基于超复代数的自然与生物医学图像处理新型计算工作流
Novel computational workflows for natural and biomedical image processing based on hypercomplex algebras
AI总结：
本文提出基于四元数与二维正交平面分解的非数据驱动超复图像处理工作流，用于重着色、去色、增强、染色分离及提升组织学学习模型性能。
摘要：
超复图像处理在一个统合代数与几何原理的范式中扩展了传统技术。本工作利用四元数和二维正交平面分解框架（将表示一个像素的四元数分解为成对的正交二维平面），通过以下计算工作流和成果开展自然/生物医学图像分析：自然/生物医学图像重新着色、自然图像去色、自然/生物医学图像对比度增强、组织学图像中的计算复染与染色分离，以及组织学图像的机器/深度学习流程性能提升。这些工作流分别针对自然图像和生物医学图像进行分析，以展示所提方法的有效性。所提工作流能够调节色彩外观（例如提供替代呈现和灰度转换）与图像对比度，可成为自动化图像处理流程的一部分（例如分离染色成分、增强学习模型），并辅助数字病理学应用（例如增强生物标志物可见性、实现色盲友好呈现）。本工作仅使用基本算术和矩阵运算，在超复数域中提供了一种计算上易于实现的方法，展示了其在各类图像处理任务以及一系列计算机视觉和生物医学应用中的多功能性与一致性。所提非数据驱动方法取得了与文献报告相当或更好的结果（尤其是在涉及知名方法的情况下），展示了兼具实际有效性的稳健理论框架的潜力。文中详细给出了结果、方法和局限性，并讨论了有前景的扩展方向，强调了面向自然与生物医学图像、特征丰富的数学/计算框架的潜力。
英文摘要：
Hypercomplex image processing extends conventional techniques in a unified paradigm encompassing algebraic and geometric principles. This work leverages quaternions and the two-dimensional orthogonal planes split framework (splitting of a quaternion - representing a pixel - into pairs of orthogonal 2D planes) for natural/biomedical image analysis through the following computational workflows and outcomes: natural/biomedical image re-colorization, natural image de-colorization, natural/biomedical image contrast enhancement, computational re-staining and stain separation in histological images, and performance gains in machine/deep learning pipelines for histological images. The workflows are analyzed separately for natural and biomedical images to showcase the effectiveness of the proposed approaches. The proposed workflows can regulate color appearance (e.g. with alternative renditions and grayscale conversion) and image contrast, be part of automated image processing pipelines (e.g. isolating stain components, boosting learning models), and assist in digital pathology applications (e.g. enhancing biomarker visibility, enabling colorblind-friendly renditions). Employing only basic arithmetic and matrix operations, this work offers a computationally accessible methodology - in the hypercomplex domain - that showcases versatility and consistency across image processing tasks and a range of computer vision and biomedical applications. The proposed non-data-driven methods achieve comparable or better results (particularly in cases involving well-known methods) to those reported in the literature, showcasing the potential of robust theoretical frameworks with practical effectiveness. Results, methods, and limitations are detailed alongside discussion of promising extensions, emphasizing the potential of feature-rich mathematical/computational frameworks for natural and biomedical images.
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