By Bernd Jahne, Horst Haussecker, Peter Geissler
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Extra resources for Handbook of Computer Vision and Applications
Example text
The chain of processes that lead from the “true” signal to the digital signal include all the steps of the image formation process as illustrated in Fig. 7. First the signal of interest, s(x), such as reflectivity, temperature, etc. of an object is somehow related to the radiance L(x) emitted by the object in a generally not linear function (Volume 1, Chapter 3). In some cases this relation is linear (e. , reflectivity), in others it is highly nonlinear (e. , temperature). Often other parameters that are not controlled or not even known, influence the signal as well.
If a convolution operator is applied to a periodic signal, only its phase and amplitude change, which can be expressed by a complex factor. This complex factor is the (wave number dependent) eigenvalue or transfer function of the convolution operator. At this point, it is also obvious why the Fourier transform is complex valued.
New York: Wiley. 1 Vector spaces and unitary transforms . . . . . . . . 1 Introduction . . . . . . . . . . . . . . 2 Basic properties of unitary transforms . . . . . 3 Significance of the Fourier transform (FT) . . . . 4 Dynamical range and resolution of the FT . . . . 38 Continuous Fourier transform (FT) . . . . . . . . . 1 One-dimensional FT . . . . . . . . . . . 2 Multidimensional FT . . . . . . . . . . . 3 Basic properties . . . .
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