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. 2012;12(8):10339-68.
doi: 10.3390/s120810339. Epub 2012 Jul 31.

Grey level and noise evaluation of a Foveon X3 image sensor: a statistical and experimental approach

Gabriel Riutort-Mayol  1 , Angel Marqués-Mateu, Ana Elena Seguí, José Luis Lerma
Affiliations

Grey level and noise evaluation of a Foveon X3 image sensor: a statistical and experimental approach

Gabriel Riutort-Mayol et al. Sensors (Basel). 2012.

Abstract

Radiometric values on digital imagery are affected by several sources of uncertainty. A practical, comprehensive and flexible procedure to analyze the radiometric values and the uncertainty effects due to the camera sensor system is described in this paper. The procedure is performed on the grey level output signal using image raw units with digital numbers ranging from 0 to 2(12)-1. The procedure is entirely based on statistical and experimental techniques. Design of Experiments (DoE) for Linear Models (LM) are derived to analyze the radiometric values and estimate the uncertainty. The presented linear model integrates all the individual sensor noise sources in one global component and characterizes the radiometric values and the uncertainty effects according to the influential factors such as the scene reflectance, wavelength range and time. The experiments are carried out under laboratory conditions to minimize the rest of uncertainty sources that might affect the radiometric values. It is confirmed the flexibility of the procedure to model and characterize the radiometric values, as well as to determine the behaviour of two phenomena when dealing with image sensors: the noise of a single image and the stability (trend and noise) of a sequence of images.

Keywords: design of experiments (DoE); digital image; grey level values; linear model (LM); noise; photon transfer method (PTM); radiometry.

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Figures

Figure 1.
Figure 1.
(a) Colorcheker chart formed by 140 regions with different reflectance characteristics; (b) Probability function of the radiometric values F; (c) Experimental light booth.
Figure 2.
Figure 2.
Goodness-of-fit graphic of the lineal model. Observed vs. adjusted radiometric values. It can be observed the linearity of the process. The separation with respect the straight line is the error or residual.
Figure 3.
Figure 3.
Residuals vs. sequential factor t.
Figure 4.
Figure 4.
(a) Residuals vs. adjusted radiometric values F illustrating the heterogeneity of the residuals; (b) Residuals vs. reflectance factor r (Note that factor r is a categorical factor); (c) Residuals vs. wavelength factor S.
Figure 5.
Figure 5.
Descriptive statistics and plots for the totality of the residuals. (a) The histogram of the residuals; (b) The normal probability plot for the residuals illustrates the slight failing of the normal distribution; (c) The skewness and kurtosis coefficients indicate the slight fail of the normal distribution.
Figure 6.
Figure 6.
Descriptive statistics (a) and plots (b) for the residuals of the wavelength R (red) for the 12 levels of the reflectance factor.
Figure 7.
Figure 7.
Interaction plot. Standard deviation vs. adjusted radiometric values F depending on the wavelength factor. It is the characterization of the sensor noise (standard deviation) of a single image according to the influential factors.
Figure 8.
Figure 8.
Signal to noise ratio for the three level of the wavelength factor: R (red colour), G (green colour) and B (blue colour).
Figure 9.
Figure 9.
Interaction plot. Standard deviation Sd vs. adjusted radiometric values F depending on the wavelength factor. It is the characterization of the sensor noise (standard deviation) of a sequence of images according to the influential factors.
Figure 10.
Figure 10.
Signal to noise ratio for the three level of the wavelength factor: R (red color), G (green color) and B (blue color).
Figure 11.
Figure 11.
Temporal evolution of the radiometric values in the sequence of images. Evolution for the spectral response factor S(λ) with λ = R (a). With λ = G (b). With λ = B (c).
Figure 12.
Figure 12.
Sttr vs. time interval factor I, according to the reflectance factor R or radiometric value factor F, equivalently.
Figure 13.
Figure 13.
Sttr vs. spectral response factor S(λ), according to the 3 levels (5, 15, 60 s) of the time interval factor I.
Scheme 1.
Scheme 1.
Scheme of the approach developed in this paper to analyze the radiometric values (grey level values), the sensor noise of a single image, the sensor noise of a sequence of images and the sensor temporal trend of a sequence of images.
See this image and copyright information in PMC

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