The length of a boundary is one of the simple boundary descriptors. The length of the boundary is approximately given by the number of pixels along that boundary.

2. Which of the following of a boundary is defined as the line perpendicular to the major axis?

a) Equilateral axis
b) Equidistant axis
c) Minor axis
d) Median axis

Answer: c

The minor axis of a boundary is defined as the line perpendicular to the major axis and of such length that a box passing through the outer four points of intersection of the boundary with the two axes completely encloses the boundary.

3. Which of the following is the useful descriptor of a boundary, whose value is given by the ratio of the length of the major axis to the minor axis?

a) Radius
b) Perimeter
c) Area
d) Eccentricity

Answer: d

Eccentricity is the useful descriptor of a boundary, whose value is given by the ratio of the length of the major axis to the minor axis.

Eccentricity, which is the ratio of the major axis to the minor axis is one of the important parameters that is used to describe a boundary.

4. The term Curvature is defined as:

a) Rate of change of area
b) Rate of change of slope
c) Slope
d) Rate of change in diameter

Answer: b

The curvature of a boundary is defined as the rate of change of slope. In general, as the boundaries tend to be locally ragged, it is difficult to obtain reliable measures of curvature at a point on a digital boundary.

5. If the boundary is traversed in the clockwise direction, a vertex point ‘p’ is said to be a part of the convex segment if the rate of change of slope at ‘p’ is:

a) Negative
b) Zero
c) Non-negative
d) Cannot be determined

Answer: c

If the boundary is traversed in the clockwise direction and the rate of change of slope at the vertex point is non-negative, then that point is said to be in the convex segment.

6. A point ‘p’ is said to be a corner point if the change of slope is less than 100.

a) True
b) False

Answer: b

In general, a point ‘p’ is said to be on the straight line segment if the change of slope is less than 100 and said to be at the corner point if the change exceeds 900.

7. Based on the 4-directional code, the first difference of smallest magnitude is called:

a) Shape number
b) Chain number
c) Difference
d) Difference number

Answer: a

We know that the first difference of a chain-coded boundary depends on the starting point. Based on such 4 directional boundaries, the first difference of smallest magnitude is called the shape number of the boundary.

8. The order of shape number for a closed boundary is:

a) Odd
b) Even
c) 1
d) Any positive value

Answer: b

The order of shape number gives the number of digits in its representation. The value of this order is even for closed boundaries and limits the number of possible different shapes.

9. What is the order of the shape number of a rectangular boundary with the dimensions of 3×3?

a) 3
b) 6
c) 9
d) 12

Answer: d

The order of shape number is also defined as the perimeter of the boundary. Since the given is a rectangle of dimensions 3×3, the perimeter of the rectangle is given as 2(3+3) = 12.

10. The chain code for the following shape is given as:

a) 000030032232221211
b) 003010203310321032
c) 022332103210201330
d) 012302301023100321

Answer: a

The effective boundary for the given figure is given as

So, the chain code is given as 000030032232221211.

11. What is the shape number for the boundary given in the previous figure?

a) 003231023101230123
b) 012301220331023010
c) 133021030012330120
d) 000310330130031303

Answer: d

The chain code for the boundary is given as 000030032232221211.
We know that shape number is the first difference of a chain-coded boundary. Thus the shape number of the above-given boundary will be 000310330130031303.

12. Statistical moments are used to describe the shape of boundary segments quantitatively.

a) True
b) False

Answer: a

Statistical moments like mean, variance, and higher-order moments can quantitatively describe the shape of boundary segments.

13. Which of the following techniques of boundary descriptions have the physical interpretation of boundary shape?

a) Fourier transform
b) Statistical moments
c) Laplace transform
d) Curvature

Answer: b

The statistical moments have an advantage over the other techniques in that it helps in the physical interpretation of the shape of the boundary.

14. Statistical moments are sensitive to rotation.

a) True
b) False

Answer: b

The statistical moment technique of describing the shape of the boundary is insensitive to the rotation of the shape. If desired, size normalization can be achieved by scaling the range of values of ‘g’ and ‘r’.

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15. What does the total number of pixels in the region defines?

a) Perimeter
b) Area
c) Intensity
d) Brightness

Answer: b

The area of a region is defined by the total number of pixels in the region. The perimeter is given the number of pixels along the length of the boundary of the region.