6. Multiscale analysis

Introduction

SReD enables multiscale analysis using a simple tweak - modulating the block-to-image size ratio. Larger ratios capture larger structures, while smaller ratios capture finer details.

For computational efficiency, it is preferable to modulate scale by downscaling the input rather than enlarging blocks, although combining both approaches often preserves structural detail best.

We demonstrate this multiscale analysis by examining a STORM image reconstruction with labelled gp210 proteins (Diekmann et al. (2020)).

Analysing small-scale structures

With the input image opened in ImageJ/Fiji, we select "Plugins > SReD > Global Repetition > Find global repetition (2D)". Then, we choose block dimensions that roughly accommodate single nucleoporins (5x5).

Select "Find global repetition (2D)	Choose block dimensions, relevance constant and metric

The global repetition map will appear automatically when SReD is finished calculating. We then enhance structural features using nonlinear mapping by transforming the repetition map using a power function with an exponent of 10000.

The global repetition map appears automatically	Features are enhanced using nonlinear mapping

Analysing intermediate-scale structures

We might be interested in detecting clusters of nucleoporins instead of individual proteins.

To do this, we simply repeat the analysis with larger blocks. With the input image opened, we select "Plugins > SReD > Global Repetition > Find global repetition (2D)". This time we choose block dimensions that can accommodate groups of nucleoporins (15x15).

Select "Find global repetition (2D)	Choose block dimensions to accommodate nucleoporin clusters

When SReD is finished calculating, we then enhance structural features using nonlinear mapping as before (power function with an exponent of 10000). This time, due to the larger block size, SReD detected larger structures comprising nucleoporin clusters.

The repetition map appears automatically once SReD is finished	Enhance structural features with nonlinear mapping

Analysing large-scale structures

Finally, if our structures of interest are the entire nuclear pores (NPCs), we could increase the blocks' dimensions even more. In this case, a block size that roughly accommodates an entire NPC is approximately 45x45 pixels. However, due to SReD's sampling scheme, the number of computations increases quadratically with the block size. This can result in long computation times or prohibitive memory requirements. Thus, we can improve the computation efficiency by combining an increase in block dimensions with downscaling of the input image.

To do this, we start by applying a Gaussian blur to our original input image. This step avoids aliasing artefacts (i.e., jagged lines) from downscaling. The rule of thumb for the Gaussian's sigma is "Sigma = 1/s" where s is the scale factor. Since we are downscaling by a factor of 0.5, the appropriate sigma for the gaussian kernel is 1/0.5 = 2.

We access the ImageJ/Fiji Gaussian blur function in "Process > Filters > Gaussian blur..." and choose a "Sigma" of 2.

Access the ImageJ/Fiji Gaussian blur function	Choose a Sigma = 1/scale factor

Then, we downscale the blurred image by clicking "Image > Scale..." and choosing 0.5 for the X and Y scale parameters.

Access the ImageJ/Fiji "Scale..." function	Choose an X and Y scale factor of 0.5	Click "Ok" and your image is downscaled

With the downscaled image, we are now ready for global repetition analysis! This time, we use a block size of 25x25 to capture structures at the scale of the entire NPC.

Access the SReD global repetition function	Select a block size of 25x25

We then apply some nonlinear mapping to enhance structural features.

The global repetition map appears automatically once SReD is finished	Enhance structural features with nonlinear mapping