digital image the sixty-four transformation marks were identified on a
monitor, with subpixel accuracy interpolated. The image co-ordinates
were transformed to the comparator co-ordinate system using the sixty-
four marks for an affine transformation.
The matchings were performed with the initial values chosen to have a
shift of 2 pixels in the stereo direction and 1 pixel in the y-direc-
tion from the correct value. The deviation of the matchings from the
manual measurements were individually shown for all check points toge-
ther with such data as standard error of the observations, estimated
standard deviation of the computed parallax, median convergency ratio
etc. Totally 4800 matchings were performed, with 29 different methods
based on the least square method, using 256 different check points.
THE LEAST SQUARE ALGORITHM
The search and mask windows are parts of the two images. The mask win-
dow is the template against which the the search window is compared in
order to find a parallax, by minimising the squares of the grey level
differences. In two dimensions a generalised observation equation could
be formulated as
I oU m m) * Rx Yn! = Inn Yan)
and
= f à z : Bb: = of
X 1 US ¥,} Ya JEL y; n gH,
where
X ,¥ ,X ,y = the co-ordinates of the pixels in the search and
mask window, respectively
I .I = the grey levels of the pixels in the search and
mask window, respectively
n = the additive noise
The simpliest two-dimensional radiometrical and geometrical functions
are
x: ‘= = I. z^]
n P1 : x Yn P, + Ye
where p, and p, are the parallaxes. A linear observation equation could
then be formulâted as
I, «P. * I : P, = AI
where the first derivative in one direction could be approximated with
1 = dl / dx = dl | dx = (1 (x+1i, y) - ! (x-i, y)) / 2
X S m m m
The observation is
Al = IU: y) - I (x, y)
After each iteration the search window is resampled from the original
images. It is not necessay to update the inverse. The computation is
repeated iteratively until the magnitude of the computed translation is
insignificant, in this case lower than one ym. The standard deviation
of the measured parallax could be computed by error propagation from
the standard error.
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