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You take a micrograph of a material. You segment it, and measure the phase fractions. How sure are you that the phase fraction of the whole material is close to your measurements?
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Here we define 'representativity' as [1]
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> A microstructure is $(c, d)$-property representative if the measured value of the microstructural property deviates by no more than $d\%$ from the bulk material property, with at least $c\%$ confidence. For example, if $(c,d)=(95,3)$, and the property is phase-fraction, this means we can be $95\%$ confident that the measured phase-fraction is within $3\%$ of the bulk material phase-fraction.
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We introduce the 'ImageRep' model for performing fast phase-fraction representativity estimation from a single microstructural image. This is achieved by estimating the Two-Point Correlation (TPC) function of the image via the FFT. From the TPC the 'Integral Range' can be directly determined - the Integral Range has previously been determined using (slow) statistical methods. We then represent the image as binary squares of length 'Integral Range' which are samples from a Bernoulli distribution with a probability determined by the measured phase fraction. From this we can establish the uncertainty in the phase fraction in the image to a given confidence, **and** the image size that would be needed to meet a given target uncertainty.
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Here we introduce the 'ImageRep' method for fast phase fraction representativity estimation from a single microstructural image. This is achieved by calculating the Two-Point Correlation (TPC) function of the image, combined with a data-driven analysis of the [MicroLib](https://microlib.io/) dataset. By applying a statistical framework that utilizes both data sources, we can establish the uncertainty in the phase fraction in the image with a given confidence, **and** the image size that would be needed to meet a given target uncertainty. Further details are provided in our [paper](CITATION.cff).
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If you use this model in your research, [please cite us](CITATION.cff).
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If you use this ImageRep in your research, [please cite us](CITATION.cff).
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## Usage:
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This model can be used as python package - see [`example.ipynb`](example.ipynb) or via the [website (imagerep.io)](https://www.imagerep.io/).
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This method can be used via the [website (imagerep.io)](https://www.imagerep.io/) or as python package - see [`example.ipynb`](example.ipynb).
NB: the website may run out of memory for large volumes (>1000x1000x1000) - if this happens run the model locally or contact us
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NB: the website may run out of memory for large volumes (>1000x1000x1000) - if this happens run the method locally or contact us
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## Limitations:
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-**This is not the only source of uncertainty!** Other sources *i.e,* segmentation uncertainty, also contribute and may be larger
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- For multi-phase materials, this model estimates the uncertainty in phase-fraction of a single (chosen) phase, counting all the others as a single phase (*i.e,* a binary microstructure)
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- For multi-phase materials, this method estimates the uncertainty in phase-fraction of a single (chosen) phase, counting all the others as a single phase (*i.e,* a binary microstructure)
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- Not validated for for images smaller than 200x200 or 200x200x200
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- Not validated for large integral ranges/features sizes (>70 px)
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- Not designed for periodic structures
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- 'Length needed for target uncertainty' is an intentionally conservative estimate - retry when you have measured the larger sample to see a more accurate estimate of that uncertainty
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## Local Installation Instructions
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These instructions are for installing and running the model locally. They assume a UNIX enviroment (mac or linux), but adapting for Windows is straightforward. Note you will need 2 terminals, one for the frontend local server and one for the backend local server.
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These instructions are for installing and running the method locally. They assume a UNIX enviroment (mac or linux), but adapting for Windows is straightforward. Note you will need 2 terminals, one for the frontend local server and one for the backend local server.
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### Preliminaries
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@@ -51,7 +45,7 @@ git clone https://github.com/tldr-group/Representativity && cd Representativity
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pip install -e .
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```
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**NOTE: this is all you need to do if you wish to use the model via the python package.** To run the website locally, follow the rest of the instructions.
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**NOTE: this is all you need to do if you wish to use the method via the python package.** To run the website locally, follow the rest of the instructions.
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2. With your virtual environment activated, and inside the `representativity/` directory, run
{(!isMobile)&&<span>Drag microstructure file or <astyle={{cursor: "pointer",color: 'blue'}}onClick={viewExample}> view example!</a></span>}
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{(!isMobile)&&<span>Drag microstructure file, or view example <astyle={{cursor: "pointer",color: 'blue'}}onClick={e=>viewExample(DEFAULT_IMAGE_2D)}>in 2D</a> or <astyle={{cursor: "pointer",color: 'blue'}}onClick={e=>viewExample(DEFAULT_IMAGE_3D)}> 3D</a></span>}
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