This paper presents an edge-detection method that is based on the morphological gradient technique and generalized type-2 fuzzy logic The theory of alpha planes is used to implement generalized type-2 fuzzy logic for edge detection For the defuzzification process, the heights and approximation methods are used Simulation results with a type-1 fuzzy inference system, an interval type-2 fuzzy inference system, and with a generalized type-2 fuzzy inference system for edge detection are presented The proposed generalized type-2 fuzzy edge-detection method was tested with benchmark images and synthetic images We used the merit of Pratt measure to illustrate the advantages of using generalized type-2 fuzzy logic

Edge-Detection Method for Image Processing Based on Generalized Type-2 Fuzzy Logic

Edge detectors have traditionally been an essential part of many computer vision systems. There are different methods that have been proposed for improving edge detection in real images. This paper proposes an edge detection method based on the Sobel technique and generalized type-2 fuzzy logic systems. To limit the complexity of handling generalized type-2 fuzzy logic, the theory of $$\alpha $$?-planes is used. Simulation results are obtained with the Sobel operator (without fuzzy logic), then with a type-1 fuzzy logic system (T1FLS), an interval type-2 fuzzy logic system (IT2FLS) and with a generalized type-2 fuzzy logic system (GT2FLS). The proposed generalized type-2 fuzzy edge detection method is tested with synthetic images with promising results. To illustrate the advantages of using generalized type-2 fuzzy logic in combination with the Sobel operator, the figure of merit of Pratt measure is applied to measure the accuracy of the edge detection process.

An improved sobel edge detection method based on generalized type-2 fuzzy logic

A comprehensive review on type 2 fuzzy logic applications: Past, present and future

The optimization of the antecedent parameters for a type 2 fuzzy system of edge detection is presented.The goal of interval type-2 fuzzy logic in edge detection methods is to provide the ability to handle uncertainty.Results show that the Cuckoo search provides better results in optimizing the type-2 fuzzy system. This paper presents the optimization of a fuzzy edge detector based on the traditional Sobel technique combined with interval type-2 fuzzy logic. The goal of using interval type-2 fuzzy logic in edge detection methods is to provide them with the ability to handle uncertainty in processing real world images. However, the optimal design of fuzzy systems is a difficult task and for this reason the use of meta-heuristic optimization techniques is also considered in this paper. For the optimization of the fuzzy inference systems, the Cuckoo Search (CS) and Genetic Algorithms (GAs) are applied. Simulation results show that using an optimal interval type-2 fuzzy system in conjunction with the Sobel technique provides a powerful edge detection method that outperforms its type-1 counterparts and the pure original Sobel technique.

Optimization of interval type-2 fuzzy systems for image edge detection

Fusion of convolution neural network, support vector machine and Sobel filter for accurate detection of COVID-19 patients using X-ray images.

An Improved Canny Edge Detection Algorithm Based on Type-2 Fuzzy Sets

Voxelation today is not only limited to discretization and representation of 3D objects, but has also been gaining tremendous importance in rapid prototyping through 3D printing. In this paper, we introduce a novel technique for discretization of a sphere in the integer space, which gives rise to a set of mathematically accurate, 3D-printable physical voxels up to the desired level of precision. The proposed technique is based on an interesting correspondence between the voxel set forming a discrete sphere and certain easy-to-compute integer intervals defined by voxel position and sphere dimension. It gives us several algorithmic leverages, such as computational sufficiency with simple integer operations and amenability to layer-by-layer additive fabrication. Theoretical analysis, prototype characteristics, and experimental results demonstrate its efficiency, versatility, and further prospects.

Layer the sphere

A discrete spherical geodesic path between two voxels s and t lying on a discrete sphere is a/the 1-connected shortest path from s to t, comprising voxels of the discrete sphere intersected by the real plane passing through s, t, and the center of the sphere. We show that the set of sphere voxels intersected by the aforesaid real plane always contains a 1-connected cycle passing through s and t, and each voxel in this set lies within an isothetic distance of $\frac32$ from the concerned plane. Hence, to compute the path, the algorithm starts from s, and iteratively computes each voxel p of the path from the predecessor of p. A novel number-theoretic property and the 48-symmetry of discrete sphere are used for searching the 1-connected voxels comprising the path. The algorithm is output-sensitive, having its time and space complexities both linear in the length of the path. It can be extended for constructing 1-connected discrete 3D circles of arbitrary orientations, specified by a few appropriate input parameters. Experimental results and related analysis demonstrate its efficiency and versatility.

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Ranita Biswas

Papers

An Improved Canny Edge Detection Algorithm Based on Type-2 Fuzzy Sets

Layer the sphere

On Finding Spherical Geodesic Paths and Circles in ℤ3

On different topological classes of spherical geodesic paths and circles in Z 3

From prima quadraginta octant to lattice sphere through primitive integer operations