By George Wolberg
This best-selling, unique textual content makes a speciality of picture reconstruction, real-time texture mapping, separable algorithms, two-pass transforms, mesh warping, and lighting tricks. The textual content, containing all unique fabric, starts off with the background of the sphere and maintains with a overview of universal terminology, mathematical preliminaries, and electronic snapshot acquisition. Later chapters talk about equations for spatial info, interpolation kernels, filtering difficulties, and fast-warping thoughts in accordance with scanline algorithms.
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Additional info for Digital Image Warping
Example text
2: PSF profile. 4. 11) where * denotes the convolution operation, h(x) is used as the convolution kernel, and 7L is the dummy variable of integration. The integration is always performed with respect to a dummy variable (such as 1) and x is a constant insofar as the integration is concerned. Kernel h (I), also known as the filter kernel, is treated as a sliding window that is shifted across the entire input signal. As it makes its way across f (x), a sum of the pointwise products betWeen the two functions is taken and assigned to output g (x).
1, F’ is a hole since it is bypassed in the input—output mapping. In contrast, overlaps occur when consecutive input samples collapse into one output pixel, as depicted in Fig. 1 by output pixel G'. The shortcomings of a point-to-point mapping are avoided by using a four-corner mapping paradigm. This considers input pixels as square patches that may be transformed into arbitrary quadrilaterals in the output image. This has the effect of allowing the input to remain contiguous after the mapping.
The data in f (x) is treated as one period of a periodic signal by replicating itself indefinitely, thereby tiling the input plane with copies of itself. This makes the opposite ends of the signal adjacent by virtue of wraparound from f (N -l) to f (0). Note that this is only a model of the infinite input, given only the small (aperiodic) segment f (x). , no physical replication is necessary. While this permits F (u) to be defined for discrete values of u. it does introduce artifacts. First, the transition across the wraparound border may be discontinuous in value or derivative(s).