5. Global Repetition
In "Global Repetition" mode, SReD enables unbiased structure analysis by using the entire universe of image blocks as a reference. Each reference block generates a repetition map that is averaged, and the average value is plotted at the coordinates corresponding to the centre of the reference block. The average uses an exponential weight function based on the distance between the standard deviations of the blocks in each comparison, which enhances structural details.
The final Global Repetition Map reflects the relative frequency of each structural pattern across the entire image.
As an example, we will use an input image containing a cell with labeled EB3 comets. The global repetition function can be accessed by clicking on "Plugins > SReD > Global Repetition > Find Global Repetition (2D)".
A window appears, allowing the user to choose the dimensions of the blocks, the relevance constant and the metric used in the analysis. The blocks' dimensions dictate the scale of the structures analysed - in this case, a 9x9 block roughly matches the size of an EB3 comet.
In this example, we are not concerned about the orientations of the structures, so we choose a rotation-insensitive metric (modified cosine similarity).
| Select "Find Global Repetition (2D)" | Choose block dimensions, relevance constant and metric |
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The ImageJ/Fiji log window will appear, providing information about the state of the analysis. The global repetition map will appear automatically once the analysis is finished.
| The ImageJ/Fiji window provides information about the state of the analysis | The global repetition map appears automatically when SReD finishes |
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In this case, SReD pinpointed several structural elements across the image, with the highest global SRSs being attributed to EB3 comets. What is great about this is that at no point did we provide any sort of reference structure or template. The analysis is, therefore, unbiased towards a specific structural prior.
Similarly to block repetition, SReD's high sensitivity can lead to unwanted or non-specific results. This can be easily overcome using nonlinear mapping, for example, by transforming the global repetition map data using a power function.
| SReD is highly sensitive to structural information | Nonlinear mapping helps enhance structural features |
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SReD's global repetition mode enables unbiased structure detection and quantitative analysis. However, it is important to understand how to interpret a global repetition map.
A global SRS translates to "the frequency of a structural element relative to every other structural element".
It is important to remember that structural elements with similar global SRSs do not necessarily share structural features. This can sometimes become confusing. For example, in the global repetition map obtained previously, EB3 comets, which clearly share structural features, and appear to be the most repetitive and defined structures in the input image, are mostly scored with high global SRSs.
However, one could postulate that the noise in the image is more prevalent than EB3 comets, and should therefore be scored higher. In this case, the dimensions of the blocks were not sufficient to capture the average noise pattern. Instead, instances of the cell's noisy background signal were perceived by SReD as structural elements with substantial variation. For this reason, noise instances scored lower than comets.
Still, SReD detects the noise variants in similar frequencies, and scores them with similar global SRSs, despite detecting their differences. This observation agrees with the idea that local noise variations are random, and should, therefore, exist in equal amounts.