Lazy Grain Boundaries 

INTRODUCTION

The purpose of the Lazy Grain Boundaries macro is to identify grain boundaries on a thin section, and to represent them in the form of a grain map (in image processing, this is called image segmentation).

The Lazy Grain Boundary detection uses gray scale input images and it is assumed that - in some way - the gray scales represent different crystallographic orientations, in the sense that a rapid change of crystallographic orientation is portrayed by a rapid change of gray value. For better results, more than one image is used per area of analysis, for example, various orientations of the polarizer/analyzer with respect to the thin section are used. Images are typically combined to a stack. The basic idea is to combine the most significant information from the different slices ("views") rather than trying to get all information out of one single image.

The procedure described in the following uses misorientation images as input. It is the "standard procedure" for quartzites. The resulting grain boundary maps are designated by the ending "cuogu-z-3tji" which is short for the sequence of key strokes that are used to carry out the segmentation. For most steps in the procedure, a number of alternatives are possible. From my experience, the "standard procedure" works best for quartzites, for other rock types and other input images, other combinations of key strokes may yield better results (and maybe new macros have to be written....).

GETTING STARTED

Load Lazy Grain Boundaries macro.

The macros are grouped in five groups according to their purpose:

 
1. import images - resize and crop stack
    
2. perform edge detection on all slices of stack
    
3. combine information on one (average / best) image
    
4. (post-)process image
    
5. "beauty case": prepare grain map for analysis

STEP 1

Open the misorientation images misE, misN and misH (= images that result from the CIP procedure: c-axis misorientation images with respect to East, North and Heaven (or Hell). Combine images to stack.

Stack of misorientation images

• .misE (from East),
• .misH (from "heaven" (=up)),
• .misN (from North)

Alternatively, color images (TIFF format) may be used, the R-G-B channels will open as three slices of a stack.

STEP 2

If the grains are very small it may be advisable to use enlarged input images, i.e., an enlarged input stack. [2] is used to enlarge the stack by bilinear interpolation. After segmentation the same routine is used in an inverse sense to obtain the original image size. Contrast enhancement [C] or median filtering [U] may not always be necessary.

STEP 3

Edge detection [O] is by the Sobel method. The Sobel edge detector is a well established and safe edge detector which is very widely used. More efficient edge detectors have been designed recently, however, they are not (yet) available on Image SXM.

STEP 4

Adaptive thresholding [G] performs a threshold on each of the slices of the satck using the mean value of the histogram. Other thresholds such as the mode of the histogram [V] etc. or interactive thresholding can be tried.

Additional median filtering is used to reduce noise.

STEP 5

To combine the thesholded slices of the stack into one image, image addition by inclusive-or [Z] (calculation of maximum image) is used here. It is possible to use other modes, such as image averaging [A], but addition by inclusive-or has proven to be the best because it is sensitive to the slightest grain boundaries found anywhere on any of the slices of the stack.

(The stack is now reduced to one image.)

STEP 6

After combining the stack into one image (by whatever method), the image is thickened [T]. Thickenning is optional, see also steps 8 and 9.

STEP 7

The image is skeletonized [J].

Note that careful noise cleaning is very useful: during skeletonization thick solid outlines reduce to single outlines, whereas white pixels on noisy outlines give rise to numerous (artifical) "bubble" grains.

STEP 8

The image is pruned [I].

Loose ends and open boundaries are trimmed. It pays to carefully close outlines - if necessary by hand - before this step is carried out.

Note that pruning cannot proceed around right-angled kinks nor across "bubble" grains

STEP 9

The image is thickened - skeletonized - pruned [T] [J] [I].

In order to to make kinks erodable and in order to close "bubble" grains, the outlines are thickened, skeletonized and pruned again.

Note that these three steps should not be applied too often - else the grain boundaries take on completely artificial shapes.

STEP 10

The outlines are thickened [T] and the image is cropped [5] and inverted [Y].

Thickening is necessary because thin outlines are not recognized by the Images SXM Analyze menu. The rim is cut off because along the edge of the image, the grains show artificial grain boundaries. The bitmap is inverted to make the grains recognizable for the Image SXM Analyze menu.

RESULTS

Input images =

6 rotation images taken with

• crossed polarizers AND lambda-plate rotated 0°, 30°, 60°, 90°, 120°, 150°,
• interference filter 660nm.

Input images =

3 rotation images taken with

• crossed polarizers AND lambda-plate rotated 0°, 60°, 120°,
• interference filter 660nm.

1 image taken with

• circular polarization (= two quarter wave plates)
• interference filter 660nm.

Input images =

2 CIP output images:

• 1 azimuth image,
• 1 primary inclination image (= circular polarization)

Input images =

3 CIP output images:

• misE: misorientation with respect to East,
• misN: misorientation with respect to North,
• misH: misorientation with respect to Heaven (Up),

i.e. with respect to horizontal axis, vertical axis and axis normal to image plane.

Input images =

1 CIP output image:

• orientation gradient image with respect to 4 neighbour pixels