Confocal microscopy allows the bioscience community to image biological processes in real time with a good spatial resolution, in particular with a higher contrast in the direction of the optical axis compared to other methods. However, the resolution on object shape is still limited by the diffraction limit, the shot noise, and possibly background fluorescence, tagging heterogeneity and fluorophore stochasticity tsien1995fluorophores ; pawley2006fundamental . Moreover, the resolution is anisotropic, typically several time worse in the optical axis than in the other axis. In many cases, these limitations can drastically hinder the ability to reconstruct a shape from an image.
To extract information from microscopy, image analysis tools are widely used. They usually involve image processing, such as background substraction and removal hwang1995adaptive , and deconvolution de2001image . Additional steps then can include segmentation and/or object recontructions using a wide variety of techniques. Methods to improve object reconstruction include model fitting, feature classification tomer2010profiling ; sommer2011ilastik , etc.
By altering the image and extracting features, image analysis can introduce artifacts pham2000current , that could remain undetected by the user when the analysis is fully automated. To assess the quality of the information obtained from imaging, it is thus necessary to know the quality of the image analysis procedure. This is however difficult because, especially in biological sample, the ground truth is not known, and the accuracy of the analysis cannot be quantified. This is why a need exist for a reliable software to generate simulated confocal microscopy data from a known ground truth.
To simulate a confocal image, software needs to address both optical limitations and noise, i.e. convolve the ground truth with the point spread function of the microscope, and add noise - either before or after convolution according to the nature of the noise. Several software (the most notable being Huygens software) allow the simulation of point spread function (PSF), based on known the microscope components, i.e. the optical path. It is possible to measure the experimental PSF from microscopy images using similar software. Possible limitations include the non-uniformity of the refraction index in real samples and the aberrations that could stem from lens misalignment and imperfections.
Starting from a known PSF, a few software suites exist to simulate confocal imaging. They include the non-free Huygens software professional and the open-source microlith. While the later does not include a noise simulator, the former allows the user to add a background as well as a Gaussian or Poisson noise ; however, knowing the correct noise intensity and distribution is not straightforward. Each source of noise background noise, autofluorescence, shot noise) can also be theoretically simulated sheppard2006signal , but the resulting noise is a complex convolution of the different the noises and distortions sources (including the PSF), and can only simulated accurately only by complex models, and in very simplified experimental setup herberich2012signal .
Overall, any confocal simulator will be limited to a certain level of detail by practicality, and ultimately by the lack of information on the sample structure and properties - which is precisely the unknown. While such detailed simulators are extremely useful, simpler alternatives are possible, especially when it comes to testing image analysis software.
We developed ConfocalGN, a minimal solution to simulate confocal data from a ground truth, a measure of the PSF, and the noise and signal distribution.
The ground truth
is provided as a high resolution image, either as a MATLAB matrix, or as a .tiff file. A pixel value corresponds to no fluorescence, and pixel values are rescaled to match the desired mean signal value.
is entered as a three components vector containing the deviation of the Gaussian that fits best the PSF, since confocal PSF can efficiently be modeled as Gaussian. We do not provide a mean to compute the PSF since several third party software offer this possibility.
The noise distribution
, but a gaussian approximation is used if the user-provided noise has no skew (i.e. the third moment is zero).
The signal distribution
is entered as the mean value of the signal observed experimentally.
Interestingly, ConfocalGN offers the possibility to directly input a sample image, from which the noise and signal distribution will be calculated. This is extremely powerful as it allows for a realistic noise without an overwhelmingly complex simulation of the noise and distorsion sources. Additionally, the user can choose to use other software to convolve the ground truth image with the PSF, and use ConfocalGN only for noise modeling.
ConfocalGN offers a minimal segmentation function doing gaussian blurring and Otsu thresholding to discriminate noise vs signal pixels, but the user can provide his own segmentation function instead. In Fig. 1 A, we show a sample image (top) and an simulated image (bottom). Fig. 1 C, shows the histogram of values for the voxels under the Otsu threshold (noise, in red) and voxels above the threshold counting (signal, in blue).
ConfocalGN offers the user a very simple tool to test his image analysis software. The minimal input by the user is only (1) a ground truth image, (2) the confocal PSF, (3) a sample image (or the moments of the noise and signal distributions). Because of the approximation of the PSF and its simplified treatment of fluorophore, background and sensor noise, it is not meant to be an exact simulation. However, the complexity of biological systems, including intra-sample heterogeneity, inter-sample diversity and experimental variations mean that exact theoretical solutions are usually not achievable. Here, we rather chose to start from measured PSF and noise values to best address experimental conditions.
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