Local orientation analysis in images by means of the Hermite transform

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.