Using integral transforms to the end of lines detection in images with
complex background, makes the detection a hard task needing additional
processing to manage the detection. As an integral transform, the Scale Space
Radon Transform (SSRT) suffers from such drawbacks, even with its great
abilities for thick lines detection. In this work, we propose a method to
address this issue for automatic detection of thick linear structures in gray
scale and binary images using the SSRT, whatever the image background content.
This method involves the calculated Hessian orientations of the investigated
image while computing its SSRT, in such a way that linear structures are
emphasized in the SSRT space. As a consequence, the subsequent maxima detection
in the SSRT space is done on a modified transform space freed from unwanted
parts and, consequently, from irrelevant peaks that usually drown the peaks
representing lines. Besides, highlighting the linear structure in the SSRT
space permitting, thus, to efficiently detect lines of different thickness in
synthetic and real images, the experiments show also the method robustness
against noise and complex background.

使用积分变换进行层析变换中复杂背景图像的线段检测，提出一种方法用于自动检测灰度和二值图像中的粗线性结构，此方法通过计算待调查图像的 Hessian 方向来突出线性结构并减少不相关峰值，实验证明该方法对噪声和复杂背景具有鲁棒性。

引导尺度空间 Radon 变换用于线性结构检测

Guided Scale Space Radon Transform for linear structures detection

Integral transforms are invaluable mathematical tools to map functions into
spaces where they are easier to characterize. We introduce the hyperdimensional
transform as a new kind of integral transform. It converts square-integrable
functions into noise-robust, holographic, high-dimensional representations
called hyperdimensional vectors. The central idea is to approximate a function
by a linear combination of random functions. We formally introduce a set of
stochastic, orthogonal basis functions and define the hyperdimensional
transform and its inverse. We discuss general transform-related properties such
as its uniqueness, approximation properties of the inverse transform, and the
representation of integrals and derivatives. The hyperdimensional transform
offers a powerful, flexible framework that connects closely with other integral
transforms, such as the Fourier, Laplace, and fuzzy transforms. Moreover, it
provides theoretical foundations and new insights for the field of
hyperdimensional computing, a computing paradigm that is rapidly gaining
attention for efficient and explainable machine learning algorithms, with
potential applications in statistical modelling and machine learning. In
addition, we provide straightforward and easily understandable code, which can
function as a tutorial and allows for the reproduction of the demonstrated
examples, from computing the transform to solving differential equations.

超维变换是一种新型的积分变换，将方块可积函数转换为噪声鲁棒、全息、高维表示的超维向量。它提供了辅助其他积分变换的理论基础和见解，与傅里叶、拉普拉斯和模糊变换密切相关。此外，它为超维计算领域提供了强大而灵活的框架，该计算范式在高效和可解释的机器学习算法方面引起了广泛关注，具有在统计建模和机器学习中应用的潜力。