From a 3d x-ray scan, I have many similar slices to analyze. Is there a way to determine the position of the three rectangles and the inner circle? 
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- $\begingroup$ Could you please post two or three different images? $\endgroup$Dr. belisarius– Dr. belisarius2014-02-07 21:13:02 +00:00Commented Feb 7, 2014 at 21:13
- $\begingroup$ Related, this and this $\endgroup$Simon Woods– Simon Woods2014-02-07 21:13:58 +00:00Commented Feb 7, 2014 at 21:13
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2 Answers
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2 This is how I did it:
(* These can be compounded into one expression *) img = Binarize[Import["https://i.sstatic.net/EY2EG.png"], 0.2]; img = DeleteSmallComponents[img, 20]; img = DeleteBorderComponents@ImageCrop@img; m = MorphologicalComponents[img]; (* Identify circles versus rectangles using Eccentricity *) {rectangles, circles} = GatherBy[ComponentMeasurements[m, "Eccentricity"], #[[2]] > 0.5 &][[All, All, 1]]; (* Visualize result *) Show[ m // Colorize, Graphics[{ PointSize[Large], White, Point /@ (circles /. ComponentMeasurements[m, "Centroid"]), Gray, Point /@ (rectangles /. ComponentMeasurements[m, "Centroid"]) }] ] 
White spots are the center of mass of rectangles. Gray spots are the center of mass of circles. There are a few values that might need to be tweaked for some images, like the size of small components, i.e. noise. Eccentricity is a very good measurement to figure out which are circles and which are rectangles. The rectangles have > .99 and circles have a very small eccentricity (in theory zero).
- $\begingroup$ Thank you for your support. I was always trying to fit a shape to the individual pieces. $\endgroup$Alex– Alex2014-02-07 21:41:09 +00:00Commented Feb 7, 2014 at 21:41
- $\begingroup$ Oops - circles have small eccentricity and rectangles large :-) $\endgroup$Simon Woods– Simon Woods2014-02-07 22:00:51 +00:00Commented Feb 7, 2014 at 22:00
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2 One way to proceed is to binarize the image and find the constituent components:
img = Import["https://i.sstatic.net/EY2EG.png"]; objects = MorphologicalComponents[Binarize[img, 0.21]]; Colorize[objects] 
Examine the various components (that are colored differently)
ComponentMeasurements[objects, "Area"] {1 -> 133874., 2 -> 3085.75, 3 -> 3063.75, 4 -> 3226.75, 5 -> 505.5, 6 -> 503.5, 7 -> 3074.13, 8 -> 2.25, 9 -> 2.25, 10 -> 6., 11 -> 13., 12 -> 4.5, 13 -> 13.} We can see that the rectangles are the three objects of nearly identical size: objects 2, 3, and 7. The bounding boxes of these rectangles are:
ComponentMeasurements[objects, "BoundingBox"][[{2, 3, 7}]] {2 -> {{160., 338.}, {279., 449.}}, 3 -> {{355., 271.}, {410., 417.}}, 7 -> {{183., 194.}, {326., 259.}}} To locate the circles, use the eccentricity:
ComponentMeasurements[objects, "Eccentricity"] {1 -> 0.0694129, 2 -> 0.989404, 3 -> 0.989675, 4 -> 0.0816974, 5 -> 0.116954, 6 -> 0.33685, 7 -> 0.989536, 8 -> 0.866025, 9 -> 0.935414, 10 -> 0.924176, 11 -> 0., 12 -> 0., 13 -> 0.} The largest (greenish) circular object #1 and the inner (greyish) circle is object #4. The center and radius of this inner circle is:
ComponentMeasurements[objects, {"BoundingDiskCenter", "BoundingDiskRadius"}][[4]] 4 -> {{285.875, 320.543}, 53.9322} 
- $\begingroup$ Oh... for some reason, I always thought that a bounding box was the tightest fitting rectangle, not necessarily upright. I've removed the comment :) $\endgroup$2014-02-07 22:05:36 +00:00Commented Feb 7, 2014 at 22:05
- $\begingroup$ @rm -rf What you are describing is what I always wished they meant by a bounding box! $\endgroup$bill s– bill s2014-02-07 23:00:10 +00:00Commented Feb 7, 2014 at 23:00