DIP Homework Assignment #2
Edge Detection, Geometrical Modification and
Morphological Processing
B93501005 CSIE 陳祺文
PROBLEM 1: EDGE DETECTION
PART(A) - Pure Edge Detection
PART(B) – Edge Detection with Pre-processing
PROBLEM 2: Geometrical Modification
PROBLEM 3: MORPHOLOGICAL PROCESSING
In this part I choose the 2-stage approach introduced on the class, since in
this approach, shrinking, thinning, skeletonizing are forms of conditional
erosion and the erosion process is controlled to avoid total erasure and to
ensure connectivity.
< flow chart >
F(j,k)
M(j,k)
Table 14.3-1
find removable
candidates
G(j,k)
Table 14.3-2/3
Conditional array
double
confirm
Stage 1 : Check Table 14.3-1 to generate a conditional array M(j,k)
If there’s a hit -> M(j,k)=1, (j,k) is a candidate for erasure. Otherwise, do
nothing.
Stage 2: Double confirm
For each M(j,k)==1, check Table 14.3-2(-3) , if there is a hit -> M(j,k)=0,
do not remove (j,k), to avoid total erasure.
 After stage 2 , if M(j,k)=1, erase (j,k) in the output G(j,k).
(In my implementation, I store patterns in the tables in the form of unsigned
char[][9] with 0 = 0 , M = 1, A=B=C=2(match all M and 0 , and (A or B or
C)==1 means hit), D=3 (don’t care) instead of pixel stack to avoid listing all
the patterns. I also construct an additional index table of table 14.3.1 index
[S|T|K] [bond-1][start~(end+1)] using pixel bond to decrease the searching
range.)
<Shrinking>
(a)Original image
(b) 1 iteration
(c) 3 iterations
(d) 5 iterations
(e) 10 iterations
(f) 50 iterations
(g) 100 iterations
(h) 200 iterations
In order to see the effects after several iterations clearly, I replaced the
pixels which should be removed with pixel value = 200.
From the above resultant images, we can see that an object without
holes become a single pixel near its center of mass, while an object with
holes become a connected ring lying midway between each hole and its outer
boundary. Moreover, if the original object is a line, the object erodes from the
end points, finally becomes a single point. (for example , the V shape line at
the bottom right corner.) And even after lots of iterations, the image won’t be
total erasure , the rings still keep the shape of the ring.
<Thinning>
(a)Original image
(d) 5 iterations
(g) 15 iterations
(b) 1 iteration
(c) 3 iterations
(e) 10 iterations
(f) 12 iterations
(h) 50 iterations
Comparing the resultant images of shrinking and thinning, in the first few
iterations (<10) the output image is almost the same. Finally, an object with
holes erodes to a connected ring, and different from the effect of shrinking, an
object without holes become a minimally connected stroke located
equidistant from its nearest outer boundaries rather than a single pixel. The
other difference is that the thinning effects stop after 15 iterations, after 50 or
more iterations the resultant image is the same, while we can see the
shrinking effects after 200 iterations, the lines erodes slowly to a single pixel,
and that cause thinning keeps more structural feature of the original feature
than shrinking.
<Skeletonizing>
(a)Original image
(d) 5 iterations
(g) 20 iterations
(b) 1 iteration
(c) 3 iterations
(e) 10 iterations
(f) 15 iterations
(h) 50 iterations
(i) 200 iterations