- 1. Computer generated cluster
of Gaussian peaks to simulate a typical image. White loops show
outlines of peaks as found by BSA.
- 2. Mesh plot of peak cluster in
3. Isophotes, or contours of constant
intensity, chosen at equal intervals. Setting one threshold would
select the peaks inside contours of one intensity. Peaks labeled
for reference in text and next caption.
4. Binary images from setting various
thresholds for Fig. 1. Thresholds for 4-1 through 4-20 are set
to levels illustrating various stages in the BSA. They are shown
in increasing order, labeled 1-20, and referred to by this number
in the text.
- 1. No peaks resolved - all included in one blob.
2. Peak f just resolved (just split
from parent blob).
3. Peaks e and f both resolved.
4. Peak e just disappearing: it has not split into smaller peaks
so its associated blob (resolved somewhere between threshold
numbers 2 and 3) is recorded as an 'object'.
5. Peak f just disappearing. Analogously
to Peak e, blob representing peak f in Fig. 2 (at threshold 2)
is stored as an object.
6. Peak d almost resolved.
7. Peak d resolved.
8. Blob d shrinking, but no splitting has occurred.
9. Peak d just disappearing. Corresponding blob in Fig. 7 recorded
10. Peaks a, b and c are all that remain, but none are yet resolved.
11. Peak c almost resolved.
12. Peak c resolved.
13. Peak c has disappeared. Since it did not split into smaller
peaks after being resolved somewhere between thresholds 10 and
11, the appropriate blob is stored as another object.
14.Peaks a and b not yet resolved.
15.Peaks a and b still not yet resolved.
16. Parent blob has just split into blobs a and b.
- Both peaks gradually disappear without further splitting
in Figs. 17-20, and are kept as the final two objects.
5. Electron diffraction pattern.
- a. Fiber with rows of spots and
very wide range of spot sizes and intensities.
b. Outlines of spots as found by algorithm.
- c). Portion of b to upper right of center spot, compressed
to 5 gray levels (darkest level not visible). a-arrow:
4 pixel spot. b-arrow: larger spot not selected because
number of gray levels is too small (see text).
6. Electron diffraction pattern.
a. All spots are hard to resolve automatically
(although they are easily resolved by eye) because of wide range
of spot sizes and brightness.
b. Rectangles surrounding individual
spots as found by BSA.
7. Electron diffraction pattern.
a. spots of varying size and brightness.
b. Rectangles outline individual spots.
Dots and circles illustrate refined peak locations needed for
diffraction pattern analysis (see text). Diffraction patterns
are inverted if necessary before applying algorithm so that spots
are brighter than background. Areas of circles are equal to areas
of corresponding blobs.
8. Electron diffraction pattern.
- b. Outlines of portions of rings
for determining beam center position, as found by algorithm.
Additional blob in background seen above rings -- to be culled
later using shape, size or position.
9. Fluorescein spheres.
a. Light micrograph, fluorescence
mode. Rectangles, from algorithm, show sphere locations.
b. Magnification of region of Fig.
9a showing that rectangles from BSA might not touch perceived
outlines of objects (highlighted in white).
10. Illustrations showing that one threshold will not resolve
all spheres of Fig. 9a.
a. Same as Fig. 9a but shrunk x2.
- b. Binary image from lower threshold
-- dim spheres resolved but boundaries often not correct. Brighter
spheres with close neighbors not resolved.
c. Binary image from higher threshold -- dim spheres missing,
some brighter spheres resolved.
d. Binary image from yet higher threshold -- two brightest spheres
just resolved, but many dimmer spheres missing.
11. Background image for fluorescein spheres.
a. Greatly enhanced minimum filter
(Bright 1987b) of Fig. 9a. Dark squares have twice edge length
of filter kernel and are due to dark specks in b.
b. Enhancement of Fig. 9a. Degree
of enhancement same as a.
12. Ion microscope aluminum image
of inclusions in steel. Outlines as found by the BSA sometimes
obscured on print by bright areas. Some inclusions have "holes".
13. Ion microscope Barium image of particles.
a. Image taken with Cameca FFF ion
b. Particle outlines as found by
c. Gradient image of a.
14. Complex agglomerate particle.
a. TEM image.
b. Fig. a with outlines showing regions
found by BSA with Amin = 500.
c. Grid superimposed on a. Finest
grid mesh shows 10 x 10 pixel squares. Curves show intensity
histogram of background region of b. (gray) and of same area
of c. (white). Background of b. taken as lower left 100 x 100
d. Image of random numbers to simulate
the background noise in b. Dark and light shaded areas show regions
found by BSA with Amin = 500.
15. Histogram of blobs for Fig. 14b
16. BSA regions of particle in Fig. 14, 256 gray level image.
a. Regions selected from Fig. 14b
using group A of Fig.15. Amin = 500 pixels.
b. Regions for Amin = 5000 pixels.
c. Regions for Amin = 50 pixels.
17. BSA regions as in Fig. 16, but for 32 gray level image.
a. Amin = 500 pixels.
b. Amin = 5000 pixels.
- c. Amin = 50 pixels