Peak-Like Structure Detection via Orthogonal Second Derivatives
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Solution Overview
Problem
Current image processing methods, such as top-hat transforms, are not selective enough to peak-like structures in biological images, leading to under-detections and false-positives due to mixed sensitivity to different morphologies.
Innovation Solution
A method that calculates the second derivative of the intensity characteristic in two orthogonal directions, including the direction of maximum curvature, and determines the output pixel value based on the product of these derivatives, with noise reduction using Gaussian derivatives, to emphasize peak-like structures while minimizing sensitivity to other features.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If top-hat transforms are used for image segmentation, then processing speed is improved and sensitivity to local details is enhanced, but shape selectivity deteriorates leading to mixed sensitivity to peak-like, ridge-like and edge-like structures
Solution Approach 1:
The patent changes the mathematical parameters used in image processing from standard top-hat transforms to second derivative calculations in orthogonal directions. By computing the product of second derivatives (∂²I/∂x² × ∂²I/∂y²) where one direction is the direction of maximum curvature, the method achieves shape-selective detection of peak-like structures while maintaining processing efficiency through systematic parameter transformation.
2Measurement precision
If top-hat transforms are used for image segmentation, then good sensitivity to local details is achieved, but false-positives and under-detections increase due to lack of shape selectivity
Solution Approach 1:
The patent applies local quality by making the processing method sensitive to different structures based on their local geometric properties. The second derivative calculation in the direction of maximum curvature adapts to the local shape characteristics of each feature, providing high sensitivity to peak-like structures while suppressing sensitivity to ridge-like and edge-like structures, thereby reducing false-positives and under-detections.
3Measurement precision
If second derivative calculation is performed in two orthogonal directions including direction of maximum curvature, then shape selectivity for peak-like structures is improved, but computational complexity increases
Solution Approach 1:
The patent applies preliminary action by first identifying the direction of maximum curvature at each pixel location before performing the second derivative calculation. This pre-computation of the principal direction allows the subsequent derivative calculations to be focused and optimized, reducing the overall computational burden while maintaining high shape selectivity for peak-like structures.
Data Source
AI summary
A method of processing an input image produces an output image emphasizing peak-like structures. The input image comprises input pixels and each input pixel has an intensity characteristic. The output image comprises corresponding output pixels and each output pixel has a value. The method comprises the step of calculating for an input pixel the second derivative of the intensity characteristic in two orthogonal directions, one of the directions being the direction of maximum curvature. The product of the two second derivatives is calculated and the value of the output pixel corresponding to the input pixel is determined in dependence on the product.