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<p>A novel, fast and simple approach to model full-analytical two-dimensional (2D) and three-dimensional (3D) spatial shapes is presented. The concept of this study is inspired from the behavior of the Butterworth Low-pass filter, used in signal and image processing, at different orders, where it behaves like ideal filter as the filter’s order goes to infinity and close to Gaussian (normal) distribution for very small orders. Different 2D polygons are modeled such as Rectangle, Parallelogram, Trapezoid, Triangle, Rhombus-Diamond, Hexagon and Octagon. Also, different 3D polygons are modeled such as Cuboid, Parallelepiped, Cylinder, Prism, Pyramid, Cone, Hexagonal-Prism, Octagon-Prism, Dough-Rolling-Pin and others. Those 2D and 3D shapes are modeled by contributing the Butterworth filter formula in the semi-axes of the ellipse and ellipsoid mathematical equations respectively. The 2D and 3D polygons can be modeled with sharp or smooth edges by changing the Butterworth order. By modifying some of the 3D shapes mathematical formula other biomedical 3D shapes can be modeled such as Bacillus-Bacteria, Bacteriophage and Sickle red blood cell 3D shapes. The 2D and 3D shapes can be selectively shifted or/and rotated with different angles using the 2D and 3D rotation matrix respectively without changing the relative Euclidean distances between the shape’s pixels. The 2D or 3D generated shapes can be detected using a&#xa0;powerful&#xa0;tool,&#xa0;for graphic element extraction from images, such as Hough transform for&#xa0;recognition&#xa0;of the scale, center coordinates and rotation angles for specific parametric shape in 2D, or 3D space respectively.</p>

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Novel method for modeling 2d and 3D shapes analytically with biomedical applications

  • 期刊论文

  • 发表日期：

    2025年3月4日

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  • Isam Abu-Qasmieh

摘要

A novel, fast and simple approach to model full-analytical two-dimensional (2D) and three-dimensional (3D) spatial shapes is presented. The concept of this study is inspired from the behavior of the Butterworth Low-pass filter, used in signal and image processing, at different orders, where it behaves like ideal filter as the filter’s order goes to infinity and close to Gaussian (normal) distribution for very small orders. Different 2D polygons are modeled such as Rectangle, Parallelogram, Trapezoid, Triangle, Rhombus-Diamond, Hexagon and Octagon. Also, different 3D polygons are modeled such as Cuboid, Parallelepiped, Cylinder, Prism, Pyramid, Cone, Hexagonal-Prism, Octagon-Prism, Dough-Rolling-Pin and others. Those 2D and 3D shapes are modeled by contributing the Butterworth filter formula in the semi-axes of the ellipse and ellipsoid mathematical equations respectively. The 2D and 3D polygons can be modeled with sharp or smooth edges by changing the Butterworth order. By modifying some of the 3D shapes mathematical formula other biomedical 3D shapes can be modeled such as Bacillus-Bacteria, Bacteriophage and Sickle red blood cell 3D shapes. The 2D and 3D shapes can be selectively shifted or/and rotated with different angles using the 2D and 3D rotation matrix respectively without changing the relative Euclidean distances between the shape’s pixels. The 2D or 3D generated shapes can be detected using a powerful tool, for graphic element extraction from images, such as Hough transform for recognition of the scale, center coordinates and rotation angles for specific parametric shape in 2D, or 3D space respectively.