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This thesis investigates advanced signal processing concepts and their application to geometric processing and transformations of images and volumes. In the first part, we discuss the class of transformations that project volume data onto a plane using par ...
We analyze the representation of periodic signals in a scaling function basis. This representation is sufficiently general to include the widely used approximation schemes like wavelets, splines and Fourier series representation. We derive a closed form ex ...
Introduction: A reliable measurement of the physical activity in everyday life should allow a better assessment of the utility and the relevance of a number of medical treatments. Continuous 24-h recordings of posture and motion can be generally useful in ...
We present a new framework for processing point-sampled objects using spectral methods. By establishing a concept of local frequencies on geometry, we introduce a versatile spectral representation that provides a rich repository of signal processing algori ...
We present a new family of 2D orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order α, which may be non-integer. The wavelets have good isotr ...
The Continuous Wavelet Transform (CWT) is an effective way to analyze nonstationary signals and to localize and characterize singularities. Fast algorithms have already been developed to compute the CWT at integer time points and dyadic or integer scales. ...
This chapter focuses on the development of a new \true" two- dimensional representation for images that can capture the intrinsic geo- metrical structure of pictorial information. Our emphasis is on the discrete framework that can lead to algorithmic imple ...
Compact support is undoubtedly one of the wavelet properties that is given the greatest weight both in theory and applications. It is usually believed to be essential for two main reasons: (1) to have fast numerical algorithms, and (2) to have good time or ...
We present a new class of wavelet bases—Fresnelets—which is obtained by applying the Fresnel transform operator to a wavelet basis of L2 . The thus constructed wavelet family exhibits properties that are particularly useful for analyzing and proc ...
We present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable mul ...
