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Non-Commensurable Scaling Ratios using Inverse/Forward/Inverse Transform Combination

IP.com Disclosure Number: IPCOM000115784D
Original Publication Date: 1995-Jun-01
Included in the Prior Art Database: 2005-Mar-30
Document File: 4 page(s) / 151K

Publishing Venue

IBM

Related People

Feig, E: AUTHOR [+3]

Abstract

Scaling objects that have been transformed from the spatial domain to a transform domain is a long standing problem. Prior art demonstrates scaling factors that are fractional multiples (commensurable ratios) of the spatial domain block size. A method of applying a more general scaling factor to an object in the transform domain, using a combination of transform to spatial domain scalings and spatial to transform domain transforms is described herein.

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Non-Commensurable Scaling Ratios using Inverse/Forward/Inverse Transform
Combination

      Scaling objects that have been transformed from the spatial
domain to a transform domain is a long standing problem.  Prior art
demonstrates scaling factors that are fractional multiples
(commensurable ratios) of the spatial domain block size.  A method of
applying a more general scaling factor to an object in the transform
domain, using a combination of transform to spatial domain scalings
and spatial to transform domain transforms is described herein.

Images and the Discrete Cosine Transform (DCT) are used to illustrate
this.

      The increasing use of lossy image compression schemes, such as
Joint Photographic Experts Group (JPEG), creates a need for fast,
efficient image scaling techniques.  Lossy JPEG image compression
employs a spatial-to-frequency domain transform known as the Discrete
Cosine Transform (DCT).  An image is segmented into 8 * 8 blocks of
samples.  A two dimensional DCT is then applied to the 8 * 8 blocks
to generate 64 DCT coefficients.  These coefficients are quantized,
then entropy coded, with control information in the form of JPEG
marker segments.  Decompression involves parsing the data stream for
the control information, entropy decoding the quantized DCT
coefficients, dequantizing the DCT coefficients, and finally applying
an Inverse Discrete Cosine Transform (IDCT) to produce a
reconstructed image.  The details of this process, defined by JPEG,
are documented in (*).

      Often, it is desirable to scale the image for purposes of
printing or displaying on a CRT.  There are many techniques, well
known in the prior art, for scaling an image in the spatial domain,
as well as for scaling an image while it is being transformed from
the transform or frequency domain back to the spatial domain.
However, these techniques have draw backs.

      Fine details are lost in the process of scaling down.  This
translates into the loss of high frequency components in the
transform or frequency domain being discarded, which in turn results
in reduced computational complexity.

      To apply spatial domain scaling, the image must be fully
transformed back to the spatial domain.  This imposes the full cost
of performing the inverse transform, which is computationally
intensive.  Then, the spatial domain scaling must be applied.  The
total number of operations required to produce the scaled image is
greater than the number of operations to generate the unscaled image.
As a result, the user pays a performance penalty for having the image
scaled.  One advantage to this scaling technique is that any scaling
factor can be applied.

      Applying the scaling while the image is being transformed from
the transform domain back to the spatial domain, called
transform-to-spatial domain scaling, or in the case of a DCT,
DCT-to-spatial domain scaling, offers significant performance
improvements over spatial dom...