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Image processing, Analysis, and Machine Vision

Milan Sonka, Václav Hlavác, Roger Boyle

Chapter 6

Segmentation I - all with Video Answers

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Chapter Questions

Problem 1

If an image histogram is bimodal, under what circumstances can a threshold be found that segments it perfectly?

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Problem 2

What are the advantages and disadvantages of edge-based segmentation?

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Problem 3

Explain the main concept of border detection using edge relaxation.

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Problem 4

List the main advantages and disadvantages of inner, outer, and extended border definitions.

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Problem 5

Mark all pixels forming the
(a) Outer
(b) Extended
border for the object given in Figure 6.55. If any pixel occurs more than once in the border, mark it more than once.

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Problem 6

Explain why the lower-bound method for modification of node costs increases the Aalgorithm graph search sperd.

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Problem 7

Consider a heuristic graph searching algorithm; explain how the accuracy of the estimate $h\left(\mathbf{x}_i\right)$ of the path cost from the current node $\mathbf{x}_i$ to the end node influences the search behavior. Specify under which conditions the optimality of the search is guaranteed.

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Problem 8

What is the main idea of the principle of optimality? How is it used in dynamic programming?

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Problem 9

What is the complexity of an optimal path search in a general graph? Give examples of how this complexity can be reduced for more constrainexl cases.

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Problem 10

What are the main differences between $A$-algorithm graph searching and dynamic programming. Explain why dynamic programming is often faster than the A-algorithm.

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Problem 11

Using a polar representation, explain the main concept of the Hough transform for line detection. Draw several lines in the image space and sketch the corresponding Hough transforms in the parameter space. Label all important points, lines, and axes.

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01:01

Problem 12

Explain why the polar co-ordinate representation of lines $s=x \cos \theta+y \sin \theta$ is more suitable for line detection using the Hough transform than the standard line representation $y=k x+q$.

Raj Bala
Raj Bala
Numerade Educator
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Problem 13

What is the dimensionality of a Hough accumulator array if circles of all sizes are to be determined in a two-dimensional image? List all necessary accumulator array variables.

Victor Salazar
Victor Salazar
Numerade Educator

Problem 14

Explain how a priori information about edge directions may increase the speed of Hough transform-besed image segmentation.

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01:33

Problem 15

Construct an R-table for the object given in Figure 6.55; use the third pixel from the left in the second row from the top as the reference point. It is enough to consider angles which are multiples of $90^{\circ}$.

Charles Carter
Charles Carter
Numerade Educator

Problem 16

Explain the main conoeptual differences in edge-based and region-based approaches to image segmentation. Are these two approaches dual?

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Problem 17

Specify mathematically the goal of region-based segmentation using the criterion of region bomogeneity.

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Problem 18

Explain the principles of and differences among the three basic approaches to region growing-merging, splitting, and split-and-merge.

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Problem 19

Explain the main principles of watershed segmentation. Discuss why filling the catchment basins from the bottom is several orders of magnitude faster than the approaches using mathematical morphology.

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Problem 20

Explain why watershed segmentation tends to over-segment images.

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Problem 21

Explain why a strategy of fast determination of a mismatch can typically speed up the process of image matching more than a strategy of increasing the efficiency of proving a match.

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