curvilinear distance

[daschneider9]

Greetings,



Looking for advice on best way to measure curvilinear distance. The task is to measure a particular region of gastrointestinal-associated lymphoid tissue (RAMALT). I am able to define  ROIs and determine area and centroids. I think I should be able to use the centroid information to determine relative distance along the intestinal tract.



As seen in the image, I wonder if this is accurately done by straightening a spline with thickness that captures the follicles. Would the X-values of the centroids as determined on the straightened spline image be an accurate linear distance left-to-right? What about area?



I'm afraid I don't understand the coded transformation used by "straighten" and I'm admittedly a weak mathematician. It seems a purely mathematical solution would require non-trivial iterative determination of the smallest normal distance to the spline, which may not always report the centroid position "along" the spline if it is highly curved. Note also that the centroids are not necessarily in the center of the thickened spline nor should they define the spline; I think the contour of the mucosal-submucosal margin may be the better definition of contour of the space within which RAMALT is situated.



Your comments and advice are greatly appreciated.



If it matters, I'm using Fiji.



Dave





David A. Schneider, DVM, PhD

Diplomate, ACVIM(LA)



Animal Disease Research Unit

USDA-Agricultural Research Service

PO Box 646630, 3003 ADBF, WSU

Pullman, WA 99164-6630