Accessible surface


#1

Dear ImageJ Users,

I’m trying to smooth the edges of a segmented layer of nuclei in the mouse retina by an approach that doesn’t clip any of the nuclei. For this reason, I wonder if there’s an ImageJ/Fiji plugin to determine in 2D the surface of a roughly-edged ROI that is accessible to a rolling circle of defined radius. The plugin might trace both the path of the circle center around the ROI as well as the closest approach of the circle’s perimeter to the ROI. These would be analogous to the solvent-accessible and Connolly surfaces of a 3D protein structure, but in 2D (https://en.wikipedia.org/wiki/Accessible_surface_area).

Thanks for any help!

Cheers,
Mark


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#2

Hi Mark,

One possible approach would be to convert your ROI to a binary mask (Edit->Selection->Create Mask), then apply a morphological dilation using a “disk” structuring element. Then you can compute area and/or perimeter of the resulting region.
For morphological dilation, use either “Process->Maximum” filter, or a plugin like MorphoLibJ.

HTH,
David


#3

Hi David,

Thanks very much for your suggestion. However, I believe that the 2D boundary created by your suggestion alters the ROI surrounding the retinal nuclear layer differently than a rolling circle would. For example, at a single nucleus that “sticks out” from the rest of the nuclear layer, the 2D boundary created by Process>Filters>Maximum is displaced from the boundary of the nucleus, whereas the 2D boundary created by a rolling circle would intersect the boundary of the nucleus (depending on the radius of the rolling circle and local concavity).

I found a related approach with multiple rounds of Process>Binary>Dilate and Process>Binary>Erode was unsatisfactory (protruding nuclei were clipped in the final ROI), although maybe if I tweaked this approach some more it would work. Edit>Selection>Enlarge was similarly unproductive. I also looked at Convex Hull, which worked well for the convex side of the retinal nuclear layer of interest (overall, retinal layers are C-shaped in cross-section) but failed on the concave side. I also looked into various approach that blurred the image before segmenting the nuclear layer, but these typically clipped protruding nuclei or were so large that unwanted nuclei from other layers were included in the ROI. I may be missing something, but a rolling circle approach seems like it might be the most effective solution to smooth without clipping occasional protruding nuclei.

So far a by no means exhaustive search of the internet has not yielded any ImageJ/Fiji algorithms or Matlab implementations of a rolling circle smoothing approach. I 'll take a closer look at your MorphoLibJ collection of plugins for something that may work instead.

Please correct me if I have the wrong ideas!

Cheers,
Mark


#4

Dear Mark,

not perfectly sure whether you mean border or surface, here is something that comes close to finding the boundary of a cell layer section.

(The disc in this example had a diameter of 12pel.
The image is an excerpt from an image recently posted to this Forum.)

Regards

Herbie


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#5

Hi Mark,

maybe you could post a sample image representing your problem, together with a manual sketch of what you are expecting. For the moment, I can not visualize the result you are expecting…

Regards,
David


#6

Hi Herbie and David,

Thanks for your input. Yes, the image Herbie provided is exactly like what I’m starting with. I was using the terms surface and boundary interchangeably (sorry!); both would correspond to the yellow line defining the edge of the nuclear layer in the image you sent.

The question is how to smooth this line without clipping any nuclei.

As I looked a bit harder, David’s suggestion of using morphological dilation is exactly right when combined with a morphological erosion. The accompanying image shows a cartoon of a thresholded nuclear layer (A, white) that includes a protruding feature and an infolded feature. B shows the result of Process>Filters>Maximum with radius 50. C shows B after removing the small hole. D shows C after Process>Filters>Minimum with radius 50. E shows a reconstruction of these operations including manually positioned circles of radius 50. The blue trace, corresponding in 2D to the Connolly (aka molecular) surface in 3D, is exactly what I want!

Thanks David and thank you Herbie for the useful image and link to another thread. I am now reassured that there is nothing ImageJ cannot do. Forgive me all for doubting.

Cheers,
Mark


Analyzing cell layer thickness
Measuring distance between two lines
#7

Thanks Mark,

when referring to your image part E, I’ve provided the curve in red which appears to correspond to the contour in part C.

Regards

Herbie


Corrosion Thickness Measurement