Within the last decade, several approaches using quaternion numbers to handle and model multiband images in a holistic manner were introduced. The quaternion Fourier transform can be efficiently used to model texture in multidimensional data such as color images. For practical application, multispectral satellite data appear as a primary source for measuring past trends and monitoring changes in forest carbon stocks. In this work, we propose a texture-color descriptor based on the quaternion Fourier transform to extract relevant information from multiband satellite images. We propose a new multiband image texture model extraction, called FOTO++, in order to address biomass estimation issues. The first stage consists in removing noise from the multispectral data while preserving the edges of canopies. Afterward, color texture descriptors are extracted thanks to a discrete form of the quaternion Fourier transform, and finally the support vector regression method is used to deduce biomass estimation from texture indices. Our texture features are modeled using a vector composed with the radial spectrum coming from the amplitude of the quaternion Fourier transform. We conduct several experiments in order to study the sensitivity of our model to acquisition parameters. We also assess its performance both on synthetic images and on real multispectral images of Cameroonian forest. The results show that our model is more robust to acquisition parameters than the classical Fourier Texture Ordination model (FOTO). Our scheme is also more accurate for aboveground biomass estimation. We stress that a similar methodology could be implemented using quaternion wavelets. These results highlight the potential of the quaternion-based approach to study multispectral satellite images.

中文翻译：

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基于四元数的多波段卫星图像纹理分析：在喀麦隆东部地区地上生物量估算中的应用

在过去十年中，引入了几种使用四元数以整体方式处理和建模多波段图像的方法。四元数傅立叶变换可以有效地用于对多维数据（如彩色图像）中的纹理进行建模。对于实际应用，多光谱卫星数据似乎是衡量过去趋势和监测森林碳储量变化的主要来源。在这项工作中，我们提出了一种基于四元数傅立叶变换的纹理颜色描述符，以从多波段卫星图像中提取相关信息。我们提出了一种新的多波段图像纹理模型提取，称为 FOTO++，以解决生物量估计问题。第一阶段包括从多光谱数据中去除噪声，同时保留冠层的边缘。之后，由于四元数傅立叶变换的离散形式，颜色纹理描述符被提取，最后使用支持向量回归方法从纹理索引推导出生物量估计。我们的纹理特征是使用由来自四元数傅立叶变换幅度的径向谱组成的向量建模的。我们进行了几次实验，以研究我们的模型对采集参数的敏感性。我们还评估了它在合成图像和喀麦隆森林的真实多光谱图像上的性能。结果表明，我们的模型比经典的傅立叶纹理排序模型（FOTO）对采集参数更稳健。我们的方案对于地上生物量估计也更准确。我们强调可以使用四元数小波实现类似的方法。