Abstract
For two decades, techniques based on Partial Differential Equations (PDEs) have been used in monochrome and color image processing for image segmentation, restoration, smoothing and multiscale image representation. Among these techniques, parabolic PDEs have found a lot of attention for image smoothing and image restoration purposes. Image smoothing by parabolic PDEs can be seen as a continuous transformation of the original image into a space of progressively smoother images identified by the "scale" or level of image smoothing. The semantically meaningful objects in an image can be of any size, that is, they can be located at different image scales, in the continuum scale-space generated by the PDE. The adequate selection of an image scale smoothes out undesirable variability that at lower scales constitute a source of error in segmentation and classification algorithms. This paper proposes a framework for generating a scale space representation for a hyperspectral image using PDE methods. We illustrate some of our ideas by hyperspectral image smoothing using nonlinear diffusion. The extension of scalar nonlinear diffusion to hyperspectral imagery and a discussion of how the spectral and spatial domains are transformed in the scale space representation are presented.