Re: The Sigma-Foveon pixel rationale

Discussion in 'Digital Photography' started by Dave Martindale, Apr 1, 2004.

  1. John Navas <> writes:

    >>Resampling a
    >>rotated square grid to a normal square grid is pretty simple, while
    >>resampling a hex grid to a square grid seems rather expensive. That's
    >>why I distinguish between square and hex grids.


    >I suspect resampling (2) to (1) would be comparable to resampling hex
    >( (4) or (5) ) to (1).


    I think it's easier, but they're all harder that resampling rotated
    square grid images (what Fuji does).

    Resampling the rotated square grid (3) to a row/column square grid with
    twice as many pixels is (nearly) trivial: You can set up the output
    grid so that half of the output pixels align with input pixels, so you
    get half the output with no processing at all. The other half of the
    output pixels are located equidistant between 4 input pixels, and you
    can use any of the common resampling methods (bicubic spline, B-spline,
    Lanczos) designed for square grid resampling, because the input *is* a
    square grid. That's it.

    With the half-pixel-shift quincunx (2), you might plausibly resample it
    to either a square grid with the same number of pixels, or 4 times as
    many pixels. In the same-size case, all the rows and columns are
    already spaced properly, but every second row needs a half-pixel shift.
    You might get away with applying a standard resampling filter,
    treating the grid as a rotated square, but the axes aren't really at 90
    degrees to each other so this isn't quite right. Or you could treat it
    as a hex grid where the hex angles aren't quite 60 degrees.

    The true hex grid (4&5) are worse yet because the output grid can have
    either its rows or columns aligned with the input ones, but not both
    (unless you're willing to accept non-square pixels. So almost none of
    the input pixels can pass directly to the output, and each output pixel
    is located somewhere other than half-way between some set of four input
    pixels.

    I have a paper somewhere that discusses hexagonal-grid images and how
    to process them, but I remember the resampling as being hard. I think
    it treated the image as a regular 2D grid in space, but with the space
    having basis vectors 60 degrees apart. Because of this, the 2D
    reconstruction filter used isn't separable, which makes the image
    processing more expensive.

    Dave
     
    Dave Martindale, Apr 1, 2004
    #1
    1. Advertising

  2. Dave Martindale

    Guest

    In message <c4gdpc$d54$>,
    (Dave Martindale) wrote:

    >Resampling the rotated square grid (3) to a row/column square grid with
    >twice as many pixels is (nearly) trivial: You can set up the output
    >grid so that half of the output pixels align with input pixels, so you
    >get half the output with no processing at all. The other half of the
    >output pixels are located equidistant between 4 input pixels, and you
    >can use any of the common resampling methods (bicubic spline, B-spline,
    >Lanczos) designed for square grid resampling, because the input *is* a
    >square grid. That's it.


    I thought that you would want to resample the whole thing; isn't that
    the best way to do it? I think even the firmware in the cameras use
    full resampling; in a TIFF file from my Sony F707, there was no ramping
    to and from any subgrid in any of the channels, or the luminance. Any
    pixel was equally capable of being a peak or low point.
    --

    <>>< ><<> ><<> <>>< ><<> <>>< <>>< ><<>
    John P Sheehy <>
    ><<> <>>< <>>< ><<> <>>< ><<> ><<> <>><
     
    , Apr 1, 2004
    #2
    1. Advertising

  3. writes:

    >I thought that you would want to resample the whole thing; isn't that
    >the best way to do it? I think even the firmware in the cameras use
    >full resampling; in a TIFF file from my Sony F707, there was no ramping
    >to and from any subgrid in any of the channels, or the luminance. Any
    >pixel was equally capable of being a peak or low point.


    You're thinking of linear interpolation, where any new pixels calculated
    between the position of existing pixels would necessarily be smaller in
    value than the larges neighbour. But that's only true of linear
    interpolation. Higher-order interpolation methods can generate new
    pixel values that are higher (or lower) in intensity than any existing
    value.

    For example, bicubic interpolation effectively fits a smooth surface to
    a 4x4 grid of input pixels. If the pattern of the pixels is such that
    the surface looks like a hill with the peak somewhere between the input
    values, then the output pixel value will be larger if it falls at the
    peak.

    Interpolation using something like an 8-lobed Lanczos filter calculates
    each output pixel based on 256 (16x16) input pixels. It's even better
    at preserving whatever high-frequency information is present in the
    original image.

    Generally, you wouldn't be able to tell whether any output pixel was
    original data or resampled data when using a good filter. And when the
    size ratio is not an integer in resampling, *none* of the output pixels
    are likely to be input pixels. But for the special case resampling
    you'd need in digital cameras, it makes sense to align the grids and
    reuse input values where you can.

    Dave
     
    Dave Martindale, Apr 1, 2004
    #3
    1. Advertising

Want to reply to this thread or ask your own question?

It takes just 2 minutes to sign up (and it's free!). Just click the sign up button to choose a username and then you can ask your own questions on the forum.
Similar Threads
  1. David J. Littleboy

    Re: The Sigma-Foveon pixel rationale

    David J. Littleboy, Apr 1, 2004, in forum: Digital Photography
    Replies:
    2
    Views:
    371
    Dave Martindale
    Apr 1, 2004
  2. Dave Martindale

    Re: The Sigma-Foveon pixel rationale

    Dave Martindale, Apr 1, 2004, in forum: Digital Photography
    Replies:
    2
    Views:
    327
    Dave Martindale
    Apr 2, 2004
  3. Dave Martindale

    Re: The Sigma-Foveon pixel rationale

    Dave Martindale, Apr 1, 2004, in forum: Digital Photography
    Replies:
    42
    Views:
    984
    Dave Haynie
    Apr 6, 2004
  4. DM

    Re: The Sigma-Foveon pixel rationale

    DM, Apr 2, 2004, in forum: Digital Photography
    Replies:
    30
    Views:
    868
    David Kilpatrick
    Apr 6, 2004
  5. George Preddy

    Re: The Sigma-Foveon pixel rationale

    George Preddy, Apr 4, 2004, in forum: Digital Photography
    Replies:
    3
    Views:
    337
Loading...

Share This Page