04-08-2012, 02:13 PM
Noise Estimation from a Single Image
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Abstract
In order to work well, many computer vision algorithms
require that their parameters be adjusted according to the
image noise level, making it an important quantity to estimate.
We show how to estimate an upper bound on the
noise level from a single image based on a piecewise smooth
image prior model and measured CCD camera response
functions. We also learn the space of noise level functions–
how noise level changes with respect to brightness–and use
Bayesian MAP inference to infer the noise level function
from a single image. We illustrate the utility of this noise
estimation for two algorithms: edge detection and featurepreserving
smoothing through bilateral filtering. For a variety
of different noise levels, we obtain good results for both
these algorithms with no user-specified inputs.
Introduction
Many computer vision algorithms can work well only
if the parameters of the algorithm are hand-tweaked to
account for characteristics of the particular images under
study. One of the most common needs for algorithm parameter
adjustment is to account for variations in noise
level over input images. These variations can be caused
by changes in the light level or acquisition modality, and
the amount of variation can be severe. An essential step
toward achieving reliable, automatic computer vision algorithms
is the ability to accurately estimate the noise level of
images. Examples of algorithms requiring noise level estimates
include motion estimation [1], denoising [12, 11],
super-resolution [5], shape-from-shading [19], and feature
extraction [9].
Related Work
There is a large literature on image denoising. Although
very promising denoising results have been achieved using a
variety of methods, such as wavelets [12], anisotropic diffusion
[11] and bilateral filtering [17], the noise level is often
assumed known and constant for varying brightness values.
In contrast, the literature on noise estimation is very limited.
Noise can be estimated from multiple images or a
single image. Estimation from multiple image is an overconstrained
problem, and was addressed in [7]. Estimation
from a single image, however, is an under-constrained problem
and further assumptions have to be made for the noise.
In the image denoising literature, noise is often assumed
to be additive white Gaussian noise (AWGN).
Noise Study
In this section, we build a model for the noise level functions
of CCD cameras. In Subsect. 3.1 we introduce the
terms of our camera noise model, showing the dependence
of the noise level function (the noise variance as function
of brightness) on the camera response function (the image
brightness as function of scene irradiance). Given a camera
response function, described in Subsect. 3.2, we can
synthesize realistic camera noise, as shown in Subsect. 3.3.
Thus, in Subsect. 3.4, from a parameterized set of camera
response functions (CRFs), we derive the set of possible
noise level functions. This restricted class of NLFs allows
us to accurately estimate the NLF from a single image, as
described in Sect. 4.
Synthetic CCD Noise
In principle, we could set up optical experiments to measure
precisely for each camera how the noise level changes
with image brightness. However, this would be time consuming
and might still not adequately sample the space of
camera response functions. Instead, we use numerical simulation
to estimate the noise function. The basic idea is to
transform the image I by the inverse camera response function
f−1 to obtain an irradiance plane L. We then take L
through the processing blocks in Figure 1 to obtain the noisy
image IN.