estimate_noise — Estimate the image noise from a single image.
The operator estimate_noise estimates the standard deviation
of additive noise within the domain of the image that is passed in
Image. The standard deviation is returned in
Sigma.
To estimate the noise, one of the following four methods can be
selected in Method:
'foerstner': If Method is set to
'foerstner', first for each pixel a homogeneity measure is
computed based on the first derivatives of the gray values of
Image. By thresholding the homogeneity measure one obtains the
homogeneous regions in the image. The threshold is computed based on a
starting value for the image noise. The starting value is obtained by
applying the method 'immerkaer' (see below) in the first step. It
is assumed that the gray value fluctuations within the homogeneous regions
are solely caused by the image noise. Furthermore it is assumed that the
image noise is Gaussian distributed. The average homogeneity measure within
the homogeneous regions is then used to calculate a refined estimate for
the image noise. The refined estimate leads to a new threshold for the
homogeneity. The described process is iterated until the estimated image
noise remains constant between two successive iterations. Finally, the
standard deviation of the estimated image noise is returned in
Sigma.
Note that in some cases the iteration falsely converges to the value 0. This happens, for example, if the gray value histogram of the input image contains gaps that are caused either by an automatic radiometric scaling of the camera or frame grabber, respectively, or by a manual spreading of the gray values using a scaling factor > 1.
Also note that the result obtained by this method is independent
of the value passed in Percent.
'immerkaer': If Method is set to
'immerkaer', first the following filter mask is applied
to the input image:
The advantage of this method is that M is almost insensitive to image structure but only depends on the noise in the image. Assuming a Gaussian distributed noise, its standard deviation is finally obtained as
where N is the number of image pixels to which M
is applied. Note that the result obtained by this method is
independent of the value passed in Percent.
'least_squares': If Method is set
to 'least_squares', the fluctuations of the gray values
with respect to a locally fitted gray value plane are used to
estimate the image noise. First, a homogeneity measure is computed
based on the first derivatives of the gray values of
Image. Homogeneous image regions are determined by
selecting the Percent percent most homogeneous pixels in
the domain of the input image, i.e., pixels with small magnitudes
of the first derivatives. For each homogeneous pixel a gray value
plane is fitted to its 3x3 neighborhood. The
differences between the gray values within the 3x3
neighborhood and the locally fitted plane are used to estimate the
standard deviation of the noise. Finally, the average standard
deviation over all homogeneous pixels is returned in
Sigma.
'mean': If Method is set to
'mean', the noise estimation is based on the difference
between the input image and a noiseless version of the input
image. First, a homogeneity measure is computed based on the first
derivatives of the gray values of Image. Homogeneous
image regions are determined by selecting the Percent
percent most homogeneous pixels in the domain of the input image,
i.e., pixels with small magnitudes of the first derivatives. A
mean filter is applied to the homogeneous image regions in order
to eliminate the noise. It is assumed that the difference between
the input image and the thus obtained noiseless version of the
image represents the image noise. Finally, the standard deviation
of the differences is returned in Sigma. It should be
noted that this method requires large connected homogeneous image
regions to be able to reliably estimate the noise.
Note that the methods 'foerstner' and 'immerkaer' assume a Gaussian distribution of the image noise, whereas the methods 'least_squares' and'mean' can be applied to images with arbitrarily distributed noise. In general, the method 'foerstner' returns the most accurate results while the method 'immerkaer' shows the fastest computation.
If the image noise could not be estimated reliably, the error 3175
is raised. This may happen if the image does not contain enough
homogeneous regions, if the image was artificially created, or if
the noise is not of Gaussian type. In order to avoid this error, it
might be useful in some cases to try one of the following
modifications in dependence of the estimation method that is passed
in Method:
Increase the size of the input image domain (useful for all methods).
Increase the value of the parameter Percent
(useful for methods 'least_squares' and 'mean').
Use the method 'immerkaer', instead of the methods 'foerstner', 'least_squares', or 'mean'. The method 'immerkaer' does not rely on the existence of homogeneous image regions, and hence is almost always applicable.
Note that filter operators may return unexpected results if an image with a reduced domain is used as input. Please refer to the chapter Filters.
Image (input_object) singlechannelimage(-array) → object (byte / uint2)
Input image.
Method (input_control) string → (string)
Method to estimate the image noise.
Default: 'foerstner'
List of values: 'foerstner', 'immerkaer', 'least_squares', 'mean'
Percent (input_control) number → (real / integer)
Percentage of used image points.
Default: 20
Suggested values: 1, 2, 5, 7, 10, 15, 20, 30, 40, 50
Restriction:
0 < Percent && Percent <= 50.
Sigma (output_control) real(-array) → (real)
Standard deviation of the image noise.
Assertion:
Sigma >= 0
read_image (Image, 'combine') estimate_noise (ImageNoise, 'foerstner', 20, SigmaFoerstner) estimate_noise (ImageNoise, 'immerkaer', 20, SigmaImmerkaer) estimate_noise (ImageNoise, 'least_squares', 20, SigmaLeastSquares) estimate_noise (ImageNoise, 'mean', 20, SigmaMean)
If the parameters are valid, the operator estimate_noise
returns the value 2 (
H_MSG_TRUE)
. If necessary an exception is raised. If
the image noise could not be estimated reliably, the error 3175 is
raised.
grab_image,
grab_image_async,
read_image,
reduce_domain
binomial_filter,
gauss_filter,
mean_image,
smooth_image
noise_distribution_mean,
intensity,
min_max_gray
gauss_distribution,
add_noise_distribution
W. Förstner: “Image Preprocessing for Feature Extraction in Digital
Intensity, Color and Range Images“, Springer Lecture Notes on Earth
Sciences, Summer School on Data Analysis and the Statistical
Foundations of Geomatics, 1999
J. Immerkaer: “Fast Noise Variance Estimation“, Computer Vision
and Image Understanding, Vol. 64, No. 2, pp. 300-302, 1996
Foundation