LL9

Question 1

What is the relationship between erosion of the foreground and dilation of the background?

Answer 1

An erosion of the foreground with s is the same as a dilation of the background with s

This characteristic is a part of the duality feature in mathematical morphology.

Question 2

What is the duality feature in mathematical morphology?

Answer 2

The duality feature states that an erosion of the foreground is equivalent to a dilation of the background and vice versa.

Question 3

Is dilation associative and commutative?

Answer 3

Yes, dilation is associative and commutative.

Question 4

Is erosion associative and commutative?

Answer 4

No, erosion is not associative or commutative.

Question 5

What is the property of idempotency in mathematical morphology?

Answer 5

An operation is idempotent if repeating it with the same structuring element does not change the result.

Question 6

What does it mean for opening and closing to be translation invariant?

Answer 6

It means that the operation produces the same result regardless of the position of the input image.

Question 7

What is the standard size of a structuring element (SE) used in dilation and erosion?

Answer 7

The standard size of a structuring element is 3x3, referred to as Z8.

Question 8

What does the Hit-or-Miss transformation operator do?

Answer 8

It looks for patterns in the foreground and background, yielding a match or miss.

Question 9

What is the definition of distance in the context of images?

Answer 9

Distance is expressed as the shortest path between two points in the grid, or two centers of pixels.

Question 10

What is a distance transform?

Answer 10

A binary image is transformed such that each pixel represents the distance to one pixel or a set of pixels in the original image.

Question 11

How does the distance transform represent spatial occupancy?

Answer 11

It converts a binary image containing an object and its background to an image where all pixels represent the distance to the nearest background pixel.

Question 12

What is a Voronoi diagram?

Answer 12

A Voronoi diagram divides a space into areas where all points in an area are closer to a defined point than to any other.

Question 13

How do Voronoi diagrams relate to distance transforms?

Answer 13

The distance transform is the equivalent of a Voronoi diagram in image space.

Question 14

What metrics are important in distance transforms?

Answer 14

Metrics include:
* City block distance
* Chessboard distance
* Chamfer distance
* Hexa-decagonal distance
* Euclidean distance
* Vector distance

Question 15

What is the difference between 4-connected and 8-connected neighborhoods?

Answer 15

4-connected considers direct neighbor pixels, while 8-connected includes diagonal neighbor pixels.

Question 16

What does city block distance measure?

Answer 16

It measures the path between pixels based on a 4-connected neighborhood.

Question 17

What does chessboard distance measure?

Answer 17

It measures the path between pixels based on an 8-connected neighborhood.

Question 18

What is the significance of the distance transform in image analysis?

Answer 18

It provides a representation of distances on a grid, allowing for various image processing applications.

Question 19

What is a complement of an image?

Answer 19

The complement of an image is the inversion of pixel values in the image.

Question 20

What is the City Block Distance also known as?

Answer 20

It is also known as Manhattan distance.

Question 21

What is another name for Chessboard distance?

Answer 21

Chebyshev distance.

Question 22

List the three types of distance metrics mentioned.

Answer 22

• City Block Distance
• Chessboard Distance
• Euclidean Distance

Question 23

True or False: The Euclidean distance metric is always the best approximation for circular shapes.

Answer 23

False

Question 24

What is the role of a metric structuring element in distance approximation?

Answer 24

It helps in the approximation of Euclidean distance.

Question 25

What does Chamfer metrics refer to?

Answer 25

Chamfer metrics refer to using specific masks to compute distance transforms.

Question 26

Fill in the blank: Erosion can be accomplished by thresholding the _______.

Answer 26

[distance transform of the object]

Question 27

What is the mathematical representation of Euler number?

Answer 27

E = C - H, where C is the number of connected regions and H is the number of holes.

Question 28

What does a topological descriptor indicate?

Answer 28

It indicates properties of an object that are unaffected by deformation.

Question 29

What is the purpose of the Vector Distance Transform (VDT)?

Answer 29

It constructs Euclidean distance from a path vector.

Question 30

List some applications of the Vector Distance Transform.

Answer 30

* Registration * Shape description * Skeletonization * Watershed transformations

Question 31

What is the significance of signed Euclidean distance transform?

Answer 31

It uses vector components to indicate direction and distance.

Question 32

What does the term 'distance map' refer to?

Answer 32

It refers to a representation of distances from points in the image.

Question 33

Fill in the blank: The _______ can be computed using Chamfer metrics.

Answer 33

[distance transform]

Question 34

What is the primary function of algorithms in distance approximation?

Answer 34

To provide computational efficiency and minimize error.

Question 35

True or False: The Euler number is preserved if topology is preserved.

Answer 35

True

Question 36

What is the relationship between erosion and distance maps?

Answer 36

Erosion can be performed by thresholding the distance transform of an object.

Question 37

What does a direction map in vector distance transform represent?

Answer 37

It represents the direction of the shortest path to a pixel.

Question 38

List types of distance metrics that provide better approximations of circular shapes.

Answer 38

* Octagonal * Hexadecagonal

Question 39

What is the main advantage of using integer arithmetic in distance calculations?

Answer 39

It speeds up computations by avoiding floating point operations.

Question 40

What does a convex shape do?

Answer 40

Curving out, extending outward

Question 41

What is a concave shape?

Answer 41

Curving in, hollowed inward quality

Question 42

What is the convex hull?

Answer 42

The minimal shape derived from a shape that is convex

Question 43

What does the convex hull H of an arbitrary set S represent?

Answer 43

The smallest convex set containing S

Question 44

What is convex deficiency?

Answer 44

D = H - S ## Footnote Can be measured through various metrics such as perimeter ratio and area ratio.

Question 45

What is the medial axis?

Answer 45

The preservation of a shape by a midline that reflects topology

Question 46

What analogy is used to describe the medial axis?

Answer 46

Analogy to a grass-fire

Question 47

What is the purpose of the medial axis transformation?

Answer 47

To reconstruct the shape using tangent circles entirely within the object

Question 48

What does the skeleton represent in image analysis?

Answer 48

The medial axis of a shape discretized on a grid

Question 49

What is the result of computing the skeleton?

Answer 49

A set of connected pixels in the middle of the original shape representing the topology

Question 50

What is thinning in image analysis?

Answer 50

Logical subtraction of pixels to preserve topology

Question 51

What is the significance of end-pixels in the skeleton?

Answer 51

Essential part of the topology that is preserved

Question 52

What are the conditions for pixel removal during thinning?

Answer 52

Continue until idempotency is reached

Question 53

What is the Hilditch skeleton?

Answer 53

The most used algorithm for skeletonization

Question 54

What are skeleton points in the computation of the skeleton?

Answer 54

Points classified as skeleton point, branch point, and end point

Question 55

What is the purpose of the distance transform in skeleton computation?

Answer 55

To identify local maxima seen as ridges corresponding to the medial axis/skeleton

Question 56

Fill in the blank: The Euler number is a ______ descriptor.

Answer 56

topological

Question 57

True or False: If topology is preserved, the Euler number is preserved.

Answer 57

True

Question 58

What is the role of structuring elements (SE) in thickening?

Answer 58

Used to apply transformations that result in a pure convex set

Question 59

What happens during a hit or miss transformation?

Answer 59

Fit results in 1 in the output image; miss results in 0

Question 60

What is the relationship between skeletonization and topology?

Answer 60

Skeletonization preserves topology