Fractional Differential Operator Edge Detection Using Gaussian Kernel Approximation
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Solution Overview
Problem
Existing edge detection methods using fractional derivatives in image processing yield unsatisfactory results due to noise sensitivity and require larger mask lengths for accurate detection.
Innovation Solution
The method employs a modified Riesz space fractional differential operator with a scaled Gaussian kernel approximation to compute fractional derivatives, allowing for more accurate edge detection with smaller mask lengths and eliminating the need for additional noise suppression integration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional fractional differential operators are used for edge detection, then edge detection capability is provided, but noise sensitivity increases and detection accuracy deteriorates
Solution Approach 1:
The patent changes the order parameter of the differential operator from conventional integer values (1st order, 2nd order) to optimized fractional values. By selecting specific fractional orders within certain ranges, the operator achieves better noise suppression while maintaining edge detection sensitivity, thus improving accuracy without increasing noise sensitivity
Solution Approach 2:
The patent introduces adaptive fractional order parameters that can dynamically adjust based on local image characteristics. This dynamic adaptation allows the operator to optimize its behavior for different regions of the image, achieving high detection accuracy while automatically adapting to noise levels in different areas
2Measurement precision
If conventional fractional differential operators are used for edge detection, then edge detection is performed, but mask length must be increased to achieve accurate detection
Solution Approach 1:
The patent optimizes the fractional order parameter to achieve accurate edge detection with shorter mask lengths. By carefully selecting fractional orders that balance local and global image information, the method achieves high detection accuracy without requiring excessively long masks, thus reducing the mask length parameter while maintaining precision
Solution Approach 2:
The patent uses fractional differential operators that capture essential edge information with partial integration over the mask region, rather than requiring complete integration over very long ranges. This partial action approach achieves sufficient detection accuracy with reduced mask lengths
Data Source
AI summary
Methods are described for detecting an edge of an object within an image with a fractional differential operator. Methods are also described for calculating 3D information using a strip pattern and the disclosed edge detection method. The fractional differential operator may be a modified Riesz space fractional differential operator. When calculating the fractional derivative of the image, a kernel approximation, in which a scaled Gaussian kernel function or a simplified scaled Gaussian kernel function, is applied to discretize the modified Riesz space fractional differential operator locally. The disclosed method improves the accuracy of edge detection, eliminates the need of applying additional fractional integration for noise suppression, and requires a smaller mask length to achieve desired accuracy.