Implementation and Theoretical Explanation of the Radon Algorithm

In the following text, I will provide a detailed explanation of the implementation and theoretical principles of the Radon algorithm. I have compiled essential materials that will assist readers in gaining a deeper understanding of the Radon algorithm. In terms of implementation, the Radon algorithm works by computing the lengths and angles of all linear segments within a given geometric object to detect its shape. This method allows for a more accurate determination of the object's shape and size without relying on conventional measurement techniques. From a coding perspective, the algorithm typically involves iterating through different angles (e.g., from 0° to 180° in discrete steps) and calculating line integrals (projections) across the image or geometric data structure. Key functions often include transformation functions for rotating coordinate systems and accumulator arrays for storing projection values. Regarding its theoretical foundation, the Radon algorithm is based on Radon transform theory, which is widely applied in image processing and computer vision. The Radon transform mathematically represents an image as a set of line integrals, forming the basis for techniques like computed tomography (CT) reconstruction. Understanding this algorithm is both fascinating and valuable, as it illuminates fundamental principles and technologies in modern computer science, particularly in areas such as feature extraction, pattern recognition, and medical imaging.