratic polynomial fitting. This substitution achieves the same goal of continuous displacement estimation but with significantly reduced computational requirements, as quadratic fitting involves solving simple polynomial equations rather than complex spline system equations.
Data Source
AI summary
Methods, systems and computer program products for estimating changes in an object represented by first and second multidimensional datasets. The first dataset is a reference dataset and the second dataset is an altered dataset. Discrete data samples of the first dataset are processed to form a piecewise continuous representation thereof. An error function is computed for comparisons between discrete data samples in the second dataset and the piecewise continuous representation of the first dataset. An alteration of the second dataset relative to the first dataset that minimizes the error function is determined.