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06/11/2009

Circle Tool - Cookie Cutter Button. 

11/5/2003

 

All of the cookie cutter commands work on the image selected by the Image! button.

Overlap, No overlap

            For cutting maximum inscribed circles out of an arbitrary shape.  Repeatedly cuts circles out of a shape by finding the maximum inscribed circle, removing it, then working on the remaining shape.First, erases the circles list.  The slow mode recalculates the distance mapevery time so that the circles do not overlap.  This is the correct way to do things, but takes much longer.  The fast mode just cuts a circle out of the distance map, then finds the global max of what is left.  This results in many circles being centered on the edge of a previous cut out, thus many circles overlap. On cursory examination, it seems that the size distributions of the circles are about the same, although the overlapping set has more of them. 

The largest circle is the same in each set.

Radius images

These images have pixel values that are calculated in some way from the Euclidian distance map. The pixel value is that of the radius of the circle that contains the pixel.  The pixel will likely not be at the center of the circle.  The cookie cutter radius image is the overlapping algorithm from the above menu item.  The max disk radius image is the radius image calculated by accumulating disks, in order of radius, for every object pixel (every pixel with a value for the distance map.

Background

                                                The radius images are for calculating an average width of an arbitrarily shaped region, after Hildebrand:

Here is Figure 1 from this paper:

and here is some of the text about the figure.

            The radius images are two-dimensional adaptations of this idea.  They have been tested using images similar

to those in Fig. 2 of the article:

The figure below shows a mask of two overlapped disks, the distance map, the max disk image and the

cookie cutter image.

Note that the max disk image tapers between the two radii values in the region corresponding to the hashed region of Fig. 2 from the article.  The cookie cutter image does not, but otherwise it is the same.

The next example is one focal plane of a confocal microscope image series of a collagen fiber network.  We wish to determine an average measurement of the ‘width’ of the black areas, as the average of the max disk image. This series shows the original image, the max disk image, the cookie cutter disk image, and the difference of the two disk images. The disk images were made from the original by thresholding it at value 150 (thresholded image not shown).

Original

Max width disk image

Cookie cutter disk image

Difference of max width image and cookie cutter image.  Light gray = 0. Note that the differences of the cookie cutter approximation with respect to the max width image are largely around the edges of the disks.

Here are some comparative statistics for the two images.

statistics for

 maxw

 maxw

cc

cc

n pixels                

262144

 

262144

 

total n pixels          

262144

 

262144

 

pixel value mean        

42.53457

 

41.14106

 

pixel value sum         

11150182

 

10784882

 

pixel value min          

0

 

0

 

min value location      

0

0

0

0

pixel value max         

136

 

140

 

max value location      

0

374

0

371

min positive pixel value

1

 

1

 

min pos val location    

142

0

33

0

pixel val wtd centroid  

180.7061

288.1245

179.7647

290.8076

sample std. dev.        

46.3427

 

45.27816

 

std. error of mean      

0.090513

 

0.088434

 

variance / mean         

50.49177

 

49.83128