The Hermite transform-theory

The author introduces a scheme for the local processing of visual information, called the Hermite transform. The problem is addressed from the point of view of image coding, and therefore the scheme is presented as an analysis/resynthesis system. The objectives of the present work, however, are not restricted to coding. The analysis part is designed so that it can also serve applications in the area of computer vision. Indeed, derivatives of Gaussians, which have found widespread application in feature detection over the past few years, play a central role in the Hermite analysis. It is also argued that the proposed processing scheme is in close agreement with current insight into the image processing that is carried out by the human visual system. In particular, it is demonstrated that the Hermite transform is in better agreement with human visual modeling than Gabor expansions