Neurophysiological data are very much variable, and while certain patterns are prominent and reproducible (e.g., action potentials, tissue textures, and cells) they by no means can be easily defined precisely in a quantitative way. The chapter is intended for biologists and computer scientists with a keen interest in the theoretical background of the employed techniques and is in part conceived as a tutorial. Presented approaches are generic and thus have broad applicability to time-varying signals and to two- and three-dimensional signals, such as microscopic images. More specialized applications, such as anisotropic diffusion and detection of blob-like and fiber-like structures, are introduced for two-dimensional images, and extensions to three-dimensional images are discussed. The main application of this approach is to build a multidimensional multiscale feature space, which can be subsequently used to learn characteristic fingerprints of the objects of interests. The chapter introduces several differential invariants, which are computed from parametrized Gaussian kernels and their derivatives. Specifically, it presents mathematical morphology and linear scale-space theories as overarching signal processing frameworks without excessive mathematical formalization. The chapter introduces multiscale methods for image analysis and their applications to segmentation of microscopic images.
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