Image Processing Reference
In-Depth Information
shapes of digital disks are different from their Euclidean counterparts. But
there are distance functions that provide good approximations of Euclidean
disks. For example, digital circles defined using distance functions like {112}
and {1112} in 2-D, are closer to Euclidean circles. Similarly, in 3-D, the {113}
distance function provides a good approximation of a Euclidean sphere. As
the computation of MAT from digital distances is simpler than techniques
using the Euclidean metric, digital distance transforms are widely used in
this case. There are several applications of MAT in the processing and shape
analysis of images. It could be used in obtaining a skeletal representation of
the shape of an object. It is convenient to use in other computations, such as
geometric transformation, computation of boundary normals of 2-D objects,
computation of cross-sections of 3-D objects, and volume rendering of 3-D
objects.
Exercises
1. Compute the chamfering mask of the distance function {12} in the 2-D
space. Can you design a chamfering mask for the inverse square root
weighted t-cost function (refer to Section 2.4.3 of Chapter 2)? Justify.
2. Find the maximum relative error in percentage for the Euclidean dis-
tance transform computed using the 8-SED algorithm.
3. Explain why MAT has redundancy in representing an object. Suggest a
method to reduce this redundancy. Find the complexity of the algorithm.
4. How many bytes are required for storing the MAT of a binary object in
2-D for an image size of 256 × 256 given the number of medial spheres
is N. Consider the header of the file stores to be the number of medial
spheres in two bytes. Design an e
cient scheme for representing the
MAT that would require fewer bytes than its simple storage scheme.
Implement the scheme using any programming language and find the
average percentage of reduction of storage size by experimenting with a
number of binary images of size 256× 256. Out of the set of octagonal
distances of neighborhood length less than 4, which distance function
would be e
cient in this respect. Justify and verify experimentally.
5. Suppose the volume of the sphere of a distance function d
1
(·) in 3-D
with the radius r is greater than the volume of a sphere of the same
radius with another distance function d
2
(·). Will the number of medial
spheres of an object using d
1
(·) be smaller than that using d
2
(·)? Justify.
6. Discuss the merits and demerits of using MAT for computing-skeleton
of binary objects.
