Taylor-Series Gradient Filters for Noise-Resilient Edge Detection
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Solution Overview
Problem
Conventional gradient-based edge detection methods are susceptible to noise, amplify undesirable image noise, and struggle with accurate edge localization due to issues like noise, image sharpness, orientation, and computational complexity, leading to false detections and missed edges, especially in low signal-to-noise ratio environments.
Innovation Solution
Development of two-dimensional high-order Taylor Series expansion-based gradient detection kernels, including a wide view filter and a line filter, which utilize a larger number of pixels for robust noise suppression and accurate edge detection, and a novel angle detection process to determine edge orientations within one degree of their true value.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional gradient-based edge detection methods (Sobel, Prewitt, Roberts kernels) are used, then the computational complexity is low and the methods are easy to apply, but the accuracy of edge detection deteriorates due to noise amplification and susceptibility to noise
Solution Approach 1:
The patent divides the gradient detection process into two separate filters: a wide view filter for noise suppression and a line filter for accurate gradient calculation. This segmentation allows each filter to specialize in one function, resolving the contradiction between ease of application and detection accuracy by combining two simple filters rather than using a single complex kernel.
Solution Approach 2:
The wide view filter acts as an intermediary that processes the image before the line filter. It suppresses noise and provides a cleaned input to the line filter, thereby improving the accuracy of the final edge detection without requiring the line filter itself to be complex.
2Object-affected harmful factors
If larger kernel sizes (5×5, 7×7) are used to improve noise suppression, then the noise suppression capability improves, but the computational complexity increases and the methods become less efficient
Solution Approach 1:
The patent segments the noise suppression function from the gradient calculation function. The wide view filter handles noise suppression with a larger effective area, while the line filter performs accurate gradient calculation with a compact structure. This segmentation achieves noise suppression without requiring the entire gradient calculation kernel to be large and complex.
Solution Approach 2:
The wide view filter serves multiple purposes: it suppresses noise and provides a cleaned input to the line filter. This multi-functionality allows the system to achieve noise suppression without adding separate processing steps, resolving the contradiction between noise suppression and computational efficiency.
3Productivity
If conventional gradient detection methods are used, then the computational speed is high, but the reliability of edge detection deteriorates in low signal-to-noise ratio environments
Solution Approach 1:
The patent segments the processing into two fast, simple filters rather than one complex filter. Both the wide view filter and line filter can be implemented efficiently, maintaining high computational speed while improving reliability through their specialized functions in noise suppression and accurate gradient calculation.
Solution Approach 2:
The wide view filter serves as an intermediary that prepares the image data for the line filter by suppressing noise. This intermediary step improves the reliability of the final edge detection without significantly impacting computational speed, as both filters are designed for efficiency.
4Object-affected harmful factors
If image smoothing filters are applied to reduce noise effects, then the noise suppression improves, but the image quality deteriorates due to edge blurring and loss of gradient information
Solution Approach 1:
The patent segments the noise suppression function into a dedicated wide view filter that is designed not to blur edges. By separating this function from the gradient calculation (performed by the line filter), the system achieves noise reduction without the edge blurring that occurs when smoothing filters are applied directly to the original image for gradient computation.
Solution Approach 2:
The wide view filter applies noise suppression with different characteristics than traditional smoothing filters. It suppresses noise while preserving edge information by designing the filter kernel to maintain local gradients, thereby achieving noise reduction without information loss.
Data Source
AI summary
The disclosure deals with system and method for image gradient and derivative computation image processing. Noise, image sharpness, orientation, empirical parameters, and computational complexity are examples of image gradient and derivative computation challenges. Many traditional kernel-based operators excel at tackling one of these problems, but trade off their ability to handle others. Two new gradient detection kernels based on two-dimensional high order Taylor Series expansion tackle many such problems. The first kernel uses a wide range of the pixels in view to suppress noise, thereby improving the gradient intensities of edges. The second kernel builds on the first to leverage its noise suppression benefits while tackling an additional problem of degraded and low contrast edge boundaries. It can detect smooth lines in the presence of discontinuities and poor quality. The filter architecture allows for precise gradient calculation, edge detection, and orientation determination to less than one degree of the true value even when faced with signal to noise ratios that exceed 0.75.