Figure 1.
Cubic Bézier curves (dashed lines) and biexponential functions (solid lines) fitting the camera responses (circle markers) making up the OECF curves for the red (a), green (b) and blue (c) colour channels of a Canon 40D digital camera and the red colour channel of a Nikon D70s camera modified for ultraviolet recording (d).
Exposure values corresponding to the total incident irradiance were calculated from Equation (2). Values were normalised by dividing the total amount of irradiance required for each camera response () by the amount of energy required to attain a camera response equal to the selected maximum pixel response
(
). See text for details.
Table 1.
Coefficients of biexponential functions fitting the OECF curves for two camera models.
Table 2.
Coordinates and 95% confidence intervals for the four control points defining each Bézier curve fitting the OECF curves for two camera models.
Figure 2.
Observed camera responses for the red channel of a Canon 40D digital camera (red × markers) and fitting results including values below the minimum pixel response value .
(A) Biexponential fit (black circle markers), (B) 19 Bézier segments (black squares).
Figure 3.
Recovered linear camera responses and confidence bounds for the (A–B) red, (C–D) green and (E–F) blue channels of a Canon 40D digital camera and; (G–H) the red channel of a Nikon D70s camera modified for ultraviolet recording, using cubic Bézier curves (left column) and biexponential functions(right column).
Linear camera responses were obtained by inverting the biexponential fitting function (Equation 4) (squares) and implementing a look up table derived after evaluating a cubic Bézier curve (Equation 3)(circles). Confidence bounds represent the standard deviation in all cases. Standard deviation of the biexponential function
for display purposes.
Figure 4.
Standard deviation of linear camera responses (cross markers) as a function of increasing values of /
recovered implementing a biexponential function (dotted line left column) and cubic Bézier curves (solid and dashed lines right column) for the (A–B) red, (C–D) green and (E–F) blue channels of a Canon 40D digital camera and; (G–H) the red channel of a Nikon D70s camera modified for ultraviolet recording.
Standard deviations for each /
recovered by the biexponential function were obtained after simulating 1,000 normally-distributed random coefficients within the 95% confidence intervals for each of the four parameters in Table 1. Standard deviation for each
/
recovered by the cubic Bézier curve were obtained from the LUTs constructed after simulating 1,000 normally-distributed pseudorandom coefficients within the 95% confidence intervals for the eight parameters in Table 2. Solid line in panels B, D, F and H corresponds to the standard deviation of the normalised camera responses (
), whilst the dashed line represents the standard deviation of the recovered normalised exposure value (
).
Table 3.
Statistical comparison of the linear camera responses obtained with two characterisation methods.