Inst. for Perception Res., Eindhoven.
IEEE Trans Image Process. 1997;6(8):1103-16. doi: 10.1109/83.605408.
We introduce new theoretical results on how the local differential structure in images can be described, processed, and coded efficiently by means of the Hermite transform. It is shown that the Hermite transform can take many alternative forms, all of which have their specific advantages. The various forms of the Hermite transform correspond to different ways of coding the local orientation in the image, and we describe a systematic theory, based on well-known principles from vector spaces, for deriving such alternative forms. One specific case, called the sampled Hermite transform, is shown to be especially interesting for adaptive image processing and coding. An application in the field of adaptive noise reduction is included by way of illustration.
我们介绍了新的理论结果，说明如何通过 Hermite 变换有效地描述、处理和编码图像中的局部微分结构。结果表明，Hermite 变换可以采用多种替代形式，所有这些形式都有其特定的优势。Hermite 变换的各种形式对应于对图像中局部方向进行编码的不同方式，我们描述了一种基于向量空间的著名原理的系统理论，用于推导出这些替代形式。一种称为采样 Hermite 变换的特殊情况，对于自适应图像处理和编码特别有趣。通过举例说明了它在自适应降噪领域的应用。
