Laplacian fractional entropy (LFE) is a measure of higher-order statistical properties of images [1-3]. The LFE measure is calculated from the relative entropy of the response histogram of an image compared to that of a Gaussian histogram matched for mean and variance [1]. The approach accounts for entropy effects from binning into a histogram. The Laplacian distribution is used as a scaling constant, since Laplacian response histograms are a model for natural scenes. The entropy relative to a Gaussian is normalized to the relative entropy of a Laplacian distribution relative to the Gaussian (and also accounting for binning effects). Thus 100% LFE can be interpreted as having non-Gausian "structure" that is equivalent to a Laplacian distribution. These measures have shown to be an effective method to evaluate the impact of anatomy and noise in mammography [1], and virtual breast phantom realism [2-3].
+ If you use this software to develop your work, cite our most recent publications for future references
[1] Abbey, Craig K et al. “Non-Gaussian statistical properties of breast images.” Med Phys vol. 39,11 (2012): 7121-30. doi:10.1118/1.4761869
[2] Abbey, Craig K et al. “Evaluation of non-Gaussian statistical properties in virtual breast phantoms.” J Med Imaging vol. 6,2 (2019):2329-4302. doi:10.1117/1.JMI.6.2.025502
[3] Barufaldi, B et al. “Computational Breast Anatomy Simulation Using Multi-scale Perlin Noise.” IEEE Trans Med Imaging vol. 0 (2021):1-10. doi:10.1109/TMI.2021.3087958
This open-source project provides a Java implementation of the LFE methods.
- JRE 8+
Make sure that you have install the Java runtime environment on your local machine.
You can run the software via command line using XML files. As example, we provide a template of a phantom image for testing and configurable XML file ("config.xml").
Use the the following command to execute the LFE software:
java -jar LFE_Measurements.jar config.xml
The XML file is divided in three sections: Gabor, LFE, and Images:
- Mask
Image path of binary mask (Gray 8-bits, format .RAW).
- Original
X-ray image path of binary mask (Gray 16-bits Unsigned, format .RAW).
- Width and height
Image and mask dimensions (pixels).
- Domain
ID used to assign Gabor filtering in spatial or Fourier domain.
0: Spatial domain.
1: Fourier domain.
- Width and height
Window dimensions of your Gabor kernels used for 2D convolution (spatial domain).
- DX and DY
Pixel pitch of the x-ray image.
- FREQ_CEN
Frequency of of Gabor kernel.
- A_RATIO
Aspect ratio of Gabor kernel.
- PSHIFT
Phase shift of Gabor kernel.
- angles
Number of rotation angles (PI/n) of Gabor kernel. Ex. n=4 (0°, 45°, 90°, and 135°).
- BW_OCT
Octave band width of Gabor kernel.
- NH
The number of histogram bins.
- EXC_FRAC
Histogram exclusion fraction. This parameter controls how many points fall in the last histogram bin which is outside the range of consideration. This is done to avoid problems with small counts in extreme values, which LFE will regard as non-gaussian behavior.
- Optmizer_Gauss_ID and Optmizer_Lap_ID
IDs of minimization algorithms used to minimize non-linear funtions to the optimal solution. These "solvers" do not require compute derivatives. For more information visit Commons Math website.
1: SIMPLEX: Simplex-based direct search optimization.
2: BOBYQA: Powell's BOBYQA algorithm.
3: POWELL: Powell's algorithm.
- Save_Plot
Flag that writes the images of the LFE plots (.PNG). The plots include the histogram and fitted probability functions. Set this flag to "false" if your system does not handle graphics.
The datapoints are saved in a separate .CSV file.