DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Schreiber, William F., and Donald E.
Troxel, “Transformations Between
Continuous and Discrete Representations
of Images: A Perceptual
Approach,” in IEEE Tr. on Pattern
Analysis and Machine Intelligence,
PAMI-7 (2): 178–186 (Mar. 1985).
Image presampling filters
In a video camera, continuous information must be
subjected to a presampling (“antialiasing”) filter.
Aliasing is minimized by optical spatial lowpass filtering
that is effected in the optical path, prior to conversion
of the image signal to electronic form. MTF limitations
in the lens impose some degree of filtering. An additional
filter can be implemented as a discrete optical
element (often employing the optical property of birefringence).
Additionally, or alternatively, some degree of
filtering may be imposed by optical properties of the
photosensor itself.
In resampling, signal power is not constrained to
remain positive; filters having negative weights can be
used. The ILPF and other sinc-based filters have negative
weights, but those filters often ring and exhibit
poor visual performance. Schreiber and Troxel found
well-designed sharpened Gaussian filters with σ = 0.375
to have superior performance to the ILFP. A filter that is
optimized for a particular mathematical criterion does
not necessarily produce the best-looking picture!
Image reconstruction filters
On page 43, I introduced “box filter” reconstruction.
This is technically known as sample-and-hold, zero-order
hold, or nearest-neighbor reconstruction.
In theory, ideal image reconstruction would be
obtained by using a PSF which has a two-dimensional
sinc distribution. This would be a two-dimensional
version of the ideal lowpass filter (ILPF) that I described
for one dimension on page 148. However, a sinc function
involves negative excursions. Light power cannot
be negative, so a sinc filter cannot be used for presampling
at an image capture device, and cannot be used as
a reconstruction filter at a display device. A box-shaped
distribution of sensitivity across each element of
a sensor is easily implemented, as is a box-shaped
distribution of intensity across each pixel of a display.
However, like the one-dimensional boxcar of
Chapter 16, a box distribution has significant response
at high frequencies. Used at a sensor, a box filter will
permit aliasing. Used in a display, scan-line or pixel
192 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES