- MIT License - all source code
- Copyright (c) -
reports/- See
reports/thesis/LICENSEfor more details about the thesis only
- See
- Copyright (c) 2020 Sherman Lo
Contains code to reproduce the thesis Lo, S.E. (2020). Characterisation of Computed Tomography Noise in Projection Space with Applications to Additive Manufacturing. PhD thesis, University of Warwick, Department of Statistics
The Java source code for the mode and empirical null filter ImageJ plugin is in the submodule modefilter. Please see the modefilter repository for further information about the empirical null filter and mode filter ImageJ plugin.
MATLAB R2019a was used.
X-ray computed tomography can be used for defect detection in additive manufacturing. Typically, several x-ray projections of the product at hundreds of angles are used to reconstruct the object in 3D to look for any defects. The process can be time-consuming. This thesis aims to investigate if it is possible to conduct defect detection from a single projection to speed up the process. An additive manufacturing test sample was created with voids to see if they can be detected.
The uncertainty of the projection was modelled using a compound Poisson distribution. This arises from x-ray photon arrivals being a Poisson process and each photon has random energy. This results in a linear relationship between the mean and variance of the grey values in the projection. Fitting of the compound Poisson distribution using the expectation-maximisation algorithm was unsuccessful due to identifiability issues with the model. Instead, a gamma-distributed generalised linear model was fitted onto sample variance-mean data and used for variance prediction to quantify the uncertainty.
Software, called aRTist, was used to simulate the projection and compared with the experimental projection in the face of uncertainty by treating each pixel as a hypothesis test. To overcome the imperfections of the simulation, the empirical null filter was used to cater for model misspecification so that sensible inference was achieved. This was done by locally normalising the test statistics using the mode. Voids with diameters in the order of millimetres were detectable.
This thesis is a contribution to real-time quality control in additive manufacturing.
The left-hand side shows an x-ray projection of an additive manufactured cuboid. Its edges appeared curved due to spot and panel effects and this can be fixed using shading correction. The right-hand side shows the p-values of the resulting inference. Lighter colours show evidence of a defect and they successfully highlighted voids put in there purposefully.
Requires Maven as well as Java Runtime Environment and Java Development Kit.
Run the command
mvn -f modefilter package
to compile the Java code for the empirical null filter. The compiled .jar files are modefilter/target/Empirical_Null_Filter-X.X.X.jar and other required libraries in modefilter/target/libs/. On startup, MATLAB read and recognise these .jar files using the file paths specified in javaclasspath.txt.
Download the data from Figshare and unzip the zip file. The data is to be stored in the directory data/. The location of the data directory is specified in the MATLAB script getDataDirectory.m.
The following MATLAB products are required:
- Curve Fitting Toolbox
- Image Processing Toolbox
- Optimization Toolbox
- Statistics and Machine Learning Toolbox
Run the file make.m to create the figures for the thesis, this is an overnight job. 16GB of RAM recommended.
The LaTeX file is stored in reports/thesis/book.tex.
Please see the modefilter repository for further information about the empirical null filter and mode filter ImageJ plugin.
The repository contains MATLAB wrapper code so that the mode and empirical null filter can be used in MATLAB for both the CPU and GPU version.
Requires Maven as well as Java Runtime Environment and Java Development Kit. For the use of a Nvidia GPU, requires CUDA Development Kit which should include a nvcc compiler.
Follow the instructions in the modefilter repository for compiling the code into .jar files. On startup, MATLAB read and recognise these .jar files using the file paths specified in javaclasspath.txt.
The wrapper code are inference/EmpiricalNullFilter.m and inference/EmpiricalNullFilterGpu.m.